MA 116 Turn-in Practice Problems 4.2 and 4.4 Pitts .docx
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MA 116 Turn-in Practice Problems 4.2 and 4.4 Pitts Name ___________________________ 1. (4.4 # 4) The price p, in dollars, and the quantity x sold of a certain product obey the demand equation 1 100 3 p x a.) Express the revenue R as a function of x. Show your work. c.) What is the revenue if 100 units are sold? d.) What quantity x maximizes the revenue? What is the maximum revenue? Show your algebra. You may use 2 b x a . Quantity x = ______________ Maximum revenue ______________ e.) What price should the company charge to maximize revenue? 2. (4.4 # 6) The price p (in dollars) and the quantity x sold of a certain product obey the demand equation 20 500 0 p 25x p . a.) Solve for p in terms of x. That is write p as a function of x. b.) Express the revenue R as a function of x. Show your work c.) What quantity x maximizes the revenue? What is the maximum revenue? Show your algebra. Y Quantity x = ______________ Maximum revenue ______________ d.) What price should the company charge to maximize revenue? 3. (4.4 # 8). Beth has 3000 feet of fencing to enclose a rectangular field. (Show algebra) a.) Express the area A of the rectangle as a function of x, where x is the length of the rectangle. b.) For what value of x is the area largest? Show algebra. c.) What is the maximum area? 3. (4.4 # 10). A farmer with 2000 meters of fencing wants to enclose a rectangular plot that borders on a straight highway, so he won’t fence the side along the highway. Express the area A of the rectangle as a function of x. highway x y For what value of x is the area a maximum? Show algebra. What is the maximum area? 5. (4.4 # 26). A shot-putter throws a ball at an inclination of 45o to the horizontal. The following data represents the height of the ball h feet at the instant that it has traveled x feet horizontally. Distance x 20 40 60 80 100 120 140 160 180 200 Height h 25 40 55 65 71 77 77 75 71 64 b.) Using your graphing calcualtor find the quadratic function of best fit that models the relation between distance and height. Record your answer rounded to four decimal places, but in your calculator store all the decimals. H(x) = _______________________________ c.) Use the function stored in your calculator to determine how far the ball will travel before it reaches its maximum height. Round to the nearest integer. d.) What is that maximum height? Round to the nearest integer. 6. See 4.2 # 22 c and g) A marketing firm wishes to find a function that relates the sales S of a product and A, the amount spent on advertising the product. The data are obtained from past experience. Advertising and sales are measure in thousands of dollars. Use your graphing calculator; find the line of best fit relating advertising expenditure ...
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4R2012 preTest2A
This document contains a math test with 4 questions. Question 1 asks students to solve algebraically and graphically to determine how many sprockets a company can produce per month given fixed and variable costs. Question 2 involves modeling the areas of a square and circle cut from a piece of wire. Question 3 models revenue based on a demand function relating price and quantity. Question 4 deals with composition of functions relating widget production costs to time.
MATH 107 FINAL EXAMINATIONMULTIPLE CHOICE1. Deter.docx
The document contains a 30-question math exam covering topics like functions, graphs, equations, inequalities, logarithms, and other math concepts. It includes multiple choice, short answer, and show work questions assessing skills like domain and range, solving equations, graphing, composites, inverses, lines, maximizing profit, and more. Students must demonstrate mathematical reasoning and problem-solving abilities.
MATH133 UNIT 2 Quadratic EquationsIndividual Project Assignment.docx
MATH133 UNIT 2: Quadratic Equations
Individual Project Assignment: Version 2A
Name (Required): __________________________________________________
Show all of your work details for these calculations. Please review this Web site to see how to type mathematics using the keyboard symbols. Handwritten scanned work is not acceptable for AIU Online.
Problem 1: Modeling Profit for a Business
IMPORTANT: See Question 3 below. This is mandatory.
Remember that the standard form for the quadratic function equation is y = f (x) = ax2 + bx + c and the vertex form is y = f (x) = a(x – h)2 + k, where (h, k) are the coordinates of the vertex of this quadratic function’s graph.
You will use P(x) = -0.2x2 + bx – c where (-0.2x2 + bx) represents the business’s variable profit and c is the business’s fixed costs.
So, P(x) is the store’s total annual profit (in $1,000) based on the number of items sold, x.
1. (List your chosen value for between 100 and 200.)
2. (List what the fixed costs might represent for your fictitious business, and be creative; also list your chosen value for c from the table below).
If your last name begins with the letter
Choose a fixed cost between
A–E
$5,000–$5,700
F–I
$5,800–$6,400
J–L
$6,500–$7,100
M–O
$7,200–$7,800
P–R
$7,800–$8,500
S–T
$8,600–$9,200
U–Z
$9,300–$10,000
3. Important: By Wednesday night at midnight, submit a Word document with only your name and your chosen values for b and c above in Parts 1 and 2. Submit this in the Unit 2 IP submissions area. This submitted Word document will be used to determine the Last Day of Attendance for government reporting purposes.
4. (State that quadratic profit model function’s equation by replacing and with your chosen values.)
5. (Choose five values of (number of items sold) between 500 and 1000. Insert those -values in the table.)
6. Plug these five values into your model for and evaluate the annual business profit given those sales volumes. (Be sure to show all your work for these calculations; complete the table below.)
7. Use the five ordered pairs of numbers from 5 and 6, and Excel or another graphing utility, to graph your quadratic profit model and insert the graph into your Word answer document. The graph of a quadratic function is called aparabola. (Insert graph below.)
8. (Show work details or explain how you found the vertex. Write the vertex in ordered-pair form: .)
9. (Write the explanation and the equation of the line of symmetry.)
10. (Write your quadratic profit function in vertex form, where is the vertex of this quadratic function’s graph. Show the details of how you found this equation.)
11. (State the maximum profit (if any), and show how you determined how many items must be sold to give the maximum profit.)
12. (State how knowing the number of items sold that produces the maximum profit help you to run business more effectively.)
13. (Give an analysis of the results of these profit calculations, and give some ...
Math 116 pres. 5
CHAPTER 6 Real Numbers: Completing a Mathematical System
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MATH133 UNIT 2 Quadratic Equations Individual Project Assignm.docx
MATH133 UNIT 2: Quadratic Equations
Individual Project Assignment: Version 2A
Show all of your work details for these calculations. Please review this Web site to see how to type mathematics using the keyboard symbols.
Problem 1: Modeling Profit for a Business
IMPORTANT: See Question 3 below for special IP instructions. This is mandatory.
Remember that the standard form for the quadratic function equation is
y
=
f
(
x
) =
ax
2
+
bx
+
c
and the vertex form is
y
=
f
(
x
) =
a
(
x
–
h
)
2
+
k
, where (
h
,
k
) are the coordinates of the vertex of this quadratic function’s graph.
You will use
P
(
x
) = −0.2
x
2
+
bx
–
c
where (−0.2
x
2
+
bx
) represents the business’ variable profit and
c
is the business’s fixed costs.
So,
P
(
x
) is the store’s total annual profit (in $1,000) based on the number of items sold,
x
.
1. Choose a value between 100 and 200 for
b
. That value does not have to be a whole number.
2. Think about and list what the fixed costs might represent for your fictitious business (be creative). Start by choosing a fixed cost,
c
, between $5,000 and $10,000, according to the first letter of your last name from the values listed in the following chart:
If your last name begins with the letter
Choose a fixed cost between
A–E
$5,000–$5,700
F–I
$5,800–$6,400
J–L
$6,500–$7,100
M–O
$7,200–$7,800
P–R
$7,800–$8,500
S–T
$8,600–$9,200
U–Z
$9,300–$10,000
4.Replace
b
and
c
with your chosen values in Parts 1 and 2 in
P
(
x
) = −0.2
x
2
+
bx
−
c
. This is your quadratic profit model function. State that quadratic profit model functions equation.
5. Next, choose 5 values of
x
(number of items sold) between 500 and 1,000. Think about the general characteristics of quadratic function graphs (parabolas) to help you with choosing these 5 values of
x
.
6. Plug these 5 values into your model for
P
(
x
), and evaluate the annual business profit given those sales volumes. (Be sure to show all of your work for these calculations.)
7. Use the 5 ordered pairs of numbers from 5 and 6 and Excel or another graphing utility to graph your quadratic profit model, and insert the graph into your Word answer document. The graph of the quadratic function is called a
parabola
.
8. What is the vertex of the quadratic function graph? (Show your work details, or explain how you found the vertex.)
9. What is the equation of the line of symmetry? Explain how you found this equation.
10. Write the vertex form for your quadratic profit function.
11. Is there a maximum profit for your business? If so, how many items must be sold to produce the maximum profit, and what is that maximum profit? If your quadratic profit function has a maximum, show your work or explain how the maximum profit figure was obtained.
12. How would knowing the number of items sold that produces the maximum profit help you to run your business more effectively.
13. Analyze the results of these profit cal.
REPRESENTATION OF FUNCTIONS.pptx
This document discusses functions and their representations. It begins by defining relations and functions, and providing examples of each. It then discusses different types of functions including linear, quadratic, constant, identity, absolute value, and piecewise functions. Examples are provided for each type. The document ends with exercises asking the reader to determine if given relations are functions, and to identify what type of function is being described.
BetterPie Industries has 3 million shares of common stock outstand.docx
BetterPie Industries has 3 million shares of common stock outstanding, 2 million shares of preferred stock outstanding, and 10,000 bonds. Assume the common shares are selling for $48 per share, the preferred shares are selling for $25.50 per share, and the bonds are selling for 99 percent of par.
What would be the weights used in the calculation of BetterPie’s WACC? (Do not round intermediate calculations and round your answers to 2 decimal places.)
Equity weight
%
Preferred stock weight
%
Debt weight
%
Algebra 2 Midterm Exam
1
Score: ______ / ______
Name: _________________________
Student Number: ________________
Multiple Choice: Type your answer choice in the blank.
_____1.
Simplify.
√
√
A. √
B. √
C. √
D. √
_____2. Find a quadratic function to model the values in the table. Predict the value
of y for x = 6.
X y
1 2
0 -2
3 10
A. y = -2x2 + 2x -2; –58
B. y = 2x2 – 2x -2; 60
C. y = 2x2 – 2x -2; 58
D. y = -2x2 + 2x +2; –58
Algebra 2 Midterm Exam
2
______3. A manufacturer of shipping boxes has a box shaped like a cube. The side length
is 5a + 4b. What is the volume of the box in terms of a and b?
A.
B.
C.
D.
_____4. In how many ways can 3 singers be selected from 5 who came to an audition?
A. 1
B. 10
C. 5
D. 60
_____5. Solve the problem by writing an inequality. A club decides to sell T-shirts for
$12 as a fund-raiser. It costs $20 plus $8 per T-shirt to make the T-shirts.
Write and solve an equation to find how many T-shirts the club needs to make
and sell in order to profit at least $100.
A. ( )
B.
C. ( )
D. ( )
Short Answer: Type your answer in the space below each question. Show your
work when applicable.
6. The velocity of sound in air is given by the equation √ , where v is
the velocity in meters per second and t is the temperature in degrees Celsius.
Find the temperature when the velocity is 329 meters per second by graphing
the equation. Round the answer to the nearest degree.
Algebra 2 Midterm Exam
3
7. The volume in cubic feet of a box can be expressed as ( ) , or
as the product of three linear factors with integer coefficients. The width of the
box is 2 – x.
Factor the polynomial to find linear expressions for the height and the width.
8. This table shows data on heating oil use for two years in three adjacent
buildings on Spring Street.
Heating Oil Use
Number of Gallons Used
Address 2002 2003
152 Spring St. 1215 1093
154 Spring St. 982 975
156 Spring St. 1562 1437
a. Write a matrix H to represent the data.
b. Find element . What does this element represent?
Algebra 2 Midterm Exam
4
9.
So ...
1 Week 2 Homework for MTH 125 Name_______________
1
Week 2 Homework for MTH 125
Name___________________________________ Date: ___July 20, 2021______________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Graph the equation by determining the missing values needed to plot the ordered pairs.
1) y + x = 3; ( 1, ), ( 3, ), ( 2, )
1) _______
A)
B)
C)
D)
2
Find the x- and y-intercepts. Then graph the equation.
2) 10y - 2x = -4
2) _______
A) ( -2, 0);
B) ; (0, -2)
3
C) ( 2, 0);
D) ; (0, 2)
Find the midpoint of the segment with the given endpoints.
4
3) ( 8, 4) and ( 7, 9) 3) _______
A) B) C) D)
Suppose that segment PQ has the given coordinates for one endpoint P and for its midpoint M. Find the coordinates
of the other endpoint Q.
4) P( 5, 5) and M 4) _______
A) Q( 4, 4) B) Q C) Q D) Q
Solve the problem.
5) The graphing calculator screen shows the graph of one of the equations below. Which equation is it?
5) _______
A) y + 3x = 15 B) y - 3x = 15 C) y = 3x + 3 D) y + 3x = 3
Find the slope.
6) m = 6) _______
A) -5 B) 5 C) 12 D) 8
Find the slope of the line through the given pair of points, if possible. Based on the slope, indicate whether the line
through the points rises from left to right, falls from left to right, is horizontal, or is vertical.
7) ( -3, -5) and ( 4, -4) 7) _______
A) - ; falls B) - 7; falls C) 7; rises D) ; rises
Find the slope of the line.
5
8)
8) _______
A) B) C) - D) -
Find the slope of the line and sketch the graph.
9) 2x + 3y = 10
9) _______
A) Slope:
6
B) Slope: -
C) Slope: -
7
D) Slope:
Decide whether the pair of lines is parallel, perpendicular, or neither.
10) 3x - 4y = 12 and 8x + 6y = -9 10) ______
A) Parallel B) Perpendicular C) Neither
Choose the graph that matches the equation.
11) y = 2x + 4 11) ______
A)
B)
C)
8
D)
Find the equation in slope-intercept form of the line satisfying the conditions.
12) m = 2, passes through ( 6, -3) 12) ______
A) y = 2x - 15 B) y = 3x + 16 C) y = 2x - 13 D) y = 2x + 14
Write the equation in slope-intercept form.
13) 17x + 5y = 7 13) ______
A) y = x + B) y = 17x - 7 C) y = - x + D) y = x -
Find the slope and the y-intercept of the line.
14) 7x + 5y = 48 14) ______
A) Slope - ; y-intercept B) Slope ; y-intercept
C) Slope ; y-intercept D) Slope - ; y-intercept
Find an equation of the line that satisfies the conditions. Write the equation in standard form.
9
15) Through ( 5, 4); m = - 15) ______
A) 4x - 9y = 56 B) 4x + 9y = -56 C) 4x + 9y = 56 D) 9x + 4y = -56
...
Recommended
4R2012 preTest2A
This document contains a math test with 4 questions. Question 1 asks students to solve algebraically and graphically to determine how many sprockets a company can produce per month given fixed and variable costs. Question 2 involves modeling the areas of a square and circle cut from a piece of wire. Question 3 models revenue based on a demand function relating price and quantity. Question 4 deals with composition of functions relating widget production costs to time.
MATH 107 FINAL EXAMINATIONMULTIPLE CHOICE1. Deter.docx
The document contains a 30-question math exam covering topics like functions, graphs, equations, inequalities, logarithms, and other math concepts. It includes multiple choice, short answer, and show work questions assessing skills like domain and range, solving equations, graphing, composites, inverses, lines, maximizing profit, and more. Students must demonstrate mathematical reasoning and problem-solving abilities.
MATH133 UNIT 2 Quadratic EquationsIndividual Project Assignment.docx
MATH133 UNIT 2: Quadratic Equations
Individual Project Assignment: Version 2A
Name (Required): __________________________________________________
Show all of your work details for these calculations. Please review this Web site to see how to type mathematics using the keyboard symbols. Handwritten scanned work is not acceptable for AIU Online.
Problem 1: Modeling Profit for a Business
IMPORTANT: See Question 3 below. This is mandatory.
Remember that the standard form for the quadratic function equation is y = f (x) = ax2 + bx + c and the vertex form is y = f (x) = a(x – h)2 + k, where (h, k) are the coordinates of the vertex of this quadratic function’s graph.
You will use P(x) = -0.2x2 + bx – c where (-0.2x2 + bx) represents the business’s variable profit and c is the business’s fixed costs.
So, P(x) is the store’s total annual profit (in $1,000) based on the number of items sold, x.
1. (List your chosen value for between 100 and 200.)
2. (List what the fixed costs might represent for your fictitious business, and be creative; also list your chosen value for c from the table below).
If your last name begins with the letter
Choose a fixed cost between
A–E
$5,000–$5,700
F–I
$5,800–$6,400
J–L
$6,500–$7,100
M–O
$7,200–$7,800
P–R
$7,800–$8,500
S–T
$8,600–$9,200
U–Z
$9,300–$10,000
3. Important: By Wednesday night at midnight, submit a Word document with only your name and your chosen values for b and c above in Parts 1 and 2. Submit this in the Unit 2 IP submissions area. This submitted Word document will be used to determine the Last Day of Attendance for government reporting purposes.
4. (State that quadratic profit model function’s equation by replacing and with your chosen values.)
5. (Choose five values of (number of items sold) between 500 and 1000. Insert those -values in the table.)
6. Plug these five values into your model for and evaluate the annual business profit given those sales volumes. (Be sure to show all your work for these calculations; complete the table below.)
7. Use the five ordered pairs of numbers from 5 and 6, and Excel or another graphing utility, to graph your quadratic profit model and insert the graph into your Word answer document. The graph of a quadratic function is called aparabola. (Insert graph below.)
8. (Show work details or explain how you found the vertex. Write the vertex in ordered-pair form: .)
9. (Write the explanation and the equation of the line of symmetry.)
10. (Write your quadratic profit function in vertex form, where is the vertex of this quadratic function’s graph. Show the details of how you found this equation.)
11. (State the maximum profit (if any), and show how you determined how many items must be sold to give the maximum profit.)
12. (State how knowing the number of items sold that produces the maximum profit help you to run business more effectively.)
13. (Give an analysis of the results of these profit calculations, and give some ...
Math 116 pres. 5
CHAPTER 6 Real Numbers: Completing a Mathematical System
6.6 Making the Connections: Is There REALly a Completion to the Number System?
MATH133 UNIT 2 Quadratic Equations Individual Project Assignm.docx
MATH133 UNIT 2: Quadratic Equations
Individual Project Assignment: Version 2A
Show all of your work details for these calculations. Please review this Web site to see how to type mathematics using the keyboard symbols.
Problem 1: Modeling Profit for a Business
IMPORTANT: See Question 3 below for special IP instructions. This is mandatory.
Remember that the standard form for the quadratic function equation is
y
=
f
(
x
) =
ax
2
+
bx
+
c
and the vertex form is
y
=
f
(
x
) =
a
(
x
–
h
)
2
+
k
, where (
h
,
k
) are the coordinates of the vertex of this quadratic function’s graph.
You will use
P
(
x
) = −0.2
x
2
+
bx
–
c
where (−0.2
x
2
+
bx
) represents the business’ variable profit and
c
is the business’s fixed costs.
So,
P
(
x
) is the store’s total annual profit (in $1,000) based on the number of items sold,
x
.
1. Choose a value between 100 and 200 for
b
. That value does not have to be a whole number.
2. Think about and list what the fixed costs might represent for your fictitious business (be creative). Start by choosing a fixed cost,
c
, between $5,000 and $10,000, according to the first letter of your last name from the values listed in the following chart:
If your last name begins with the letter
Choose a fixed cost between
A–E
$5,000–$5,700
F–I
$5,800–$6,400
J–L
$6,500–$7,100
M–O
$7,200–$7,800
P–R
$7,800–$8,500
S–T
$8,600–$9,200
U–Z
$9,300–$10,000
4.Replace
b
and
c
with your chosen values in Parts 1 and 2 in
P
(
x
) = −0.2
x
2
+
bx
−
c
. This is your quadratic profit model function. State that quadratic profit model functions equation.
5. Next, choose 5 values of
x
(number of items sold) between 500 and 1,000. Think about the general characteristics of quadratic function graphs (parabolas) to help you with choosing these 5 values of
x
.
6. Plug these 5 values into your model for
P
(
x
), and evaluate the annual business profit given those sales volumes. (Be sure to show all of your work for these calculations.)
7. Use the 5 ordered pairs of numbers from 5 and 6 and Excel or another graphing utility to graph your quadratic profit model, and insert the graph into your Word answer document. The graph of the quadratic function is called a
parabola
.
8. What is the vertex of the quadratic function graph? (Show your work details, or explain how you found the vertex.)
9. What is the equation of the line of symmetry? Explain how you found this equation.
10. Write the vertex form for your quadratic profit function.
11. Is there a maximum profit for your business? If so, how many items must be sold to produce the maximum profit, and what is that maximum profit? If your quadratic profit function has a maximum, show your work or explain how the maximum profit figure was obtained.
12. How would knowing the number of items sold that produces the maximum profit help you to run your business more effectively.
13. Analyze the results of these profit cal.
REPRESENTATION OF FUNCTIONS.pptx
This document discusses functions and their representations. It begins by defining relations and functions, and providing examples of each. It then discusses different types of functions including linear, quadratic, constant, identity, absolute value, and piecewise functions. Examples are provided for each type. The document ends with exercises asking the reader to determine if given relations are functions, and to identify what type of function is being described.
BetterPie Industries has 3 million shares of common stock outstand.docx
BetterPie Industries has 3 million shares of common stock outstanding, 2 million shares of preferred stock outstanding, and 10,000 bonds. Assume the common shares are selling for $48 per share, the preferred shares are selling for $25.50 per share, and the bonds are selling for 99 percent of par.
What would be the weights used in the calculation of BetterPie’s WACC? (Do not round intermediate calculations and round your answers to 2 decimal places.)
Equity weight
%
Preferred stock weight
%
Debt weight
%
Algebra 2 Midterm Exam
1
Score: ______ / ______
Name: _________________________
Student Number: ________________
Multiple Choice: Type your answer choice in the blank.
_____1.
Simplify.
√
√
A. √
B. √
C. √
D. √
_____2. Find a quadratic function to model the values in the table. Predict the value
of y for x = 6.
X y
1 2
0 -2
3 10
A. y = -2x2 + 2x -2; –58
B. y = 2x2 – 2x -2; 60
C. y = 2x2 – 2x -2; 58
D. y = -2x2 + 2x +2; –58
Algebra 2 Midterm Exam
2
______3. A manufacturer of shipping boxes has a box shaped like a cube. The side length
is 5a + 4b. What is the volume of the box in terms of a and b?
A.
B.
C.
D.
_____4. In how many ways can 3 singers be selected from 5 who came to an audition?
A. 1
B. 10
C. 5
D. 60
_____5. Solve the problem by writing an inequality. A club decides to sell T-shirts for
$12 as a fund-raiser. It costs $20 plus $8 per T-shirt to make the T-shirts.
Write and solve an equation to find how many T-shirts the club needs to make
and sell in order to profit at least $100.
A. ( )
B.
C. ( )
D. ( )
Short Answer: Type your answer in the space below each question. Show your
work when applicable.
6. The velocity of sound in air is given by the equation √ , where v is
the velocity in meters per second and t is the temperature in degrees Celsius.
Find the temperature when the velocity is 329 meters per second by graphing
the equation. Round the answer to the nearest degree.
Algebra 2 Midterm Exam
3
7. The volume in cubic feet of a box can be expressed as ( ) , or
as the product of three linear factors with integer coefficients. The width of the
box is 2 – x.
Factor the polynomial to find linear expressions for the height and the width.
8. This table shows data on heating oil use for two years in three adjacent
buildings on Spring Street.
Heating Oil Use
Number of Gallons Used
Address 2002 2003
152 Spring St. 1215 1093
154 Spring St. 982 975
156 Spring St. 1562 1437
a. Write a matrix H to represent the data.
b. Find element . What does this element represent?
Algebra 2 Midterm Exam
4
9.
So ...
1 Week 2 Homework for MTH 125 Name_______________
1
Week 2 Homework for MTH 125
Name___________________________________ Date: ___July 20, 2021______________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Graph the equation by determining the missing values needed to plot the ordered pairs.
1) y + x = 3; ( 1, ), ( 3, ), ( 2, )
1) _______
A)
B)
C)
D)
2
Find the x- and y-intercepts. Then graph the equation.
2) 10y - 2x = -4
2) _______
A) ( -2, 0);
B) ; (0, -2)
3
C) ( 2, 0);
D) ; (0, 2)
Find the midpoint of the segment with the given endpoints.
4
3) ( 8, 4) and ( 7, 9) 3) _______
A) B) C) D)
Suppose that segment PQ has the given coordinates for one endpoint P and for its midpoint M. Find the coordinates
of the other endpoint Q.
4) P( 5, 5) and M 4) _______
A) Q( 4, 4) B) Q C) Q D) Q
Solve the problem.
5) The graphing calculator screen shows the graph of one of the equations below. Which equation is it?
5) _______
A) y + 3x = 15 B) y - 3x = 15 C) y = 3x + 3 D) y + 3x = 3
Find the slope.
6) m = 6) _______
A) -5 B) 5 C) 12 D) 8
Find the slope of the line through the given pair of points, if possible. Based on the slope, indicate whether the line
through the points rises from left to right, falls from left to right, is horizontal, or is vertical.
7) ( -3, -5) and ( 4, -4) 7) _______
A) - ; falls B) - 7; falls C) 7; rises D) ; rises
Find the slope of the line.
5
8)
8) _______
A) B) C) - D) -
Find the slope of the line and sketch the graph.
9) 2x + 3y = 10
9) _______
A) Slope:
6
B) Slope: -
C) Slope: -
7
D) Slope:
Decide whether the pair of lines is parallel, perpendicular, or neither.
10) 3x - 4y = 12 and 8x + 6y = -9 10) ______
A) Parallel B) Perpendicular C) Neither
Choose the graph that matches the equation.
11) y = 2x + 4 11) ______
A)
B)
C)
8
D)
Find the equation in slope-intercept form of the line satisfying the conditions.
12) m = 2, passes through ( 6, -3) 12) ______
A) y = 2x - 15 B) y = 3x + 16 C) y = 2x - 13 D) y = 2x + 14
Write the equation in slope-intercept form.
13) 17x + 5y = 7 13) ______
A) y = x + B) y = 17x - 7 C) y = - x + D) y = x -
Find the slope and the y-intercept of the line.
14) 7x + 5y = 48 14) ______
A) Slope - ; y-intercept B) Slope ; y-intercept
C) Slope ; y-intercept D) Slope - ; y-intercept
Find an equation of the line that satisfies the conditions. Write the equation in standard form.
9
15) Through ( 5, 4); m = - 15) ______
A) 4x - 9y = 56 B) 4x + 9y = -56 C) 4x + 9y = 56 D) 9x + 4y = -56
...
1 Week 2 Homework for MTH 125 Name_______________
1
Week 2 Homework for MTH 125
Name___________________________________ Date: ___July 20, 2021______________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Graph the equation by determining the missing values needed to plot the ordered pairs.
1) y + x = 3; ( 1, ), ( 3, ), ( 2, )
1) _______
A)
B)
C)
D)
2
Find the x- and y-intercepts. Then graph the equation.
2) 10y - 2x = -4
2) _______
A) ( -2, 0);
B) ; (0, -2)
3
C) ( 2, 0);
D) ; (0, 2)
Find the midpoint of the segment with the given endpoints.
4
3) ( 8, 4) and ( 7, 9) 3) _______
A) B) C) D)
Suppose that segment PQ has the given coordinates for one endpoint P and for its midpoint M. Find the coordinates
of the other endpoint Q.
4) P( 5, 5) and M 4) _______
A) Q( 4, 4) B) Q C) Q D) Q
Solve the problem.
5) The graphing calculator screen shows the graph of one of the equations below. Which equation is it?
5) _______
A) y + 3x = 15 B) y - 3x = 15 C) y = 3x + 3 D) y + 3x = 3
Find the slope.
6) m = 6) _______
A) -5 B) 5 C) 12 D) 8
Find the slope of the line through the given pair of points, if possible. Based on the slope, indicate whether the line
through the points rises from left to right, falls from left to right, is horizontal, or is vertical.
7) ( -3, -5) and ( 4, -4) 7) _______
A) - ; falls B) - 7; falls C) 7; rises D) ; rises
Find the slope of the line.
5
8)
8) _______
A) B) C) - D) -
Find the slope of the line and sketch the graph.
9) 2x + 3y = 10
9) _______
A) Slope:
6
B) Slope: -
C) Slope: -
7
D) Slope:
Decide whether the pair of lines is parallel, perpendicular, or neither.
10) 3x - 4y = 12 and 8x + 6y = -9 10) ______
A) Parallel B) Perpendicular C) Neither
Choose the graph that matches the equation.
11) y = 2x + 4 11) ______
A)
B)
C)
8
D)
Find the equation in slope-intercept form of the line satisfying the conditions.
12) m = 2, passes through ( 6, -3) 12) ______
A) y = 2x - 15 B) y = 3x + 16 C) y = 2x - 13 D) y = 2x + 14
Write the equation in slope-intercept form.
13) 17x + 5y = 7 13) ______
A) y = x + B) y = 17x - 7 C) y = - x + D) y = x -
Find the slope and the y-intercept of the line.
14) 7x + 5y = 48 14) ______
A) Slope - ; y-intercept B) Slope ; y-intercept
C) Slope ; y-intercept D) Slope - ; y-intercept
Find an equation of the line that satisfies the conditions. Write the equation in standard form.
9
15) Through ( 5, 4); m = - 15) ______
A) 4x - 9y = 56 B) 4x + 9y = -56 C) 4x + 9y = 56 D) 9x + 4y = -56
...
1 College Algebra Final Examination---FHSU Math & C.S.docx
1
College Algebra
Final Examination---FHSU Math & C.S. Department
Form G Name ____________________________
Multiple Choice:
Mark through (horizontally) the space on the answer card corresponding to the best answer for each
problem.
1. Solve the equation by factoring: 2 9 18 0x x
[A] 6, 3 [B] 6, 3 [C] 6, 3 [D] 6, 3
2. Write the product in the standard form a + bi: (2 6 )(2 9 )i i
[A] 58 6i [B] 50 30i [C] 58 6i [D]
2
54 6 4i i
3. Find the real solutions of the equation 14 21 2 .x x
[A] 5 [B] 3 [C] 4 [D] 5
4. Solve the inequality 3 7 2 4x x . Express your answer using interval notation.
[A] 11, [B] [3, ) [C] 3, [D] ( , 3]
5. Solve the equation 3 3 18.x
[A] 3, 9 [B] 3 [C] 9, 3 [D] no solution
6. Solve the inequality 5 1 5x . Express your answer using interval notation.
[A] 645 5, or , [B]
64
5 5
,
[C] 645 5, [D]
64
5 5
, or ,
7. A bank loaned $68,000, part of it at a rate of 15% per year and the rest at a rate of 5% per year. If the
interest received was $6600, how much was loaned at 15%?
[A] $36, 000 [B] $33, 000 [C] $32, 000 [D] $35, 000
8. Find the distance between the points 1 2(2, 2) and ( 10, 3).PP
[A] 14 [B] 26 [C] 169 [D] 13
9. List the intercepts for the graph of the equation
2
16 0.x y
[A] ( 4, 0), (0,16), (4, 0) [B] (4, 0), (0,16), (0, 16)
[C] (0, 4), (16, 0), (0, 4) [D] ( 4, 0), (0, 16), (4, 0)
2
10. Find the slope-intercept form of the equation of the line that is parallel with the given properties:
( 2, 3); and 9 20y x
[A] 9 15y x [B] 9 20y x [C]
1
20
9
y x [D]
1
20
9
y x
11. Write the standard from of the equation of the circle with radius 5 and center (1, 4) .
[A]
2 2
4 1 25x y [B]
2 2
1 4 5x y
[C]
2 2
4 1 25x y [D]
2 2
1 4 5x y
12. Write a general formula to describe the variation.
The illumination I produced on a surface by a source of light varies directly as the candlepower c of
the source and inversely as the square of the distance d between the source and the surface.
[A]
2
I kcd [B]
2
2
kc
I
d
[C]
2
kc
I
d
[D]
2
kd
I
c
13. For the given functions ( ) 6 3 and ( ) 7 9f x x g x x , determine ( )( ).f g x
[A]
2
( )( ) 4 27f g x x [B]
2
( )( ) 13 33 6f g x x x
[C]
2
( )( ) 42 33 27f g x x x [D]
2
( )( ) 42 12 27f g x x x
14. The graph of a function f is given. For what values of x is
( ) 0f x ?
[A] 15,17.5
[B] 15,17.5, 25
[C] 15
[D] 25, 15,17.5, 25
15. Determine whether the function
3 2
( ) 4 9f x x is even, odd, neither, or ...
1. Write an equation in standard form of the parabola that has th.docx
1.
Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 2x
2
, but with the given point as the vertex (5, 3).
A. f(x) = (2x - 4) + 4
B. f(x) = 2(2x + 8) + 3
C. f(x) = 2(x - 5)
2
+ 3
D. f(x) = 2(x + 3)
2
+ 3
2 of 20
5.0 Points
Find the coordinates of the vertex for the parabola defined by the given quadratic function.
f(x) = 2(x - 3)
2
+ 1
A. (3, 1)
B. (7, 2)
C. (6, 5)
D. (2, 1)
3 of 20
5.0 Points
Find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of the following rational function.
g(x) = x + 3/x(x + 4)
A. Vertical asymptotes: x = 4, x = 0; holes at 3x
B. Vertical asymptotes: x = -8, x = 0; holes at x + 4
C. Vertical asymptotes: x = -4, x = 0; no holes
D. Vertical asymptotes: x = 5, x = 0; holes at x - 3
4 of 20
5.0 Points
"Y varies directly as the n
th
power of x" can be modeled by the equation:
A. y = kx
n
.
B. y = kx/n.
C. y = kx
*n
.
D. y = kn
x
.
5 of 20
5.0 Points
40 times a number added to the negative square of that number can be expressed as:
A.
A(x) = x
2
+ 20x.
B. A(x) = -x + 30x.
C.
A(x) = -x
2
- 60x.
D.
A(x) = -x
2
+ 40x.
6 of 20
5.0 Points
The graph of f(x) = -x
3
__________ to the left and __________ to the right.
A. rises; falls
B. falls; falls
C. falls; rises
D. falls; falls
Solve the following formula for the specified variable:
V = 1/3 lwh for h
7 of 20
Write an equation that expresses each relationship. Then solve the equation for y.
x varies jointly as y and z
A. x = kz; y = x/k
B. x = kyz; y = x/kz
C. x = kzy; y = x/z
D. x = ky/z; y = x/zk
8 of 20
8 times a number subtracted from the squared of that number can be expressed as:
A. P(x) = x + 7x.
B.P(x) = x
2
- 8x.
C. P(x) = x - x.
P(x) = x
2
+ 10x.
9of 20
Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.
f(x) = x
4
- 9x
2
A. x = 0, x = 3, x = -3; f(x) crosses the x-axis at -3 and 3; f(x) touches the x-axis at 0.
B. x = 1, x = 2, x = 3; f(x) crosses the x-axis at 2 and 3; f(x) crosses the x-axis at 0.
C. x = 0, x = -3, x = 5; f(x) touches the x-axis at -3 and 5; f(x) touches the x-axis at 0.
D. x = 1, x = 2, x = -4; f(x) crosses the x-axis at 2 and -4; f(x) touches the x-axis at 0.
10 of 20
Find the domain of the following rational function.
f(x) = x + 7/x
2
+ 49
A. All real numbers < 69
B. All real numbers > 210
C. All real numbers ≤ 77
D. All real numbers
11 of 20
Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 3x
2
or g(x) = -3x
2
, but with the given maximum or minimum.
Minimum = 0 at x = 11
A. f(x) = 6(x - 9)
B. f(x) = 3(x - 11)
2
C. f(x) = 4(x + 10)
D. f(x) = 3(x
2
- 15)
2
12 of 20
Solve the following polynomial inequality.
3x
2
+ 10x - 8 ≤ 0
A. [6, 1/3]
B. [-4, 2/3]
C. [-9, 4/5]
D. [8, 2/7]
13 of 20
Find the coordinate.
Goldie chapter 4 function
This document discusses composite functions and the order of operations when combining functions.
It provides an example of a mother converting the temperature of her baby's bath water from Celsius to Fahrenheit using two separate functions. The first function converts the Celsius reading to Fahrenheit, and the second maps the Fahrenheit reading to whether the water is too cold, alright, or too hot. Together these functions form a composite function.
Algebraically, a composite function f∘g(x) is defined as applying the inner function f first to the input x, and then applying the outer function g to the output of f. The domain of the inner function must be contained within the range of the outer function. The order of
1988 FRQs AP Calculus
This document contains 6 multi-part calculus problems involving functions, derivatives, integrals, areas, volumes and series. The problems cover topics like finding derivatives and integrals of functions, analyzing graphs of functions, calculating areas and volumes of revolved regions, determining convergence of series, and relating functions to their derivatives.
1988 FRQ
This document contains 6 multi-part calculus problems involving functions, derivatives, integrals, areas, volumes and series. The problems cover topics like finding derivatives and integrals of functions, analyzing graphs of functions, finding critical points and intervals of increase/decrease, calculating areas and volumes of revolved regions, and determining convergence of series.
88AB6 WorkBook Integration Example AP Calculus Exam
This document contains 6 multi-part calculus problems involving functions, derivatives, integrals, areas, volumes and average values. The problems cover topics like finding derivatives and integrals of functions, determining domains and critical points, sketching graphs, solving optimization problems, and evaluating limits of series.
LAC2013 UNIT preTESTs!
This document contains instructions for solving calculus problems and presenting solutions clearly. It provides 17 multi-part problems testing various calculus concepts. Responses must show all work and be supported analytically, graphically, numerically, and/or verbally. Approximations must be stated to three decimal places or in scientific notation. Graphs must be complete sketches with labeled axes, scales, intercepts, asymptotes and functions.
2010 assessment review_homework_1-4-done
The document provides an assessment review with multiple choice questions about math concepts like algebra, geometry, and coordinate planes. It includes 15 questions testing skills like simplifying expressions, solving equations, factoring polynomials, and graphing lines. The questions are formatted with explanations of steps required to arrive at the answers.
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Math 107 Final ExaminationSummer, 20151
Math 107 College AlgebraName______________________________
Final Examination: Summer, 2015Instructor __________________________
Answer Sheet
Instructions:
This is an open-book exam. You may refer to your text and other course materials as you work on the exam, and you may use a calculator.
Record your answers and work in this document.
There are 30 problems.
Problems #1-12 are multiple choice. Record your choice for each problem.
Problems #13-21 are short answer. Record your answer for each problem.
Problems #22-30 are short answer with work required. When requested, show all work and write all answers in the spaces allotted on the following pages. You may type your work using plain-text formatting or an equation editor, or you may hand-write your work and scan it. In either case, show work neatly and correctly, following standard mathematical conventions. Each step should follow clearly and completely from the previous step. If necessary, you may attach extra pages.
.
Name _____________________Date___________________
MULTIPLE CHOICE. Record your answer choices.
1.7.
2.8.
3.9.
4.10.
5.11.
6.12.
SHORT ANSWER. Record your answers below.
13.
14.
15.
16.
17.
18.
19. (a)
(b)
(c)
20. (a)
(b)
(c)
(d)
21. (a)
(b)
(c)
(d)
SHORT ANSWER with Work Shown. Record your answers and work.
Problem Number
Solution
22
Answers:
(a)
(b)
Work/for part (a) and explanation for part (b):
23
Answers:
(a)
(b)
(c)
Work for part (a):
24
Answer:
Work:
25
Answer:
Work:
26
Answers:
(a)
(b)
Work for part (a) and for part (b):
27
Answer:
Work:
28
Answer:
Work:
29
Answers:
(a)
(b)
Work for (b):
30
Answer:
Work:
College Algebra MATH 107 Summer, 2015, V3.1
Page 1 of 11
MATH 107 FINAL EXAMINATION
This is an open-book exam. You may refer to your text and other course materials as you work
on the exam, and you may use a calculator. You must complete the exam individually.
Neither collaboration nor consultation with others is allowed.
Record your answers and work on the separate answer sheet provided.
There are 30 problems.
Problems #1–12 are Multiple Choice.
Problems #13–21 are Short Answer. (Work not required to be shown)
Problems #22–30 are Short Answer with work required to be shown.
MULTIPLE CHOICE
1. Determine the domain and range of the piecewise functi.
MA 141 Turn in Homework Quiz 4.2 Pitts Name ___.docx
MA 141 Turn in Homework Quiz 4.2
Pitts Name ____________________________
1. (#34) Let f(x) = 3x4 – 6x3 + x – 8. Determine where the function is concave upward and where it is concave
downward. Show your calculus. Show your sign graph.
In interval notation: concave up ______________________ concave down _______________________
2. (#38) Let ( ) 2g x x . Determine where the function is concave upward and where it is concave downward.
Show your calculus.
3. Let
2
( )
3
x
f x
x
. Determine where the function is concave upward and where it is concave downward. Show
your calculus. Show your sign graph.
In interval notation: concave up ______________________ concave down _______________________
4. Consider the function
4 3
( ) 4 5f x x x . Show your calculus.
a.) Using the first derivative, find all critical values for potential relative extrema.
b.) Use the second derivative test to find all relative maximum and minimum points.
c.) Determine if there are any points of inflection. Show your calculus! Show your sign graph.
5. (# 60) Determine the intervals where the function is concave up or down, and also determine if there are any
points of inflection for the function
3
( ) 2f x
x
.
6. (# 72) Using the second derivative test, determine if there are any relative extrema for the function
2 2
( )g x x
x
.
7. (#74) Consider function
2
1
( )
1
g x
x
. Find any relative extrema. Use the first or second derivative test to
justify whether it is a maximum or a minimum. You do not need to simplify the second derivative.
8. (#78) Sketch the graph of a function (2) 2f , (0) 1f , '(2) 0f , '( ) 0f x for x < 2, '( ) 0f x for
2x , ''( ) 0f x for x < 2, and "( ) 0f x for x > 2.
9. In a study conducted in 2003, it was projected that worldwide PC shipments (in millions) through 2005 will
be given by
3 2
( ) 0.75 1.5 8.25 133 (0 t 4)n t t t t where t is measured in years, with t = 0
corresponding to 2001. Make sure to show sign graphs were necessary. Determine the intervals where N is
concave upward and where it is concave downward. Also find an inflection point(s) and interpret the results.
MA 141 Homework 4.1
Pitts SHOW YOUR WORK! Name _______________________
1. (See # 20) Find the interval(s) where the function
3
( ) 3 4f x x x is increasing and the interval(s)
where it is decreasing. Show your calculus to justify your answer. Show your sign graph clearly
In interval notation: increasing over ______________________ decreasing over ______________________
2. (See # 28) Find the interval(s) where the function
2
2
( )
1
t
g t
t
is increasing and the interval(s) where it
is decreasing. Show your calculus to justify your answer. Show your sign graph clea ...
Pre calculus chapter-4
This document discusses solving quadratic equations graphically by relating them to their corresponding quadratic functions. It explains that the roots of a quadratic equation are the same as the zeros of the corresponding quadratic function, which are the x-intercepts of the graph. It provides examples of solving quadratic equations with one real root, two distinct real roots, and no real roots. Methods for solving graphically include paper-and-pencil, spreadsheets, and graphing calculators. The key ideas are that the number of real roots corresponds to the number of real x-intercepts on the graph.
Application of derivative
Additional Applications of the Derivative related to engineering maths
this presentation is only for the knowledge...............
1_Representation_of_Functions.pptx
This document covers representing functions including objectives like defining functions and related terms, determining if a relation is a function, defining piecewise functions, and representing real-life situations
1 representation of_functions
This document covers representing functions including objectives like defining functions and related terms, determining if a relation is a function, defining piecewise functions, and representing real-life situations
EVALUATING INTEGRALS.Evaluate the integral shown below. (H.docx
EVALUATING INTEGRALS.
Evaluate the integral shown below. (Hint: Try the substitution u = (7x2 + 3).)
1)
x dx
(7x2 + 3)5
Evaluate the integral shown below. (Hint: Apply a property of logarithms first.)
2)
ln x6
x
dx
1
Use the Fundamental Theorem of Calculus to find the derivative shown below.
3)
d
dx
x5
0
sin t dt
For the function shown below, sketch a graph of the function, and then find the SMALLEST possible value and the
LARGEST possible value for a Riemann sum of the function on the given interval as instructed.
4) f(x) = x2 ; between x = 3 and x = 7 with four rectangles of equal width.
^
CHARACTERISTICS and BEHAVIOR OF FUNCTIONS.
Use l'Hopital's rule to find the limit below.
5) lim
x
5x + 9
6x2 + 3x - 9
^
Use l'Hopital's rule to find the limit below. (Hint: The indeterminate form is f(x)g(x).)
6) lim
x
1 + 2
x3
x
2
Solve the following problem.
7) The 9 ft wall shown here stands 30 feet from the building. Find the length of the shortest straight beam that will
reach to the side of the building from the ground outside the wall.
9' wall
30'
Hint: Let "h" be the height on the building where the ladder touches; let "x" be the distance on the ground
between the wall and the foot of the ladder. Use similar triangles and the Pythagorean Theorem to write the
length of the beam "L" as a function of "x". Also note that a radical function is minimized when it radicand is
minimized.
For the function shown below, identify its local and absolute extreme values (if any), saying where they occur.
8) f(x) = -x3- 9x2 - 24x + 3
3
Find a value for "c" that satisfies the equation f(b) - f(a)
b - a
= f (c) in the conclusion of the Mean Value Theorem for the
function and interval shown below.
9) f(x) = x +
75
x
, on the interval [3, 25]
DERIVATIVES.
Find the equation of the tangent line to the curve whose function is shown below at the given point.
10) x5y5 = 32, tangent at (2, 1)
Use implicit differentiation to find dy/dx.
11) xy + x + y = x2y2
Given y = f(u) and u = g(x), find dy/dx = f (g(x))g (x).
12) y = u(u - 1), u = x2 + x
4
Find y .
13) y = (4x - 5)(4x3 - x2 + 1)
Find the derivative of the function "y" shown below.
14) y =
x2 + 8x + 3
x
Solve the problem below.
15) One airplane is approaching an airport from the north at 163 km/hr. A second airplane approaches from the east
at 261 km/hr. Find the rate at which the distance between the planes changes when the southbound plane is 31
km away from the airport and the westbound plane is 18 km from the airport.
FUNCTIONS, LIMITS and CONTINUITY.
Find the intervals on which the function shown below is continuous.
16) y =
x + 2
x2 - 8x + 7
5
A function f(x), a point c, the limit of f(x) as x approaches c, and a positive number is given. Find a number > 0 such
that for all x, 0 < x - c < f(x) - L < .
17) f(x) = 10x - 1, L = 29, c = 3, and = 0.01
Find all points "x" where the function shown below is discontinuous.
18)
Solve the "composite function ...
Pre-Calculus Midterm Exam 1 Score ______ ____.docx
Pre-Calculus Midterm Exam
1
Score: ______ / ______
Name: ____________________________
Student Number: ___________________
Short Answer: Type your answer below each question. Show your work.
1 Verify the identity. Show your work.
cot θ ∙ sec θ = csc θ
2 A gas company has the following rate schedule for natural gas usage in single-family residences:
Monthly service charge $8.80
Per therm service charge
1st 25 therms $0.6686/therm
Over 25 therms $0.85870/therm
What is the charge for using 25 therms in one month? Show your work.
What is the charge for using 45 therms in one month? Show your work.
Construct a function that gives the monthly charge C for x therms of gas.
Pre-Calculus Midterm Exam
2
3 The wind chill factor represents the equivalent air temperature at a standard wind speed that would
produce the same heat loss as the given temperature and wind speed. One formula for computing
the equivalent temperature is
W(t) = {
𝑡
33 −
(10.45+10√𝑣−𝑣)(33−𝑡)
2204
33 − 1.5958(33 − 𝑡)
if 0 ≤ v < 1.79
if 1.79 ≤ v < 20
if v ≥ 20
where v represents the wind speed (in meters per second) and t represents the air temperature .
Compute the wind chill for an air temperature of 15°C and a wind speed of 12 meters per second.
(Round the answer to one decimal place.) Show your work.
4 Complete the following:
(a) Use the Leading Coefficient Test to determine the graph's end behavior.
(b) Find the x-intercepts. State whether the graph crosses the x-axis or touches the x-axis
and turns around at each intercept. Show your work.
(c) Find the y-intercept. Show your work.
f(x) = x2(x + 2)
(a).
(b).
(c).
Pre-Calculus Midterm Exam
3
5 For the data set shown by the table,
a. Create a scatter plot for the data. (You do not need to submit the scatter plot)
b. Use the scatter plot to determine whether an exponential function or a logarithmic function is
the best choice for modeling the data.
Number of Homes Built in a Town by Year
6 Verify the identity. Show your work.
(1 + tan2u)(1 - sin2u) = 1
Pre-Calculus Midterm Exam
4
7 Verify the identity. Show your work.
cot2x + csc2x = 2csc2x - 1
8 Verify the identity. Show your work.
1 + sec2xsin2x = sec2x
Pre-Calculus Midterm Exam
5
9 Verify the identity. Show your work.
cos(α - β) - cos(α + β) = 2 sin α sin β
10 The following data represents the normal monthly precipitation for a certain city.
Draw a scatter diagram of the data for one period. (You
Lesson 5: Functions and surfaces
A function of two variables is defined similar to a function of one variable. It has a domain (in the plane) and a range. The graph of such a function is a surface in space and we try to sketch some.
Write solution for these problems -Is targeting only mommy blo.docx
Write solution for these problems
-Is targeting only mommy bloggers is a good idea and why?
-how would J&J guarantee that these bloggers won't give a bad feedback?
-if J&J announced about their product only through social media, then how would it reach the other people who don't use social media?
-do you see any value in offering this type of incentive for the users? or, is all the benefit for the company only?
MATH 115 Precalculus Fall, 2018, V1.4
Page 1 of 7
MATH 115 FINAL EXAMINATION
This is an open-book exam. You may refer to your text and other course materials as you work
on the exam, and you may use a calculator. You must complete the exam individually.
Neither collaboration nor consultation with others is allowed.
Record your answers and work on the separate answer sheet provided.
There are 28 problems.
Problems #1–6 are Multiple Choice.
Problems #7–17 are Short Answer. (Work not required to be shown)
Problems #18–28 are Short Answer with work required to be shown.
MULTIPLE CHOICE
1. Solve | 7 – 5x | 8 and write interval notation for the solution set. 1. _______
A. (−∞, −
1
5
] ∪ [3, ∞)
B. (−∞, 3] ∪ [−
1
5
, ∞)
C. [−
1
5
, ∞)
D. [−
1
5
, 3]
2. Which of the following polynomials has a graph which exhibits the end behavior of
upward to the left and upward to the right? 2. ______
A. f (x) = x3 – 3x2 – x
B. f (x) = 3x6 + x2 – x
C. f (x) = –7x4 – x3 – 5
D. f (x) = –6x5 + x3 + 8
3. Write as an equivalent expression: 9 log x – log (y + 3) + log 1 3. _______
A.
9
log
log ( 3)
x
y +
B. ( )log 9 2x y− −
C.
9 1
log
3
x
y
+
+
D.
9
log
3
x
y
+
vvvv
MATH 115 Precalculus Fall, 2018, V1.4
Page 2 of 7
4. Determine the interval(s) on which the function is decreasing. 4. ______
A. (–, –3.5) (0, 3.5)
B. (– 5.3, 5.3)
C. (– 3.5, 3.5)
D. (– 2, 2)
5. Which of the functions corresponds to the graph? 5. ______
A. ( ) 1xf x e−= +
B. ( ) 2xf x e−= +
C. ( ) 2xf x e−=
D. ( ) 2 xf x e−=
MATH 115 Precalculus Fall, 2018, V1.4
Page 3 of 7
6. Which of the functions corresponds to the graph? 6. ______
A. f (x) = 3 – sin x
B. f (x) = sin x + 3
C. f (x) = 2 cos x + 1
D. f (x) = cos(2x) + 2
SHORT ANSWER:
7. Points (–9, 2) and (–5, 8) are endpoints of the diameter of a circle.
(a) What is the exact length of the diameter? (Simplify as much as possible) Answer: ________
(b) What is the center of the circle? Answer: ____________
(c) What is the equation of the circle? Answer: ___________________________
8. Find the value of the logarithm: log8 (
1
64
). Answer: ____________
9. A salesperso.
Mid module review
The document provides a mid-module review for algebra that includes 14 problems. The problems cover topics such as writing expressions to represent word problems, expanding expressions using the distributive property, finding equivalent expressions, and modeling algebraic expressions visually. Students are expected to show their work, use proper notation, and provide unit labels where appropriate to receive full credit.
PART B Please response to these two original posts below. Wh.docx
PART B
Please response to these two original posts below. When
responding to these posts, please either expand the
thought, add additional insights, or respectfully disagree
and explain why. Remember that we are after reasons
and arguments, and not simply the statement of
opinions.
Original Post 1
Are human lives intrinsically valuable? If so, in virtue of what? (Is
it our uniqueness, perhaps, or our autonomy, or something else?)
To begin, I would like to remind us that being intrinsically valuable
means having values for just being us and nothing else. I believe
that human lives are intrinsically valuable in virtue of our
uniqueness. As a bio nerd, I would like to state the fact that there
are a lot of crossover events during meiosis, which create trillions
of different DNA combinations. Hence, from a biological
standpoint, without considering other aspects, being you is
already valuable because you are that one sperm that won the
race and got fertilized. On a larger scale, there are hardly two
people whose look and behaviors are the same in the same
family, unless they are identical twins. However, identical twins
still act differently and have differences (such as fingerprints).
Since we are raised in different families, we are taught different
things and have different cultures. In general, we all have
different genetic information, appearances, personalities, senses
of humor, ambitions, talents, interests and life experiences. These
characteristics make up our “unique individual value” and make
us so unique and irreplaceable.
I would also love to discuss how our diversities enrich and
contribute to society, but that would be a talk about our extrinsic
values.
Original Post 2
Are human lives intrinsically valuable? If so, in virtue of what? (Is
it our uniqueness, perhaps, or our autonomy, or something else?)
I believe that human lives are intrinsically valuable due to a
number of reasons. Firstly, human lives aren’t replaceable. You
can’t replace a human being with another just like you can
replace a broken laptop with brand new one. Part of the reason
why we tend to think this way is that we were nurtured with the
notion that there is, indeed, a special value to human life. This
could be in virtue of our uniqueness-- the fact that we are
sentient and capable of complex thoughts and emotions
separates us from any other species on this planet. From a
scientific standpoint, this is also one of the reasons as to why
humans became the dominant species in today’s age.
Moreover, human lives aren’t disposable. I think this is largely due
to us humans having the ability to empathize with others. We
understand that it’s morally inappropriate to take the life of
another individual even if they’re complete strangers because
they’re another human being like us who has their own thoughts,
values, memories, and stories. In a way, we have a strong
emotional connection to our own species. As .
Part C Developing Your Design SolutionThe Production Cycle.docx
Part C Developing Your Design
Solution
The Production Cycle
Within the four stages of the design workflow there are two distinct parts.
The first three stages, as presented in Part B of this book, were described
as ‘The Hidden Thinking’ stages, as they are concerned with undertaking
the crucial behind-the-scenes preparatory work. You may have completed
them in terms of working through the book’s contents, but in visualisation
projects they will continue to command your attention, even if that is
reduced to a background concern.
You have now reached the second distinct part of the workflow which
involves developing your design solution. This stage follows a production
cycle, commencing with rationalising design ideas and moving through to
the development of a final solution.
The term cycle is appropriate to describe this stage as there are many loops
of iteration as you evolve rapidly between conceptual, practical and
technical thinking. The inevitability of this iterative cycle is, in large part,
again due to the nature of this pursuit being more about optimisation rather
than an expectation of achieving that elusive notion of perfection. Trade-
offs, compromises, and restrictions are omnipresent as you juggle ambition
and necessary pragmatism.
How you undertake this stage will differ considerably depending on the
nature of your task. The creation of a relatively simple, single chart to be
slotted into a report probably will not require the same rigour of a formal
production cycle that the development of a vast interactive visualisation to
be used by the public would demand. This is merely an outline of the most
you will need to do – you should edit, adapt and participate the steps to fit
with your context.
There are several discrete steps involved in this production cycle:
Conceiving ideas across the five layers of visualisation design.
Wireframing and storyboarding designs.
Developing prototypes or mock-up versions.
219
Testing.
Refining and completing.
Launching the solution.
Naturally, the specific approach for developing your design solution (from
prototyping through to launching) will vary hugely, depending particularly
on your skills and resources: it might be an Excel chart, or a Tableau
dashboard, an infographic created using Adobe Illustrator, or a web-based
interactive built with the D3.js library. As I have explained in the book’s
introduction, I’m not going to attempt to cover the myriad ways of
implementing a solution; that would be impossible to achieve as each task
and tool would require different instructions.
For the scope of this book, I am focusing on taking you through the first
two steps of this cycle – conceiving ideas and wireframing/storyboarding.
There are parallels here with the distinctions between architecture (design)
and engineering (execution) – I’m effectively chaperoning you through to
the conclusion of your design thinking.
To fulfil this, Part C presents a detailed breakdown of the many design
.
More Related Content
Similar to MA 116 Turn-in Practice Problems 4.2 and 4.4 Pitts .docx
1 Week 2 Homework for MTH 125 Name_______________
1
Week 2 Homework for MTH 125
Name___________________________________ Date: ___July 20, 2021______________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Graph the equation by determining the missing values needed to plot the ordered pairs.
1) y + x = 3; ( 1, ), ( 3, ), ( 2, )
1) _______
A)
B)
C)
D)
2
Find the x- and y-intercepts. Then graph the equation.
2) 10y - 2x = -4
2) _______
A) ( -2, 0);
B) ; (0, -2)
3
C) ( 2, 0);
D) ; (0, 2)
Find the midpoint of the segment with the given endpoints.
4
3) ( 8, 4) and ( 7, 9) 3) _______
A) B) C) D)
Suppose that segment PQ has the given coordinates for one endpoint P and for its midpoint M. Find the coordinates
of the other endpoint Q.
4) P( 5, 5) and M 4) _______
A) Q( 4, 4) B) Q C) Q D) Q
Solve the problem.
5) The graphing calculator screen shows the graph of one of the equations below. Which equation is it?
5) _______
A) y + 3x = 15 B) y - 3x = 15 C) y = 3x + 3 D) y + 3x = 3
Find the slope.
6) m = 6) _______
A) -5 B) 5 C) 12 D) 8
Find the slope of the line through the given pair of points, if possible. Based on the slope, indicate whether the line
through the points rises from left to right, falls from left to right, is horizontal, or is vertical.
7) ( -3, -5) and ( 4, -4) 7) _______
A) - ; falls B) - 7; falls C) 7; rises D) ; rises
Find the slope of the line.
5
8)
8) _______
A) B) C) - D) -
Find the slope of the line and sketch the graph.
9) 2x + 3y = 10
9) _______
A) Slope:
6
B) Slope: -
C) Slope: -
7
D) Slope:
Decide whether the pair of lines is parallel, perpendicular, or neither.
10) 3x - 4y = 12 and 8x + 6y = -9 10) ______
A) Parallel B) Perpendicular C) Neither
Choose the graph that matches the equation.
11) y = 2x + 4 11) ______
A)
B)
C)
8
D)
Find the equation in slope-intercept form of the line satisfying the conditions.
12) m = 2, passes through ( 6, -3) 12) ______
A) y = 2x - 15 B) y = 3x + 16 C) y = 2x - 13 D) y = 2x + 14
Write the equation in slope-intercept form.
13) 17x + 5y = 7 13) ______
A) y = x + B) y = 17x - 7 C) y = - x + D) y = x -
Find the slope and the y-intercept of the line.
14) 7x + 5y = 48 14) ______
A) Slope - ; y-intercept B) Slope ; y-intercept
C) Slope ; y-intercept D) Slope - ; y-intercept
Find an equation of the line that satisfies the conditions. Write the equation in standard form.
9
15) Through ( 5, 4); m = - 15) ______
A) 4x - 9y = 56 B) 4x + 9y = -56 C) 4x + 9y = 56 D) 9x + 4y = -56
...
1 College Algebra Final Examination---FHSU Math & C.S.docx
1
College Algebra
Final Examination---FHSU Math & C.S. Department
Form G Name ____________________________
Multiple Choice:
Mark through (horizontally) the space on the answer card corresponding to the best answer for each
problem.
1. Solve the equation by factoring: 2 9 18 0x x
[A] 6, 3 [B] 6, 3 [C] 6, 3 [D] 6, 3
2. Write the product in the standard form a + bi: (2 6 )(2 9 )i i
[A] 58 6i [B] 50 30i [C] 58 6i [D]
2
54 6 4i i
3. Find the real solutions of the equation 14 21 2 .x x
[A] 5 [B] 3 [C] 4 [D] 5
4. Solve the inequality 3 7 2 4x x . Express your answer using interval notation.
[A] 11, [B] [3, ) [C] 3, [D] ( , 3]
5. Solve the equation 3 3 18.x
[A] 3, 9 [B] 3 [C] 9, 3 [D] no solution
6. Solve the inequality 5 1 5x . Express your answer using interval notation.
[A] 645 5, or , [B]
64
5 5
,
[C] 645 5, [D]
64
5 5
, or ,
7. A bank loaned $68,000, part of it at a rate of 15% per year and the rest at a rate of 5% per year. If the
interest received was $6600, how much was loaned at 15%?
[A] $36, 000 [B] $33, 000 [C] $32, 000 [D] $35, 000
8. Find the distance between the points 1 2(2, 2) and ( 10, 3).PP
[A] 14 [B] 26 [C] 169 [D] 13
9. List the intercepts for the graph of the equation
2
16 0.x y
[A] ( 4, 0), (0,16), (4, 0) [B] (4, 0), (0,16), (0, 16)
[C] (0, 4), (16, 0), (0, 4) [D] ( 4, 0), (0, 16), (4, 0)
2
10. Find the slope-intercept form of the equation of the line that is parallel with the given properties:
( 2, 3); and 9 20y x
[A] 9 15y x [B] 9 20y x [C]
1
20
9
y x [D]
1
20
9
y x
11. Write the standard from of the equation of the circle with radius 5 and center (1, 4) .
[A]
2 2
4 1 25x y [B]
2 2
1 4 5x y
[C]
2 2
4 1 25x y [D]
2 2
1 4 5x y
12. Write a general formula to describe the variation.
The illumination I produced on a surface by a source of light varies directly as the candlepower c of
the source and inversely as the square of the distance d between the source and the surface.
[A]
2
I kcd [B]
2
2
kc
I
d
[C]
2
kc
I
d
[D]
2
kd
I
c
13. For the given functions ( ) 6 3 and ( ) 7 9f x x g x x , determine ( )( ).f g x
[A]
2
( )( ) 4 27f g x x [B]
2
( )( ) 13 33 6f g x x x
[C]
2
( )( ) 42 33 27f g x x x [D]
2
( )( ) 42 12 27f g x x x
14. The graph of a function f is given. For what values of x is
( ) 0f x ?
[A] 15,17.5
[B] 15,17.5, 25
[C] 15
[D] 25, 15,17.5, 25
15. Determine whether the function
3 2
( ) 4 9f x x is even, odd, neither, or ...
1. Write an equation in standard form of the parabola that has th.docx
1.
Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 2x
2
, but with the given point as the vertex (5, 3).
A. f(x) = (2x - 4) + 4
B. f(x) = 2(2x + 8) + 3
C. f(x) = 2(x - 5)
2
+ 3
D. f(x) = 2(x + 3)
2
+ 3
2 of 20
5.0 Points
Find the coordinates of the vertex for the parabola defined by the given quadratic function.
f(x) = 2(x - 3)
2
+ 1
A. (3, 1)
B. (7, 2)
C. (6, 5)
D. (2, 1)
3 of 20
5.0 Points
Find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of the following rational function.
g(x) = x + 3/x(x + 4)
A. Vertical asymptotes: x = 4, x = 0; holes at 3x
B. Vertical asymptotes: x = -8, x = 0; holes at x + 4
C. Vertical asymptotes: x = -4, x = 0; no holes
D. Vertical asymptotes: x = 5, x = 0; holes at x - 3
4 of 20
5.0 Points
"Y varies directly as the n
th
power of x" can be modeled by the equation:
A. y = kx
n
.
B. y = kx/n.
C. y = kx
*n
.
D. y = kn
x
.
5 of 20
5.0 Points
40 times a number added to the negative square of that number can be expressed as:
A.
A(x) = x
2
+ 20x.
B. A(x) = -x + 30x.
C.
A(x) = -x
2
- 60x.
D.
A(x) = -x
2
+ 40x.
6 of 20
5.0 Points
The graph of f(x) = -x
3
__________ to the left and __________ to the right.
A. rises; falls
B. falls; falls
C. falls; rises
D. falls; falls
Solve the following formula for the specified variable:
V = 1/3 lwh for h
7 of 20
Write an equation that expresses each relationship. Then solve the equation for y.
x varies jointly as y and z
A. x = kz; y = x/k
B. x = kyz; y = x/kz
C. x = kzy; y = x/z
D. x = ky/z; y = x/zk
8 of 20
8 times a number subtracted from the squared of that number can be expressed as:
A. P(x) = x + 7x.
B.P(x) = x
2
- 8x.
C. P(x) = x - x.
P(x) = x
2
+ 10x.
9of 20
Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.
f(x) = x
4
- 9x
2
A. x = 0, x = 3, x = -3; f(x) crosses the x-axis at -3 and 3; f(x) touches the x-axis at 0.
B. x = 1, x = 2, x = 3; f(x) crosses the x-axis at 2 and 3; f(x) crosses the x-axis at 0.
C. x = 0, x = -3, x = 5; f(x) touches the x-axis at -3 and 5; f(x) touches the x-axis at 0.
D. x = 1, x = 2, x = -4; f(x) crosses the x-axis at 2 and -4; f(x) touches the x-axis at 0.
10 of 20
Find the domain of the following rational function.
f(x) = x + 7/x
2
+ 49
A. All real numbers < 69
B. All real numbers > 210
C. All real numbers ≤ 77
D. All real numbers
11 of 20
Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 3x
2
or g(x) = -3x
2
, but with the given maximum or minimum.
Minimum = 0 at x = 11
A. f(x) = 6(x - 9)
B. f(x) = 3(x - 11)
2
C. f(x) = 4(x + 10)
D. f(x) = 3(x
2
- 15)
2
12 of 20
Solve the following polynomial inequality.
3x
2
+ 10x - 8 ≤ 0
A. [6, 1/3]
B. [-4, 2/3]
C. [-9, 4/5]
D. [8, 2/7]
13 of 20
Find the coordinate.
Goldie chapter 4 function
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Algebraically, a composite function f∘g(x) is defined as applying the inner function f first to the input x, and then applying the outer function g to the output of f. The domain of the inner function must be contained within the range of the outer function. The order of
1988 FRQs AP Calculus
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1988 FRQ
This document contains 6 multi-part calculus problems involving functions, derivatives, integrals, areas, volumes and series. The problems cover topics like finding derivatives and integrals of functions, analyzing graphs of functions, finding critical points and intervals of increase/decrease, calculating areas and volumes of revolved regions, and determining convergence of series.
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This document contains instructions for solving calculus problems and presenting solutions clearly. It provides 17 multi-part problems testing various calculus concepts. Responses must show all work and be supported analytically, graphically, numerically, and/or verbally. Approximations must be stated to three decimal places or in scientific notation. Graphs must be complete sketches with labeled axes, scales, intercepts, asymptotes and functions.
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A.B. .docx
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Math 107 Final ExaminationSummer, 20151
Math 107 College AlgebraName______________________________
Final Examination: Summer, 2015Instructor __________________________
Answer Sheet
Instructions:
This is an open-book exam. You may refer to your text and other course materials as you work on the exam, and you may use a calculator.
Record your answers and work in this document.
There are 30 problems.
Problems #1-12 are multiple choice. Record your choice for each problem.
Problems #13-21 are short answer. Record your answer for each problem.
Problems #22-30 are short answer with work required. When requested, show all work and write all answers in the spaces allotted on the following pages. You may type your work using plain-text formatting or an equation editor, or you may hand-write your work and scan it. In either case, show work neatly and correctly, following standard mathematical conventions. Each step should follow clearly and completely from the previous step. If necessary, you may attach extra pages.
.
Name _____________________Date___________________
MULTIPLE CHOICE. Record your answer choices.
1.7.
2.8.
3.9.
4.10.
5.11.
6.12.
SHORT ANSWER. Record your answers below.
13.
14.
15.
16.
17.
18.
19. (a)
(b)
(c)
20. (a)
(b)
(c)
(d)
21. (a)
(b)
(c)
(d)
SHORT ANSWER with Work Shown. Record your answers and work.
Problem Number
Solution
22
Answers:
(a)
(b)
Work/for part (a) and explanation for part (b):
23
Answers:
(a)
(b)
(c)
Work for part (a):
24
Answer:
Work:
25
Answer:
Work:
26
Answers:
(a)
(b)
Work for part (a) and for part (b):
27
Answer:
Work:
28
Answer:
Work:
29
Answers:
(a)
(b)
Work for (b):
30
Answer:
Work:
College Algebra MATH 107 Summer, 2015, V3.1
Page 1 of 11
MATH 107 FINAL EXAMINATION
This is an open-book exam. You may refer to your text and other course materials as you work
on the exam, and you may use a calculator. You must complete the exam individually.
Neither collaboration nor consultation with others is allowed.
Record your answers and work on the separate answer sheet provided.
There are 30 problems.
Problems #1–12 are Multiple Choice.
Problems #13–21 are Short Answer. (Work not required to be shown)
Problems #22–30 are Short Answer with work required to be shown.
MULTIPLE CHOICE
1. Determine the domain and range of the piecewise functi.
MA 141 Turn in Homework Quiz 4.2 Pitts Name ___.docx
MA 141 Turn in Homework Quiz 4.2
Pitts Name ____________________________
1. (#34) Let f(x) = 3x4 – 6x3 + x – 8. Determine where the function is concave upward and where it is concave
downward. Show your calculus. Show your sign graph.
In interval notation: concave up ______________________ concave down _______________________
2. (#38) Let ( ) 2g x x . Determine where the function is concave upward and where it is concave downward.
Show your calculus.
3. Let
2
( )
3
x
f x
x
. Determine where the function is concave upward and where it is concave downward. Show
your calculus. Show your sign graph.
In interval notation: concave up ______________________ concave down _______________________
4. Consider the function
4 3
( ) 4 5f x x x . Show your calculus.
a.) Using the first derivative, find all critical values for potential relative extrema.
b.) Use the second derivative test to find all relative maximum and minimum points.
c.) Determine if there are any points of inflection. Show your calculus! Show your sign graph.
5. (# 60) Determine the intervals where the function is concave up or down, and also determine if there are any
points of inflection for the function
3
( ) 2f x
x
.
6. (# 72) Using the second derivative test, determine if there are any relative extrema for the function
2 2
( )g x x
x
.
7. (#74) Consider function
2
1
( )
1
g x
x
. Find any relative extrema. Use the first or second derivative test to
justify whether it is a maximum or a minimum. You do not need to simplify the second derivative.
8. (#78) Sketch the graph of a function (2) 2f , (0) 1f , '(2) 0f , '( ) 0f x for x < 2, '( ) 0f x for
2x , ''( ) 0f x for x < 2, and "( ) 0f x for x > 2.
9. In a study conducted in 2003, it was projected that worldwide PC shipments (in millions) through 2005 will
be given by
3 2
( ) 0.75 1.5 8.25 133 (0 t 4)n t t t t where t is measured in years, with t = 0
corresponding to 2001. Make sure to show sign graphs were necessary. Determine the intervals where N is
concave upward and where it is concave downward. Also find an inflection point(s) and interpret the results.
MA 141 Homework 4.1
Pitts SHOW YOUR WORK! Name _______________________
1. (See # 20) Find the interval(s) where the function
3
( ) 3 4f x x x is increasing and the interval(s)
where it is decreasing. Show your calculus to justify your answer. Show your sign graph clearly
In interval notation: increasing over ______________________ decreasing over ______________________
2. (See # 28) Find the interval(s) where the function
2
2
( )
1
t
g t
t
is increasing and the interval(s) where it
is decreasing. Show your calculus to justify your answer. Show your sign graph clea ...
Pre calculus chapter-4
This document discusses solving quadratic equations graphically by relating them to their corresponding quadratic functions. It explains that the roots of a quadratic equation are the same as the zeros of the corresponding quadratic function, which are the x-intercepts of the graph. It provides examples of solving quadratic equations with one real root, two distinct real roots, and no real roots. Methods for solving graphically include paper-and-pencil, spreadsheets, and graphing calculators. The key ideas are that the number of real roots corresponds to the number of real x-intercepts on the graph.
Application of derivative
Additional Applications of the Derivative related to engineering maths
this presentation is only for the knowledge...............
1_Representation_of_Functions.pptx
This document covers representing functions including objectives like defining functions and related terms, determining if a relation is a function, defining piecewise functions, and representing real-life situations
1 representation of_functions
This document covers representing functions including objectives like defining functions and related terms, determining if a relation is a function, defining piecewise functions, and representing real-life situations
EVALUATING INTEGRALS.Evaluate the integral shown below. (H.docx
EVALUATING INTEGRALS.
Evaluate the integral shown below. (Hint: Try the substitution u = (7x2 + 3).)
1)
x dx
(7x2 + 3)5
Evaluate the integral shown below. (Hint: Apply a property of logarithms first.)
2)
ln x6
x
dx
1
Use the Fundamental Theorem of Calculus to find the derivative shown below.
3)
d
dx
x5
0
sin t dt
For the function shown below, sketch a graph of the function, and then find the SMALLEST possible value and the
LARGEST possible value for a Riemann sum of the function on the given interval as instructed.
4) f(x) = x2 ; between x = 3 and x = 7 with four rectangles of equal width.
^
CHARACTERISTICS and BEHAVIOR OF FUNCTIONS.
Use l'Hopital's rule to find the limit below.
5) lim
x
5x + 9
6x2 + 3x - 9
^
Use l'Hopital's rule to find the limit below. (Hint: The indeterminate form is f(x)g(x).)
6) lim
x
1 + 2
x3
x
2
Solve the following problem.
7) The 9 ft wall shown here stands 30 feet from the building. Find the length of the shortest straight beam that will
reach to the side of the building from the ground outside the wall.
9' wall
30'
Hint: Let "h" be the height on the building where the ladder touches; let "x" be the distance on the ground
between the wall and the foot of the ladder. Use similar triangles and the Pythagorean Theorem to write the
length of the beam "L" as a function of "x". Also note that a radical function is minimized when it radicand is
minimized.
For the function shown below, identify its local and absolute extreme values (if any), saying where they occur.
8) f(x) = -x3- 9x2 - 24x + 3
3
Find a value for "c" that satisfies the equation f(b) - f(a)
b - a
= f (c) in the conclusion of the Mean Value Theorem for the
function and interval shown below.
9) f(x) = x +
75
x
, on the interval [3, 25]
DERIVATIVES.
Find the equation of the tangent line to the curve whose function is shown below at the given point.
10) x5y5 = 32, tangent at (2, 1)
Use implicit differentiation to find dy/dx.
11) xy + x + y = x2y2
Given y = f(u) and u = g(x), find dy/dx = f (g(x))g (x).
12) y = u(u - 1), u = x2 + x
4
Find y .
13) y = (4x - 5)(4x3 - x2 + 1)
Find the derivative of the function "y" shown below.
14) y =
x2 + 8x + 3
x
Solve the problem below.
15) One airplane is approaching an airport from the north at 163 km/hr. A second airplane approaches from the east
at 261 km/hr. Find the rate at which the distance between the planes changes when the southbound plane is 31
km away from the airport and the westbound plane is 18 km from the airport.
FUNCTIONS, LIMITS and CONTINUITY.
Find the intervals on which the function shown below is continuous.
16) y =
x + 2
x2 - 8x + 7
5
A function f(x), a point c, the limit of f(x) as x approaches c, and a positive number is given. Find a number > 0 such
that for all x, 0 < x - c < f(x) - L < .
17) f(x) = 10x - 1, L = 29, c = 3, and = 0.01
Find all points "x" where the function shown below is discontinuous.
18)
Solve the "composite function ...
Pre-Calculus Midterm Exam 1 Score ______ ____.docx
Pre-Calculus Midterm Exam
1
Score: ______ / ______
Name: ____________________________
Student Number: ___________________
Short Answer: Type your answer below each question. Show your work.
1 Verify the identity. Show your work.
cot θ ∙ sec θ = csc θ
2 A gas company has the following rate schedule for natural gas usage in single-family residences:
Monthly service charge $8.80
Per therm service charge
1st 25 therms $0.6686/therm
Over 25 therms $0.85870/therm
What is the charge for using 25 therms in one month? Show your work.
What is the charge for using 45 therms in one month? Show your work.
Construct a function that gives the monthly charge C for x therms of gas.
Pre-Calculus Midterm Exam
2
3 The wind chill factor represents the equivalent air temperature at a standard wind speed that would
produce the same heat loss as the given temperature and wind speed. One formula for computing
the equivalent temperature is
W(t) = {
𝑡
33 −
(10.45+10√𝑣−𝑣)(33−𝑡)
2204
33 − 1.5958(33 − 𝑡)
if 0 ≤ v < 1.79
if 1.79 ≤ v < 20
if v ≥ 20
where v represents the wind speed (in meters per second) and t represents the air temperature .
Compute the wind chill for an air temperature of 15°C and a wind speed of 12 meters per second.
(Round the answer to one decimal place.) Show your work.
4 Complete the following:
(a) Use the Leading Coefficient Test to determine the graph's end behavior.
(b) Find the x-intercepts. State whether the graph crosses the x-axis or touches the x-axis
and turns around at each intercept. Show your work.
(c) Find the y-intercept. Show your work.
f(x) = x2(x + 2)
(a).
(b).
(c).
Pre-Calculus Midterm Exam
3
5 For the data set shown by the table,
a. Create a scatter plot for the data. (You do not need to submit the scatter plot)
b. Use the scatter plot to determine whether an exponential function or a logarithmic function is
the best choice for modeling the data.
Number of Homes Built in a Town by Year
6 Verify the identity. Show your work.
(1 + tan2u)(1 - sin2u) = 1
Pre-Calculus Midterm Exam
4
7 Verify the identity. Show your work.
cot2x + csc2x = 2csc2x - 1
8 Verify the identity. Show your work.
1 + sec2xsin2x = sec2x
Pre-Calculus Midterm Exam
5
9 Verify the identity. Show your work.
cos(α - β) - cos(α + β) = 2 sin α sin β
10 The following data represents the normal monthly precipitation for a certain city.
Draw a scatter diagram of the data for one period. (You
Lesson 5: Functions and surfaces
A function of two variables is defined similar to a function of one variable. It has a domain (in the plane) and a range. The graph of such a function is a surface in space and we try to sketch some.
Write solution for these problems -Is targeting only mommy blo.docx
Write solution for these problems
-Is targeting only mommy bloggers is a good idea and why?
-how would J&J guarantee that these bloggers won't give a bad feedback?
-if J&J announced about their product only through social media, then how would it reach the other people who don't use social media?
-do you see any value in offering this type of incentive for the users? or, is all the benefit for the company only?
MATH 115 Precalculus Fall, 2018, V1.4
Page 1 of 7
MATH 115 FINAL EXAMINATION
This is an open-book exam. You may refer to your text and other course materials as you work
on the exam, and you may use a calculator. You must complete the exam individually.
Neither collaboration nor consultation with others is allowed.
Record your answers and work on the separate answer sheet provided.
There are 28 problems.
Problems #1–6 are Multiple Choice.
Problems #7–17 are Short Answer. (Work not required to be shown)
Problems #18–28 are Short Answer with work required to be shown.
MULTIPLE CHOICE
1. Solve | 7 – 5x | 8 and write interval notation for the solution set. 1. _______
A. (−∞, −
1
5
] ∪ [3, ∞)
B. (−∞, 3] ∪ [−
1
5
, ∞)
C. [−
1
5
, ∞)
D. [−
1
5
, 3]
2. Which of the following polynomials has a graph which exhibits the end behavior of
upward to the left and upward to the right? 2. ______
A. f (x) = x3 – 3x2 – x
B. f (x) = 3x6 + x2 – x
C. f (x) = –7x4 – x3 – 5
D. f (x) = –6x5 + x3 + 8
3. Write as an equivalent expression: 9 log x – log (y + 3) + log 1 3. _______
A.
9
log
log ( 3)
x
y +
B. ( )log 9 2x y− −
C.
9 1
log
3
x
y
+
+
D.
9
log
3
x
y
+
vvvv
MATH 115 Precalculus Fall, 2018, V1.4
Page 2 of 7
4. Determine the interval(s) on which the function is decreasing. 4. ______
A. (–, –3.5) (0, 3.5)
B. (– 5.3, 5.3)
C. (– 3.5, 3.5)
D. (– 2, 2)
5. Which of the functions corresponds to the graph? 5. ______
A. ( ) 1xf x e−= +
B. ( ) 2xf x e−= +
C. ( ) 2xf x e−=
D. ( ) 2 xf x e−=
MATH 115 Precalculus Fall, 2018, V1.4
Page 3 of 7
6. Which of the functions corresponds to the graph? 6. ______
A. f (x) = 3 – sin x
B. f (x) = sin x + 3
C. f (x) = 2 cos x + 1
D. f (x) = cos(2x) + 2
SHORT ANSWER:
7. Points (–9, 2) and (–5, 8) are endpoints of the diameter of a circle.
(a) What is the exact length of the diameter? (Simplify as much as possible) Answer: ________
(b) What is the center of the circle? Answer: ____________
(c) What is the equation of the circle? Answer: ___________________________
8. Find the value of the logarithm: log8 (
1
64
). Answer: ____________
9. A salesperso.
Mid module review
The document provides a mid-module review for algebra that includes 14 problems. The problems cover topics such as writing expressions to represent word problems, expanding expressions using the distributive property, finding equivalent expressions, and modeling algebraic expressions visually. Students are expected to show their work, use proper notation, and provide unit labels where appropriate to receive full credit.
Similar to MA 116 Turn-in Practice Problems 4.2 and 4.4 Pitts .docx (20)
1 College Algebra Final Examination---FHSU Math & C.S.docx
1 College Algebra Final Examination---FHSU Math & C.S.docx
1. Write an equation in standard form of the parabola that has th.docx
1. Write an equation in standard form of the parabola that has th.docx
88AB6 WorkBook Integration Example AP Calculus Exam
88AB6 WorkBook Integration Example AP Calculus Exam
MA 141 Turn in Homework Quiz 4.2 Pitts Name ___.docx
MA 141 Turn in Homework Quiz 4.2 Pitts Name ___.docx
EVALUATING INTEGRALS.Evaluate the integral shown below. (H.docx
EVALUATING INTEGRALS.Evaluate the integral shown below. (H.docx
Pre-Calculus Midterm Exam 1 Score ______ ____.docx
Pre-Calculus Midterm Exam 1 Score ______ ____.docx
Write solution for these problems -Is targeting only mommy blo.docx
Write solution for these problems -Is targeting only mommy blo.docx
More from smile790243
PART B Please response to these two original posts below. Wh.docx
PART B
Please response to these two original posts below. When
responding to these posts, please either expand the
thought, add additional insights, or respectfully disagree
and explain why. Remember that we are after reasons
and arguments, and not simply the statement of
opinions.
Original Post 1
Are human lives intrinsically valuable? If so, in virtue of what? (Is
it our uniqueness, perhaps, or our autonomy, or something else?)
To begin, I would like to remind us that being intrinsically valuable
means having values for just being us and nothing else. I believe
that human lives are intrinsically valuable in virtue of our
uniqueness. As a bio nerd, I would like to state the fact that there
are a lot of crossover events during meiosis, which create trillions
of different DNA combinations. Hence, from a biological
standpoint, without considering other aspects, being you is
already valuable because you are that one sperm that won the
race and got fertilized. On a larger scale, there are hardly two
people whose look and behaviors are the same in the same
family, unless they are identical twins. However, identical twins
still act differently and have differences (such as fingerprints).
Since we are raised in different families, we are taught different
things and have different cultures. In general, we all have
different genetic information, appearances, personalities, senses
of humor, ambitions, talents, interests and life experiences. These
characteristics make up our “unique individual value” and make
us so unique and irreplaceable.
I would also love to discuss how our diversities enrich and
contribute to society, but that would be a talk about our extrinsic
values.
Original Post 2
Are human lives intrinsically valuable? If so, in virtue of what? (Is
it our uniqueness, perhaps, or our autonomy, or something else?)
I believe that human lives are intrinsically valuable due to a
number of reasons. Firstly, human lives aren’t replaceable. You
can’t replace a human being with another just like you can
replace a broken laptop with brand new one. Part of the reason
why we tend to think this way is that we were nurtured with the
notion that there is, indeed, a special value to human life. This
could be in virtue of our uniqueness-- the fact that we are
sentient and capable of complex thoughts and emotions
separates us from any other species on this planet. From a
scientific standpoint, this is also one of the reasons as to why
humans became the dominant species in today’s age.
Moreover, human lives aren’t disposable. I think this is largely due
to us humans having the ability to empathize with others. We
understand that it’s morally inappropriate to take the life of
another individual even if they’re complete strangers because
they’re another human being like us who has their own thoughts,
values, memories, and stories. In a way, we have a strong
emotional connection to our own species. As .
Part C Developing Your Design SolutionThe Production Cycle.docx
Part C Developing Your Design
Solution
The Production Cycle
Within the four stages of the design workflow there are two distinct parts.
The first three stages, as presented in Part B of this book, were described
as ‘The Hidden Thinking’ stages, as they are concerned with undertaking
the crucial behind-the-scenes preparatory work. You may have completed
them in terms of working through the book’s contents, but in visualisation
projects they will continue to command your attention, even if that is
reduced to a background concern.
You have now reached the second distinct part of the workflow which
involves developing your design solution. This stage follows a production
cycle, commencing with rationalising design ideas and moving through to
the development of a final solution.
The term cycle is appropriate to describe this stage as there are many loops
of iteration as you evolve rapidly between conceptual, practical and
technical thinking. The inevitability of this iterative cycle is, in large part,
again due to the nature of this pursuit being more about optimisation rather
than an expectation of achieving that elusive notion of perfection. Trade-
offs, compromises, and restrictions are omnipresent as you juggle ambition
and necessary pragmatism.
How you undertake this stage will differ considerably depending on the
nature of your task. The creation of a relatively simple, single chart to be
slotted into a report probably will not require the same rigour of a formal
production cycle that the development of a vast interactive visualisation to
be used by the public would demand. This is merely an outline of the most
you will need to do – you should edit, adapt and participate the steps to fit
with your context.
There are several discrete steps involved in this production cycle:
Conceiving ideas across the five layers of visualisation design.
Wireframing and storyboarding designs.
Developing prototypes or mock-up versions.
219
Testing.
Refining and completing.
Launching the solution.
Naturally, the specific approach for developing your design solution (from
prototyping through to launching) will vary hugely, depending particularly
on your skills and resources: it might be an Excel chart, or a Tableau
dashboard, an infographic created using Adobe Illustrator, or a web-based
interactive built with the D3.js library. As I have explained in the book’s
introduction, I’m not going to attempt to cover the myriad ways of
implementing a solution; that would be impossible to achieve as each task
and tool would require different instructions.
For the scope of this book, I am focusing on taking you through the first
two steps of this cycle – conceiving ideas and wireframing/storyboarding.
There are parallels here with the distinctions between architecture (design)
and engineering (execution) – I’m effectively chaperoning you through to
the conclusion of your design thinking.
To fulfil this, Part C presents a detailed breakdown of the many design
.
PART A You will create a media piece based around the theme of a.docx
PART A:
You will create a media piece based around the theme of “alternative facts.
Fake News:
Create a
series of 3
short, “fake news” articles or news videos. They should follow a specific theme. Make sure to have a clear understanding of WHY your fake news is being created (fake news is used by people, groups, companies, etc to convince an unsuspecting audience of something. It’s supposed to seem real, but the motivation behind it is to deceive. As part of this option, consider what your motivations are for your deception).
Part A: should be around 750 words for written tasks (or 250 for each 3 part task)
PART B:
The focus for this assignment is to demonstrate a
clear understanding of media conventions
, as well as
purpose
and
audience
. Therefore, along with your media product, you’ll also be required to submit a short
reflection
detailing why you created your product and for whom it was intended. You must discuss and analyze the elements within your media product (including why & how you used the persuasive techniques of ethos, logos and pathos) as well as the other elements of media you used and why.
.
Part 4. Implications to Nursing Practice & Implication to Patien.docx
Part 4. Implications to Nursing Practice & Implication to Patient Outcomes
Provide a paragraph summary addressing the topics implications to nursing practice and patient outcomes. This section is NOT another review of the literature or introduction of new topics related to the PICOT question.
You may find if helpful to begin each topic with -
Nurses need to know …
Important patient outcomes include …
Example
– please note this is an older previous students work and so some references are older than 5 years.
Be sure to provide the PICOT question to begin this post.
PICOT Question:
P=Patient Population
I=Intervention
C=Comparison
O=Outcome
T=Time (duration):
In patients in the hospital, (P)
how does frequently provided patient hand washing (I)
compared with patient initiated hand washing (C)
affect hospital acquired infection (O)
within the hospital stay (T)
Implications to Nursing Practice & Patient Outcomes
Nurses need to know that they play a significant role in the reduction of hospital acquired infection by ensuring by health care workers and patients wash hands since nurses have the most interactions with patients. Implementing hand hygiene protocol with patients can enhance awareness and decrease healthcare associated infection (HAI). Both nurses and patients need to know that HAI is associated with increased morbidity and mortality as well cost of treatment and length of hospital stay. Nurses and patients also need to know that most HAI is preventable. Gujral (2015) notes that proper hand hygiene is the single most important, simplest, and least expensive means of reducing prevalence of HAI and the spread of antimicrobial resistance. Nurse and patient hand washing plays a vital role in decreasing healthcare costs and infections in all settings.
References
Gujral, H. (2015.) Survey shows importance of hand washing for infection prevention. American Nurse Today, 10 (10), 20. Retrieved from hEp://www.nursingworld.org/AmericanNurseToday
.
PART AHepatitis C is a chronic liver infection that can be e.docx
PART A
Hepatitis C is a chronic liver infection that can be either silent (with no noticeable symptoms) or debilitating. Either way, 80% of infected persons experience continuing liver destruction. Chronic hepatitis C infection is the leading cause of liver transplants in the United States. The virus that causes it is blood borne, and therefore patients who undergo frequent procedures involving transfer of blood are particularly susceptible to infection. Kidney dialysis patients belong to this group. In 2008, a for-profit hemodialysis facility in New York was shut down after nine of its patients were confirmed as having become infected with hepatitis C while undergoing hemodialysis treatments there between 2001 and 2008.
When the investigation was conducted in 2008, investigators found that 20 of the facility’s 162 patients had been documented with hepatitis C infection at the time they began their association with the clinic. All the current patients were then offered hepatitis C testing, to determine how many had acquired hepatitis C during the time they were receiving treatment at the clinic. They were considered positive if enzyme-linked immunosorbent assay (ELISA) tests showed the presence of antibodies to the hepatitis C virus.
Health officials did not test the workers at the hemodialysis facility for hepatitis C because they did not view them as likely sources of the nine new infections. Why not?
Why do you think patients were tested for antibody to the virus instead of for the presence of the virus itself?
Ref.: Cowan, M. K. (2014) (4th Ed.). Microbiology: A Systems Approach, McGraw Hill
PART B
Summary:
Directions for the students: There are 4 essay questions. Please be sure to complete all of them with thorough substantive responses. Current APA Citations are required for all responses.
1. Precisely what is microbial death?
2. Why does a population of microbes not die instantaneously when exposed to an antimicrobial agent?
3. Explain what is wrong with this statement: “Prior to vaccination, the patient’s skin was sterilized with alcohol.” What would be a more correct wording?
4. Conduct additional research on the use of triclosan and other chemical agents in antimicrobial products today. Develop an opinion on whether this process should continue, providing evidence and citations to support your stance.
.
Part A post your answer to the following question1. How m.docx
Potential negative reactions from others to an adolescent questioning their sexual identity or gender role could negatively impact their social environment, behavior, and self-esteem. As social workers, we can play a role in creating a supportive environment for these adolescents by educating families and communities, advocating for inclusive policies, and providing counseling and resources to help adolescents accept themselves and develop coping strategies.
PART BPlease response to these two original posts below..docx
PART B
Please response to these two original posts below. When responding to
these posts, please either expand the thought, add additional insights, or
respectfully disagree and explain why. Remember that we are after reasons
and arguments, and not simply the statement of opinions.
Original Post 1
"What is moral relativism? Why might people be attracted to it? Is
it plausible?"
First of all, moral relativism is the view that moral truths are
subjective and depend on each individual's standpoints. Based
on this, everyone's moral view is legitimate. This can be attracted
because it sounds liberating and there is no need to argue for a
particular position. Moral relativism seems convincing in some
cases. For example, some people are okay with giving money to
homeless people, thinking that it's good to provide for the people
in need. Some people, on the other hand, claim that they can
work to satisfy their own needs. Moral relativism works well in
these cases because they all seem legitimate. However, there are
cases that moral relativism does not seem reasonable. For
example, child sacrifice in some cultures seems cruel and
uncivilized to most people. Hence, moral relativism is not
absolutely true.
Original Post 2
“Is your death bad for you, specifically, or only (at most) for others? Why
might someone claim that it isn’t bad for you?”
I'd start off by acknowledging what the two ancient philosophers,
Lucretius and Epicurus, outlined about death. They made the
point that death isn't necessarily bad for you since no suffering
takes place and that you yourself don't realize your own death. In
this way, one could make the claim that death isn't intrinsically
bad for you.
Another perspective I wanted to add was the influence of death
(both on you and others around you). Specifically, the event of
death itself may not be bad for you, but the idea of impending
death could impact one's life. Some may live freely, totally care-
free, accepting of death and enjoy life in the moment. Others may
be frightened by the idea of death that they live in constant fear
and hence death causing their mental health to take its toll. In
this way, I'd argue that death could, in fact, be bad for you. One
common reason for being afraid of death is the fear of being
forgotten. Not to mention the death of an individual certainly
affects others; death doesn't affect one's life but also all that is
connected to it. Focusing back to the point, it's clear that the
very idea of death directly affects the concerned individual. The
fact that those who live in fear of death are looking for legacies
and footprints to leave after they leave this world is telling of how
death could be arguably bad for you before it even happens.
PART A
Pick one or more questions below and write a substantive post
with >100 words. Please try to provide evidence(s) to support
your idea(s).
Questions:
• Do we have a duty to work out whe.
Part A (50 Points)Various men and women throughout history .docx
Part A (50 Points):
Various men and women throughout history have made important contributions to the development of statistical science. Select any one (1) individual from the list below and write a 2 page summary of their influence on statistics. Be specific in detail to explain the concepts they developed and how this advanced our understanding and application of statistics.
Florence Nightingale
Francis Galton
Thomas Bayes
Part B (50 Points):
Select any one statistical concept you learned in this course and explain how it can be applied to our understanding of the Covid-19 pandemic (2 pages). You should use a specific example and include at least one diagram to illustrate your answer.
Please note: Your work must be original and not copied directly from other sources. No citations are needed. Be sure to submit this assignment in Blackboard on the due date specified.
.
Part A1. K2. D3. N4. C5. A6. O7. F8. Q9. H10..docx
This document discusses urinary tract infections (UTIs). It begins with a matching exercise identifying structures of the urinary system. The second part addresses UTIs in more detail. It defines a UTI, discusses the microorganisms that cause UTIs and where they enter the body. It also explains common signs and symptoms of UTIs, as well as diagnostic tests and treatments. The document concludes by noting that UTIs are more common in women and describes some ways women can reduce their risk.
Part A Develop an original age-appropriate activity for your .docx
The document describes developing two original age-appropriate activities for preschoolers. The first activity uses either Froebel's cube gift, parquetry gift, or Lincoln Logs and identifies two skills it develops. The second activity promotes the same skills but is based on the Montessori method. The summary describes each activity and notes two key differences between them.
Part 3 Social Situations2. Identify multicultural challenges th.docx
Part 3: Social Situations
2. Identify multicultural challenges that your chosen individual may face as a recent
refugee.
• What are some of the issues that can arise for someone who has recently
immigrated to a new country?
• Explain how these multicultural challenges could impact your chosen individual’s
four areas of development?
3. Suggest plans of action or resources that you feel should be provided to this family to
assist them in proper develop
Part 3: Social Situations
• Proposal paper which identifies multicultural challenges that your chosen individual may face as a recent refugee.
• Suggested plan of action and/or resources which should be implemented to address the multicultural challenges.
• 2-3 Pages in length
• APA Formatting
• Submission will be checked for plagiaris
.
Part A (1000 words) Annotated Bibliography - Create an annota.docx
Part A
(1000 words): Annotated Bibliography - Create an annotated bibliography that focuses on ONE particular aspect of current Software Engineering that face a world with different cultural standards. At least seven (7) peer-reviewed articles must be used for this exercise.
Part B
(3000 words):
Research Report
- Write a report of the analysis and synthesis using the
(Part A
) foundational
Annotated Bibliography
.
Part C (500 words): Why is it important to try to minimize complexity in a software system.
Part D (500 words): What are the advantages and disadvantages to companies that are developing software products that use cloud servers to support their development process?
Part E (500 words): Explain why each microservice should maintain its own data. Explain how data in service replicas can be kept consistent?
.
Part 6 Disseminating Results Create a 5-minute, 5- to 6-sli.docx
Part 6: Disseminating Results
Create a 5-minute, 5- to 6-slide narrated PowerPoint presentation of your Evidence-Based Project:
· Be sure to incorporate any feedback or changes from your presentation submission in Module 5.
· Explain how you would disseminate the results of your project to an audience. Provide a rationale for why you selected this dissemination strategy.
Points Range: 81 (81%) - 90 (90%)
The narrated presentation accurately and completely summarizes the evidence-based project. The narrated presentation is professional in nature and thoroughly addresses all components of the evidence-based project.
The narrated presentation accurately and clearly explains in detail how to disseminate the results of the project to an audience, citing specific and relevant examples.
The narrated presentation accurately and clearly provides a justification that details the selection of this dissemination strategy that is fully supported by specific and relevant examples.
The narrated presentation provides a complete, detailed, and specific synthesis of two outside resources related to the dissemination strategy explained. The narrated presentation fully integrates at least two outside resources and two or three course-specific resources that fully support the presentation.
Written Expression and Formatting—Paragraph Development and Organization:
Paragraphs make clear points that support well-developed ideas, flow logically, and demonstrate continuity of ideas. Sentences are carefully focused—neither long and rambling nor short and lacking substance. A clear and comprehensive purpose statement and introduction is provided which delineates all required criteria.
Points Range: 5 (5%) - 5 (5%)
Paragraphs and sentences follow writing standards for flow, continuity, and clarity.
A clear and comprehensive purpose statement, introduction, and conclusion is provided which delineates all required criteria.
Written Expression and Formatting—English Writing Standards:
Correct grammar, mechanics, and proper punctuation.
Points Range: 5 (5%) - 5 (5%)
Uses correct grammar, spelling, and punctuation with no errors.
Evidenced Based Change
Leslie Hill
Walden University
Introduction/PurposeChange is inevitable.Health care organizations need change to improve.There are challenges that need to be addressed(Baraka-Johnson et al. 2019).Challenges should be addressed using evidence-based research.These changes enhance professionalism therefore improving quality of care and quality of life.The purpose of this paper is to identify an existing problem in health care and suggest a change idea that would be effective in addressing the problem. The paper also articulates risks associated with the change process, how to distribute the change information and how to implement change successfully.
Organizational CultureThe Organization is a hospice facilityOffers end of life care for pain and symptom managementThe health care providers cu.
Part 3 Social Situations • Proposal paper which identifies multicul.docx
Part 3: Social Situations • Proposal paper which identifies multicultural challenges that your chosen individual may face as a recent refugee. • Suggested plan of action and/or resources which should be implemented to address the multicultural challenges. • 2-3 Pages in length • APA Formatting • Submission will be checked for plagiarism
Part 3: Social Situations 2. Identify multicultural challenges that your chosen individual may face as a recent refugee. • What are some of the issues that can arise for someone who has recently immigrated to a new country? • Explain how these multicultural challenges could impact your chosen individual’s four areas of development? 3. Suggest plans of action or resources that you feel should be provided to this family to assist them in proper development.
.
Part 3 Social Situations 2. Identify multicultural challenges that .docx
Part 3: Social Situations 2. Identify multicultural challenges that your chosen individual may face as a recent refugee. • What are some of the issues that can arise for someone who has recently immigrated to a new country? • Explain how these multicultural challenges could impact your chosen individual’s four areas of development? 3. Suggest plans of action or resources that you feel should be provided to this family to assist them in proper development.
Part 3: Social Situations • Proposal paper which identifies multicultural challenges that your chosen individual may face as a recent refugee. • Suggested plan of action and/or resources which should be implemented to address the multicultural challenges. • 2-3 Pages in length • APA Formatting • Submission will be checked for plagiarism
.
Part 2The client is a 32-year-old Hispanic American male who c.docx
Part 2
The client is a 32-year-old Hispanic American male who came to the United States when he was in high school with his father. His mother died back in Mexico when he was in school. He presents today to the PMHNPs office for an initial appointment for complaints of depression. The client was referred by his PCP after “routine” medical work-up to rule out an organic basis for his depression. He has no other health issues except for some occasional back pain and “stiff” shoulders which he attributes to his current work as a laborer in a warehouse. the “Montgomery- Asberg Depression Rating Scale (MADRS)” and obtained a score of 51 (indicating severe depression). reports that he always felt like an outsider as he was “teased” a lot for being “black” in high school. States that he had few friends, and basically kept to himself. He also reports a remarkably diminished interest in engaging in usual activities, states that he has gained 15 pounds in the last 2 months. He is also troubled with insomnia which began about 6 months ago, but have been progressively getting worse. He does report poor concentration which he reports is getting in “trouble” at work.
· Decision #1: start Zoloft 25mg orally daily
· Which decision did you select?
· Why did you select this decision? Support your response with evidence and references to the Learning Resources.
· What were you hoping to achieve by making this decision? Support your response with evidence and references to the Learning Resources.
· Explain any difference between what you expected to achieve with Decision #1 and the results of the decision. Why were they different?
· Decision #2: Client returns to clinic in four weeks, reports a 25% decrease in symptoms but concerned over the new onset of erectile dysfunction
*add Augmentin Wellbutrin IR 150mg in the morning
· Why did you select this decision? Support y our response with evidence and references to the Learning Resources.
· What were you hoping to achieve by making this decision? Support your response with evidence and references to the Learning Resources.
· Explain any difference between what you expected to achieve with Decision #2 and the results of the decision. Why were they different?
· Decision #3: Client returns to clinic in four weeks, Client stated that depressive symptoms have decreased even more and his erectile dysfunction has abated
· Client reports that he has been feeling “jittery” and sometimes “nervous”
*change to Wellbutrin XL 150mg daily
· Why did you select this decision? Support your response with evidence and references to the Learning Resources.
· What were you hoping to achieve by making this decision? Support your response with evidence and references to the Learning Resources.
· Explain any difference between what you expected to achieve with Decision #3 and the results of the decision. Why were they different?
Explain how ethical considerations might impact your treatment plan and communication with clients.
Conclusion.
Part 2For this section of the template, focus on gathering deta.docx
Part 2:
For this section of the template, focus on gathering details about common, specific learning disabilities. These disabilities fall under the IDEA disability categories you researched for the chart above. Review the textbook and the topic study materials and use them to complete the chart.
Learning Disability Definition Characteristics Common Assessments for Diagnosis Potential Effect on Learning and Other Areas of Life Basic Strategies for Addressing the Disability
Attention Deficit Hyperactivity Disorder (ADHD)
Auditory Processing Disorder (APD)
Dyscalculia
Dysgraphia
Dyslexia
Dysphasia/Aphasia
Dyspraxia
Language Processing Disorder (LPD)
Non-Verbal Learning Disabilities
Visual Perceptual/Visual Motor Deficit
.
Part 2 Observation Summary and Analysis • Summary paper of observat.docx
Part 2: Observation Summary and Analysis • Summary paper of observation findings for each area of development and connection to the observed participant. • Comprehensive description of the observed participant. • Analyzed observation experience with course material to determine whetherthe participant is developmentally on track for each area of development. • 4 Pages in length • APA Formatting • Submission will be checked for plagiarism
Part 2: Observation Summary and Analysis 1. Review and implement any comments from your instructor for Part 1: Observation. 2. Describe the participant that you observed. • Share your participant’s first name (can be fictional name if participant wants to remain anonymous), age, physical attributes, and you initial impressions. 3. Analyze your observation findings for each area of development (physical, cognitive, social/emotional, and spiritual/moral). • Explain how your observations support the 3-5 bullets for each area of development that you identified in your Development Observation Guidefrom Part 1: Observation. • Explain whether or not your participant is developmentally on track for each area of development. 4. What stood out the most to you about the observation? 5. Include at least 2 credible sources
.
Part 2 Observation Summary and Analysis 1. Review and implement any.docx
Part 2: Observation Summary and Analysis 1. Review and implement any comments from your instructor for Part 1: Observation. 2. Describe the participant that you observed. • Share your participant’s first name (can be fictional name if participant wants to remain anonymous), age, physical attributes, and you initial impressions. 3. Analyze your observation findings for each area of development (physical, cognitive, social/emotional, and spiritual/moral). • Explain how your observations support the 3-5 bullets for each area of development that you identified in your Development Observation Guidefrom Part 1: Observation. • Explain whether or not your participant is developmentally on track for each area of development. 4. What stood out the most to you about the observation? 5. Include at least 2 credible sources
Part 2: Observation Summary and Analysis • Summary paper of observation findings for each area of development and connection to the observed participant. • Comprehensive description of the observed participant. • Analyzed observation experience with course material to determine whetherthe participant is developmentally on track for each area of development. • 4-6 Pages in length • APA Formatting • Submission will be checked for plagiarism
.
Part 2Data collectionfrom your change study initiative,.docx
Part 2:
Data collection
from your change study initiative, sample, method, display of the results of the data itself, process, and method of analysis (graphs, charts, frequency counts, descriptive statistics of the data, narrative)
Part 3: Interpretation of the results of the Data
Collection and
Analysis, address likely resistance, and provide recommendations for continuing
the study
or evaluating your change study/initiative.
.
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- 1. MA 116 Turn-in Practice Problems 4.2 and 4.4 Pitts Name ___________________________ 1. (4.4 # 4) The price p, in dollars, and the quantity x sold of a certain product obey the demand equation 1 100 3 a.) Express the revenue R as a function of x. Show your work. c.) What is the revenue if 100 units are sold? d.) What quantity x maximizes the revenue? What is the maximum revenue? Show your algebra. You may use 2 b x
- 2. a Quantity x = ______________ Maximum revenue ______________ e.) What price should the company charge to maximize revenue? 2. (4.4 # 6) The price p (in dollars) and the quantity x sold of a certain product obey the demand equation 20 500 0 p 25 a.) Solve for p in terms of x. That is write p as a function of x. b.) Express the revenue R as a function of x. Show your work c.) What quantity x maximizes the revenue? What is the maximum revenue? Show your algebra. Y
- 3. Quantity x = ______________ Maximum revenue ______________ d.) What price should the company charge to maximize revenue? 3. (4.4 # 8). Beth has 3000 feet of fencing to enclose a rectangular field. (Show algebra) a.) Express the area A of the rectangle as a function of x, where x is the length of the rectangle. b.) For what value of x is the area largest? Show algebra.
- 4. c.) What is the maximum area? 3. (4.4 # 10). A farmer with 2000 meters of fencing wants to enclose a rectangular plot that borders on a straight highway, so he won’t fence the side along the highway. Express the area A of the rectangle as a function of x. highway x y For what value of x is the area a maximum? Show algebra. What is the maximum area? 5. (4.4 # 26). A shot-putter throws a ball at an inclination of 45o to the horizontal. The following data represents the height of the ball h feet at the instant that it has traveled x feet horizontally. Distance x 20 40 60 80 100 120 140 160 180 200
- 5. Height h 25 40 55 65 71 77 77 75 71 64 b.) Using your graphing calcualtor find the quadratic function of best fit that models the relation between distance and height. Record your answer rounded to four decimal places, but in your calculator store all the decimals. H(x) = _______________________________ c.) Use the function stored in your calculator to determine how far the ball will travel before it reaches its maximum height. Round to the nearest integer. d.) What is that maximum height? Round to the nearest integer. 6. See 4.2 # 22 c and g) A marketing firm wishes to find a function that relates the sales S of a product and A, the amount spent on advertising the product. The data are obtained from past experience. Advertising and sales are measure in thousands of dollars. Use your graphing calculator; find the line of best fit relating advertising expenditures and sales. Round to two decimal
- 6. places. Advertising A 20 22 22.5 24 24 27 28.3 Sales, S 335 339 338 343 341 350 351 Equation: S = _______________________________ Round to two decimal places. g.) Predict sales if advertising expenditures are $25,000. Sales: ________________ Round to nearest integer MA 116 Turn in Practice Problems (4.1 and 4.3) Pitts Name ________________________________ 1. (See 4.1 # 40) Suppose that the quantity supplied S and quantity demanded D of hot dogs at a baseball game are given by the following functions: S(p) = -2000 + 3000p and D(p) = 10,000 – 1000p where p is the price in dollars. The equilibrium price of a market is defined as the price at which quantity supplied equals quantity demanded (S = D). Show your work!! a.) Find the equilibrium price for hot dogs at the baseball game. What is the equilibrium quantity?
- 7. Equilibrium price = __________ Equilibrium quantity = _______ 2. (See 4.1 # 46) Suppose that a company has just purchased a new machine for its manufacturing facility for $120,000. The company chooses to depreciate the machine using the straight-line method over 10 years. a.) Write a linear function that expresses the book value of the machine as a function of its age. b.) What is the book value of the machine after 4 years? c.) When will the machine be worth $60,000? Show your algebra 3. Consider the function 2
- 8. Using the completing the square technique, write f(x) in the form 2 What is the vertex? What is the axis of symmetry? Using algebra show your work to find the x intercepts. (ie. where f(x) =0.) What is the y-intercept. (i.e. f(0)). Graph the function.
- 9. 4. (4.3 # 36) Consider the function 2 What is the vertex? You may use 2 b x a What is the axis of symmetry? Using algebra show your work to find the x intercepts. What is the y-intercept.
- 10. Give intervals where the function is increasing and decreasing. Graph the function. 5. (4.3 # 50) Determine the quadratic function for a parabola that has a vertex at (2, 3) and a y-intercept of (0, -1). Show the algebra to come up with the leading coefficient. Leave your answer in the form 2 6. (4.3 # 90) The marginal cost C (in dollars) of manufacturing x cell phones (in thousands) is given by 2 manufactured to minimize the marginal cost?
- 11. What is the minimum marginal cost? Show your algebra. (You can use 2 b x a 7. (4.3 # 92) The daily revenue R achieved by selling x boxes of candy is modeled by 2 ( ) 9.5 The daily cost C of selling x boxes of candy is ( ) 1.25 250C x a.) How many boxes of candy must the firm sell to maximize revenue? What is that maximum revenue? Show algebra. b.) Profit is given as P(x) = R(x) – C(x). What is the profit function? d.) How many boxes of candy must the firm sell to maximize profit? What is the maximum profit? Show
- 12. your algebra. 8. Use the figure to answer the following question. a.) Solve f(x) = 0 b.) Solve g(x) < 0 c.) Solve f(x) > g(x) d.) Solve g(x) = 9
- 13. 9. (4.3 # 88) The John Deere Company has found that the revenue, in dollars from sales of riding mowers is a function of the unit price p, in dollars, that it charges. If the revenue R is 21 ( ) 1900 2 a.) What unit price should be charge to maximize revenue? Show your algebra. b.) What is the maximum revenue? f(x) g(x) (1,6) (0,9) (0,4) (3,0)
- 14. MA 116 Turn-in Practice Problems 3.5 Pitts Name ___________________________ 1. Look at the graphs in 3.5 # 1 – 14. Give the equation of the following ones: a.) # 8 b.) # 10 2. Write the function whose graph is the graph of y = x3, but is: a.) # 20: Shifted to the left 4 units. b.) #22: Shifted down 4 units c.) # 24: Reflected about the x-axis. d.) # 26: Horizontally stretched by a factor of 4. 3. Find the function that is finally graphed after the following transformation are applied to the a.) (# 28) that is reflected about the x-axis, shifted right 3 units and shifted down 2 units.
- 15. Y = _____________________________________ b.) (# 30) shift up 2 units, reflect about the y-axis, and shift left 3 units. Y = ___________________________________ 4. (# 32) If (3, 6) is a point on the graph of y = f(x), what point is on the graph of y = f(-x)? 5. (# 34.) If (4, 2) is a point on the graph of y = f(x), which point is on the graph of y = f(2x)? 6. Graph each of the following, Make sure to clearly show three key points and give their coordinates. a.) # 46 3 ( ) ( 2
- 16. 7. (See the graph in 3.5 # 69). Suppose y = f(x) is the graph in the text. Graph the function - 4, -2), (0, 2), (2,2) and (4, 0) are moved. f points H points (-4, -2) (0, 2) (2, 2) (4, 0 ) Using interval notation give the domain and range of H(x) Domain ________________ range _________________ Explain in words what is happening. (i.e. what kinds of shifting, stretching or
- 17. shrinking and reflections are occurring.) 8. (See the graph in # 70). Suppose y = f(x) is the graph in the text. Graph the function ( ) 2 1 2 x H x f , showing clearly where (-4, -2),(-2, -2), (2,2) and (4, -2) are moved. F points H points (-4, -2) (-2, -2) (2, 2)
- 18. (4, -2) Using interval notation give the domain and range of H(x) Domain ________________ range _________________ Explain in words what is happening. (i.e. what kinds of shifting, stretching or shrinking and reflections are occurring.) MA 116 Turn in Practice Problems 3.4 Pitts Name _____________________________ 1. (#26) If
- 19. 2 -3x if x < -1 ( ) 0 if x = -1 2x +1 if x >-1 f x . Find the following: a.) f(-2) b.) f(-1) c.) f(0) 2. Graph the following. Indicate carefully the open and closed circles. Also give coordiates of key points. Give the domain and range in interval notation. a.) # 32) 3 if x < -2 ( ) -2x - 3 if x -2 x
- 20. f x b.) # 34.) 2 5 if -3 x<0 ( ) 3 if x = 0 5 if x > 0 x f x x Domain: __________________ Domain _________________ Range: ___________________ Range ___________________ 3. Write the definition for the piecewise-defined function given in the picture in the text. Also give
- 21. the domain and range. a.) # 42 ( )f x domain: ____________ range ____________ b.) (# 44) ( )f x domain ____________ range ____________ MA 116 Turn-in Practice Problems (5.1 & 5.6) Pitts
- 22. Name __________________________ Give the x-intercepts, give the multiplicity, and tell whether the curve touches or crosses at each. Zero multiplicity touches or crosses What is the degree? ________________ Determine the end behavior: ________________________ 2. (5.1 # 54) 3 2 )1( 3 1
- 23. Give the x-intercepts, give the multiplicity, and tell whether the curve touches or crosses at each. Zero multiplicity touches or crosses What is the degree? ________________ Determine the end behavior: ________________________ 3. Construct a polynomial function of degree 4 that has x- intercepts (zeroes) at -1, 1, and 2, crosses at x = -1 and x = 2, and touches at x = 1 and has has a y-intercept at (0, 4). You may leave it in factored form, but make sure you find the correct leading coefficient. Show your algebra! f(x) = ______________________________________ 4. Factor 5 4 3 2 by grouping or use your calculator.
- 24. 5. Use your calculator and what you know about polynomials to factor: 3 2 6. (5.6 # 24) Solve 3 2 Leave your answer in interval notation. Answer in interval notation: ______________________ 7. (5.6 # 28) Solve the following inequality 3 2 leave your answer in interval notation. Answer in interval notation: _______________________________
- 25. 8. (5.6 # 34) Solve the inequality showing your sign graph. ( 3) 0 1 x x . Leave your answer in interval notation. Answer in interval notation: _____________________________ 9. (5.6 # 38). Solve the inequality showing your sign graph. 2 2 ( 5) 0 4 x
- 26. x . Leave your answer in interval notation. Answer in interval notation: _____________________________ 10. (5.6 # 44) Solve the following inequality 5 3 3 1x x . Show your algebra. Show your sign graph, and leave your answer in interval notation. Warning: don’t cross multiply! I won’t give this hint on the test.
- 27. Answer in interval notation: _____________________________ 11. (5.6 # 58) Solve the following inequality 12 7x x . Show your algebra. Show your sign graph, and leave your answer in interval notation. Warning: don’t multiply both sides by x!!! Answer in interval notation: _____________________________ 12. Find the domain of 2 25 ( ) 4 x
- 28. f x x . Show your work, including your sign graph. Leave your answer in interval notation. Answer in interval notation: _____________________________