More on graphing trig functions and finding equations from graphs. Properties of the three basic trig functions and the relationship between sine and cosine.
More on graphing trig functions and finding equations from graphs. Properties of the three basic trig functions and the relationship between sine and cosine.
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1. Write an equation in standard form of the parabola that has th.docxKiyokoSlagleis
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.
Analytic Geometry A Accelerated Week 3 Page 35 of 5.docxLynellBull52
Analytic Geometry A Accelerated Week 3 Page 35 of 51
Analytic Geometry A ‐ Accelerated Week 3
Lesson 2.1 Introduction to Right Triangle Trigonometry
Lesson 2.2 Sine Ratio
Lesson 2.3 Cosine Ratio
Lesson 2.4 Tangent Ratio
Lesson 2.5 Review
Lesson 2.6 Inverse Trigonometric Ratios
Lesson 2.7 Solve Right Triangles
Lesson 2.8 Solve Right Triangles in Applied Problems
Before working the problems, study the lesson listed above each problem set.
Record the answers on the answer sheet. Turn in the answer sheet to be graded.
For some problem sets, answer boxes are given. Choices may be used more than
once if necessary.
Lesson 2.1 Introduction to Right Triangle Trigonometry
True or False. Choose ‘A’ for True or ‘B’ for False.
1. The word “trigonometry” comes from the Greek words that mean “triangle measurement.”
2. The study of trigonometry did not begin until long after the beginning of the Christian era.
3. The longest side of any right triangle is the hypotenuse.
4. A right triangle contains one right angle and two acute angles.
5. The hypotenuse of a right triangle can be opposite an acute angle of a triangle.
6. The legs of a right triangle form the right angle.
Analytic Geometry A Accelerated Week 3 Page 36 of 51
Multiple Choice.
Use the given triangle to answer problems 7‐11.
A
C B
7. Which of the following is the side opposite of A ?
A) AB B) BC C) AC D) B
8. Which of the following is the side opposite of B ?
A) AC B) BC C) AB D) B
9. Which of the following is the hypotenuse?
A) AC B) BC C) AB D) C
10. Which of the following is the side adjacent to A ?
A) AB B) AC C) BC D) B
11. Which of the following is the side adjacent to B ?
A) AB B) AC C) BC D) A
Lesson 2.2 Sine Ratio
A
C B
12. What is the sine ratio for A ?
A)
BC
AC
B)
BC
AB
C)
AC
AB
D)
AB
BC
13. What is the sine ratio for B ?
A)
BC
AC
B)
.
EVALUATING INTEGRALS.Evaluate the integral shown below. (H.docxgitagrimston
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 ...
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
Honest Reviews of Tim Han LMA Course Program.pptxtimhan337
Personal development courses are widely available today, with each one promising life-changing outcomes. Tim Han’s Life Mastery Achievers (LMA) Course has drawn a lot of interest. In addition to offering my frank assessment of Success Insider’s LMA Course, this piece examines the course’s effects via a variety of Tim Han LMA course reviews and Success Insider comments.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
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