1a- The revenue for a company is given by R(x) - --9x^2 + 285x- the co.docx
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1a. The revenue for a company is given by R(x) = -.9x^2 + 285x, the cost is C(x) = .1x^2 + 35x + 15,000, and the profit is P(x) = R(x) - C(x) = -x^2 + 250x - 15,000. Find the two break-even points for this company. Give your answers separated by a comma, with a smaller value first. 1b. The revenue for a company is given by R(x) = -.9x^2 + 285x, the cost is C(x) = .1x^2 + 35x + 15,000, and the profit is P(x) = R(x) - C(x) = -x^2 + 250x - 15,000. Find the number of items that must be produced to obtain the maximum profit. (Give the value of x.) 1c. Find maximum profit for the company. (State the maximum profit.) 1b. The revenue for a company is given by R(x) = -.9x^2 + 285x, the cost is C(x) = .1x^2 + 35x + 15,000, and the profit is P(x) = R(x) - C(x) = -x^2 + 250x - 15,000. Find the number of items that must be produced to obtain the maximum profit. (Give the value of x.) 1b. The revenue for a company is given by R(x) = -.9x^2 + 285x, the cost is C(x) = .1x^2 + 35x + 15,000, and the profit is P(x) = R(x) - C(x) = -x^2 + 250x - 15,000. Find the number of items that must be produced to obtain the maximum profit. (Give the value of x.) 1c. Find maximum profit for the company. (State the maximum profit.) .
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A gas company has the following rate schedule for natural gas usage in single-family residences:
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- Solving equations may require transforming them into polynomial equations first through methods like factoring or factoring by grouping.
Economic Optimization Numerical
This document contains sample optimization problems related to profit maximization for a firm. It includes questions about finding the profit-maximizing output level given total revenue and cost functions, the impact of subsidies, and the output level that maximizes total revenue. It also provides examples of determining the profit-maximizing level of output, average cost function, and minimum average cost given total cost functions, as well as finding the output level where average cost is minimized and the corresponding marginal cost.
17 integrals of rational functions x
This document discusses integrating rational functions. It begins by defining rational functions as functions of the form P(x)/Q(x) where P and Q are polynomials. It states that integrating rational functions involves decomposing them into simpler fractions using the Rational Decomposition Theorem. Examples are then provided to demonstrate how to decompose rational functions and integrate each term using substitution.
Factoring polynomials
Factoring is writing a polynomial as a product of two or more polynomials. The main techniques for factoring polynomials are finding the greatest common factor, factoring trinomials of the form ax^2 + bx + c, using special factoring patterns like the difference and sum of squares, and factoring polynomials with four or more terms by grouping. The goal is to factor the polynomial completely into prime factors that cannot be further factored.
0.5 Rational Expressions
This document discusses rational expressions and operations involving them. It defines rational expressions as the quotient of two polynomials where the denominator is not equal to 0. It explains how to find the domain of a rational expression by setting the denominator equal to 0 and solving. The document provides examples of multiplying, dividing, adding and subtracting rational expressions by treating them as fractions and using properties of fractions. It emphasizes writing rational expressions in lowest terms and finding the lowest common denominator when adding or subtracting.
2.1 order of operations w
The document discusses order of operations and exponents. It explains that when evaluating arithmetic expressions, operations should be performed in a specific order: 1) operations within grouping symbols, 2) multiplication and division from left to right, and 3) addition and subtraction from left to right. Exponents are defined as the number of times a base is used as a factor, with the exponent written as a superscript. Examples are provided to demonstrate applying order of operations correctly.
Matrix chain multiplication in design analysis of algorithm
This document discusses the matrix chain multiplication problem and provides an algorithm to solve it using dynamic programming. Specifically:
- The problem is to find the most efficient way to multiply a sequence of matrices by determining the optimal parenthesization that minimizes the number of scalar multiplications.
- A dynamic programming approach is used where the problem is broken down into optimal subproblems and a bottom-up method is employed to compute the solution.
- Recursive formulas are defined to calculate the minimum number of multiplications (m) needed to compute matrix chain products of increasing length. Additional data (s) tracks the optimal splitting points.
- The algorithm fills a table from bottom to top and left to right using the
Marginal-analysis.pptx
This document discusses marginal analysis in business and economics. It provides an example problem involving the demand and cost functions of producing computer sets. It asks to: (1) Express price as a function of demand, (2) Find marginal cost, (3) Find revenue function and its domain, (4) Find marginal revenue, (5) Interpret marginal revenue at two production levels, (6) Graph cost and revenue and find break-even points, (7) Find profit function, (8) Find marginal profit, and (9) Interpret marginal profit at two production levels. The solutions provide mathematical derivations and economic interpretations.
Name ____________________________Student Number ________________.docx
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.
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) =
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) = x
2
(x + 2)
(a).
(b).
(c).
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 + tan
2
u)(1 - sin
2
u) = 1
7
Verify the identity
. Show your work.
cot
2
x + csc
2
x = 2csc
2
x - 1
8
Verify the identity. Show your work.
1 + sec
2
xsin
2
x = sec
2
x
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 do not need to submit the scatter diagram). Find the sinusoidal function of the form that fits the data. Show your work.
.
11.
The graph below shows the percentage of students enrolled in the College of Engineering at State University. Use the graph to answer the question.
Does the graph represent a function? Explain
12.
Find the vertical asymptotes, if any, of the graph of the rational function. Show your work.
f(x) =
13.
The formula A = 118e
0.024t
models the popula.
Las expresiones algebraicas y Factorización de productos notables
This document discusses algebraic expressions and factorizing notable products. It begins by defining algebra and different algebraic terms such as monomials and polynomials. It then explains operations like addition, subtraction, multiplication, and division of algebraic expressions. It also covers evaluating algebraic expressions for numeric values. The document focuses on notable products, describing different types like the square of a binomial, binomials with similar terms, conjugate binomials, and the cube of a binomial. It provides examples for each type. Finally, it discusses factorizing expressions using notable products, including the difference of squares, common factors, and perfect square trinomials.
Solving linear equation
The document provides information about linear equations and functions. It includes:
1. A list of 5 students with identification numbers.
2. An overview of topics to be covered related to linear equations and functions, including solving linear equations and inequalities, functions, linear functions, and systems of linear equations.
3. Details on solving linear equations and inequalities in one variable, including examples and properties.
4. Information on different types of functions, including algebraic, trigonometric, exponential, and logarithmic functions.
5. Examples of using linear functions in business and economics, such as profit functions, break-even points, supply and demand curves.
Square Roots without a Calculator - John Doe
This is an example of an exemplar student presentation for the Square Root Algorithm Assignment in Mr. Stafford's Class.
Square Roots without a Calculator - J. Doe
The document describes a step-by-step process for finding the square root of 8259876 without a calculator. It breaks the number down into place values of thousands, hundreds, tens and ones. It uses a guess and check method to systematically determine each place value by subtracting squares and products until it arrives at the final square root of 2874.
Producción Escrita Matemática.
Suma, resta, multiplicación y división de expresiones algebraicas. La suma y resta de monomios y polinomios siguen las mismas reglas que las operaciones numéricas. La multiplicación requiere aplicar las propiedades de las potencias y la distribución. Existen productos notables cuya factorización se obtiene por inspección. La factorización transforma expresiones en productos de factores.
Formulation Lpp
The document discusses linear programming problems and how to formulate them. It provides definitions of key terms like linear, programming, objective function, decision variables, and constraints. It then explains the steps to formulate a linear programming problem, including defining the objective, decision variables, mathematical objective function, and constraints. Several examples of formulated linear programming problems are provided to maximize profit or minimize costs subject to various constraints.
An Introduction to Linear Programming
The document introduces linear programming through an example of a candy manufacturer that must determine how many cases of two candy products to make to maximize profit given constraints on available ingredients. It defines variables and constraints, graphs the feasible region, determines the optimal solution that maximizes profit, and discusses how linear programming can be applied to problems with multiple variables and constraints.
6.1 Exponential Functions
* Evaluate exponential functions.
* Find the equation of an exponential function.
* Use compound interest formulas.
* Evaluate exponential functions with base e.
1.3 solving equations
The document discusses expressions and equations. It provides examples of using expressions to calculate total costs given individual costs, and using equations to solve for unknown variables. Specifically, it gives an example of calculating the total cost of x pizzas using the expression "8x + 10" and solving the equation "8x + 10 = 810" to determine that x = 100 pizzas were ordered. It then discusses how to solve rational equations by clearing denominators using the lowest common denominator. An example problem demonstrates solving the rational equation (x - 2)/(x + 1) = 2/4 + 1 through multiplying both sides by the LCD (x - 2)(x + 1).
Simplex part 1 of 4
1. The simplex method involves 6 steps to find the optimal solution for a linear programming problem.
2. The first step is to convert all equations (objective function and constraints) to standard form. This allows starting the problem at the origin while preserving mathematical rules.
3. For less than or equal to constraints, slack variables are added. For equal constraints, artificial variables are added. For greater than or equal constraints, surplus variables are subtracted and artificial variables are added.
4. The objective function is modified to include all slack, artificial, and surplus variables with coefficients of 0, except for artificial variables which use a very large coefficient M if maximizing or -M if minimizing.
Similar to 1a- The revenue for a company is given by R(x) - --9x^2 + 285x- the co.docx (20)
Matrix chain multiplication in design analysis of algorithm
Matrix chain multiplication in design analysis of algorithm
Name ____________________________Student Number ________________.docx
Name ____________________________Student Number ________________.docx
Las expresiones algebraicas y Factorización de productos notables
Las expresiones algebraicas y Factorización de productos notables
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The Internet Committee for Assigned Names and Numbers (ICANN)
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allocates Data Link layer address ranges to network adapter card manufacturers.
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it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
clinical examination of hip joint (1).pdf
described clinical examination all orthopeadic conditions .
Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...
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In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
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South African Journal of Science: Writing with integrity workshop (2024)
1a- The revenue for a company is given by R(x) - --9x^2 + 285x- the co.docx
- 1. 1a. The revenue for a company is given by R(x) = -.9x^2 + 285x, the cost is C(x) = .1x^2 + 35x + 15,000, and the profit is P(x) = R(x) - C(x) = -x^2 + 250x - 15,000. Find the two break-even points for this company. Give your answers separated by a comma, with a smaller value first. 1b. The revenue for a company is given by R(x) = -.9x^2 + 285x, the cost is C(x) = .1x^2 + 35x + 15,000, and the profit is P(x) = R(x) - C(x) = -x^2 + 250x - 15,000. Find the number of items that must be produced to obtain the maximum profit. (Give the value of x.) 1c. Find maximum profit for the company. (State the maximum profit.) 1b. The revenue for a company is given by R(x) = -.9x^2 + 285x, the cost is C(x) = .1x^2 + 35x + 15,000, and the profit is P(x) = R(x) - C(x) = -x^2 + 250x - 15,000. Find the number of items that must be produced to obtain the maximum profit. (Give the value of x.) 1b. The revenue for a company is given by R(x) = -.9x^2 + 285x, the cost is C(x) = .1x^2 + 35x + 15,000, and the profit is P(x) = R(x) - C(x) = -x^2 + 250x - 15,000. Find the number of items that must be produced to obtain the maximum profit. (Give the value of x.) 1c. Find maximum profit for the company. (State the maximum profit.)