Precalculus: Mathematics for Calculus - 6th Edition
Precalculus: Mathematics for Calculus - 6th Edition
6th Edition
ISBN: 9780840068071
Author: Stewart, James, Redlin, Lothar, Watson, Saleem
Publisher: Cengage Learning
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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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Textbook Question
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Chapter 2.1, Problem 77E

Internet Purchases An Internet bookstore charges $15 shipping for orders under $100 but provides free shipping for orders of $100 or more. The cost C of an order is a function of the total price x of the books purchased, given by

C ( x ) = { x + 15 if   x < 100 x if   x ≥ 100

  1. (a) Find C(75), C(90), C( 100), and C(105).
  2. (b) What do your answers in part (a) represent ?

(a)

Expert Solution
Check Mark
To determine

To find: The internet bookstore charges at given orders.

Answer to Problem 77E

Internet bookstore charges at order C(75) is 90 , at order C(90) is 105 , order C(100) is 100 , at order C(105) is 105 .

Explanation of Solution

The given function is,

C(x)={x+15                            if x<100x                                  if x≥100       

Function for order $75 is,

C(x)=x+15

Substitute 75 for x in the above function to find the value of C(75) ,

C(x)=x+15=75+15=90

So, internet bookstore charges at order C(75) is 90 .

Function for order $90 is,

C(x)=x+15

Substitute 90 for x in the above function to find the value of C(90) ,

C(x)=x+15=90+15=105

So, internet bookstore charges at order C(90) is 105 .

Function for order $100 is,

C(x)=x

Substitute 100 for x in the above function to find the value of C(100) ,

C(x)=100

So, internet bookstore charges at order C(100) is 100 .

Function for order $105 is,

C(x)=x

Substitute 105 for x in the above function to find the value of C(105) ,

C(x)=105

So, internet bookstore charges at order C(105) is 105 .

Hence, internet bookstore charges at order C(75) is 90 , at order C(90) is 105 , order C(100) is 100 , at order C(105) is 105 .

(b)

Expert Solution
Check Mark
To determine

To explain:  Answer represent in part (a).

Answer to Problem 77E

There are no shipping charges at order $100 or more than $100.

Explanation of Solution

From part (a),

Internet bookstore charges at order C(75) is 90 , at order C(90) is 105 , order C(100) is 100 , at order C(105) is 105 .

There are no shipping charges at order $100 or more than $100.

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Chapter 2.1, Problem 76E
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Chapter 2.1, Problem 78E

Chapter 2 Solutions

Precalculus: Mathematics for Calculus - 6th Edition

Ch. 2.1 - Prob. 1ECh. 2.1 - For a function f, the set of all possible inputs...Ch. 2.1 - (a) Which of the following functions have 5 in...Ch. 2.1 - A function is given algebraically by the formula...Ch. 2.1 - Prob. 5ECh. 2.1 - Prob. 6ECh. 2.1 - Prob. 7ECh. 2.1 - Prob. 8ECh. 2.1 - Prob. 9ECh. 2.1 - Prob. 10E
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What is a Linear Equation in One Variable?; Author: Don't Memorise;https://www.youtube.com/watch?v=lDOYdBgtnjY;License: Standard YouTube License, CC-BY
Linear Equation | Solving Linear Equations | What is Linear Equation in one variable ?; Author: Najam Academy;https://www.youtube.com/watch?v=tHm3X_Ta_iE;License: Standard YouTube License, CC-BY