BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 3.1, Problem 74E
To determine

To find: The function that models the total area enclosed by two squares and also the value of x that minimizes the total area of two squares.

Expert Solution

Answer to Problem 74E

The function that models the total area enclosed by two squares is equal to A=(x4)2+(10x4)2 and also the value of x that minimizes the total area of two squares is x=5 .

Explanation of Solution

Given information:

A wire 10cm long is cut into two pieces, one of length x and other of length 10x , as shown in figure below. Each piece is bent in shape of a square.

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 3.1, Problem 74E , additional homework tip  1

Calculation:

As given the length of one wire is x and the wire is bent in shape of square. So, the length of each side of square is x4 .

As given the length of other wire is 10x and the wire is bent in shape of square. So, the length of each side of second square is 10x4 .

The area of the first square is equal to (x4)2 and the area of the second square is equal to (10x4)2 . The total area of the squares is equal to A=(x4)2+(10x4)2 .

So, the function of the total area of the squares is given by g(x)=(x4)2+(10x4)2 . To minimize the total area of squares graph the function g(x)=(x4)2+(10x4)2 .

To graph a function y=(x4)2+(10x4)2 , follow the steps using graphing calculator.

First press “ON” button on graphical calculator, press Y= key and enter right hand side of the equation y=(x4)2+(10x4)2 after the symbol Y1 . Enter the keystrokes (X÷4)^2+((10X)÷4)^2 .

The display will show the equation,

  Y1=(X/4)^2+((10X)/4)^2

Now, press the GRAPH key and TRACE key to produce the graph of given function in standard window as shown in Figure (1).

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 3.1, Problem 74E , additional homework tip  2

Figure (1)

As observed from the graph, the area function has minimum value at x=5 .

Therefore, the function that models the total area enclosed by two squares is equal to A=(x4)2+(10x4)2 and also the value of x that minimizes the total area of two squares is x=5 .

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