Chapter 8.1, Problem 31E

a.

To determine

To find the wideness of the mouth of the glass.

Answer to Problem 31E

  $8\text{ cm}$

Explanation of Solution

Given:

The following diameter shows the parabolic cross section of the glass-

  

Calculation:

From figure the width of the horizontal distance is

  $w=\left|-4-4\right|=8$

Hence, the wideness of the mouth of the glass is $8\text{ cm}$

b.

To determine

To find whether your friend is correct or not.

Answer to Problem 31E

No, he is wrong.

Explanation of Solution

Given:

The friend says the model should be $y=0.1x^2$

Calculation:

The parabola model should be in the form:-

  $y=a{x}^2$

Substitute $(4,3.2)$ to find the value of $a$

  $\begin{array}{l}y=a{x}^2\\ 3.2=16a\\ a=0.2\end{array}$

Therefore the equation of the model should be-

  $y=0.2x^2$

Hence the friend is wrong.