Chapter 8.4, Problem 77E

a.

To determine

To find which bird bath is deeper.

Answer to Problem 77E

The second bird bath.

Explanation of Solution

Given:

The given cross-section of bird bath is $y=\frac{1}{81}{(x-18)}^2-4$ where, $x\text{ and }y$ are measured in inches.

Calculation:

Here it is given that $k=-4$ , that means the first bird bath is $4$ inches deep and the graph shows that second bird bath is $6$ inches deep. Therefore, the second bird bath is deeper.

b.

To determine

To find which bird bath is wider.

Answer to Problem 77E

The first bird bath.

Explanation of Solution

Given:

The given cross-section of bird bath is $y=\frac{1}{81}{(x-18)}^2-4$ where, $x\text{ and }y$ are measured in inches.

Calculation:

Find the ends of the first bird bath.

  $\begin{array}{l}$ y=\frac{1}{81}{(x-18)}^2-4$$ 0=\frac{1}{81}{(x-18)}^2-4$x=0\text{ or }x=36\end{array}$

Now find the ends of second bird bath

  $\begin{array}{l}$ y=\frac{2}{75}{(x)}^2-\frac{4}{5}x$$ 0=\frac{2}{75}{(x)}^2-\frac{4}{5}x$x=0\text{ or }x=30\end{array}$

Since the first bath is $36$ inches wide and the second bird bath is $30$ inches wide, therefore the first bath is wider.