Chapter 8.3, Problem 29E

a.

To determine

To find the distance of the lowest point from the tower.

Answer to Problem 29E

  $200$ Feet.

Explanation of Solution

Given:

The given figure of tower is −

  

Calculation:

The distance of the lowest point is the difference of the x coordinate of the location of the towers and the vertex.

So,

  $\begin{array}{l}x=-\frac{b}{2a}\\ x=-\frac{-1}{2\times \frac{1}{400}}\\ x=200\end{array}$

Hence, the distance of lowest point is $200$ feet.

b.

To determine

To find the height of the road above the water.

Answer to Problem 29E

The firework will explode at $256\text{ feet}$ from ground.

Explanation of Solution

Given:

The given function is

  $y=\frac{1}{400}{x}^2-x+150$

Calculation:

Substitute $x=200$ to find the value of $y$

  $\begin{array}{l}y=\frac{1}{400}{x}^2-x+150\\ $ y=\frac{1}{400}{(200)}^2-200+150$y=50\end{array}$

Therefore the height is $50$ feet.

c.

To determine

To find the domain and range of the function.

Answer to Problem 29E

The domain is $0\le x\le 200$ and the range is $0\le y\le 50$

Explanation of Solution

Given:

The given function is

  $y=\frac{1}{400}{x}^2-x+150$

Calculation:

Using the vertex $(200,50)$ to find the domain and range.

Therefore the domain is $0\le x\le 200$

And the range is $0\le y\le 50$