Chapter 9.1, Problem 5P

Solution

(a)

To calculate: Thetime required for the acorn drops from the tree branch.

Therequired time is $2\sqrt{35}$ second.

Given information:

The given height of the tree branch is 70 ft.

The function is $h=-t^2+70$

Calculation:

Consider the given function $h=-t^2+70$ .

Now, draw the graph,

  

It is given that height is 70 ft.

Substitute the value $h=70$ in the equation $h=-t^2+70$ .

  $\begin{array}{c}70=-t^2+70\\ t^2=140\\ t=2\sqrt{35}\end{array}$

Hence , the required time is $2\sqrt{35}$ second.

(b)

To find: The domain and the range of the function.

The required domain is 70 and the range is $\left(-2\sqrt{3},2\sqrt{3}\right)$ .

Given information:

The function is $h=-t^2+70$

Explanation:

Consider the given function $h=-t^2+70$ .

Now,the graph of the function is,

  

Hence, the required domain is 70 and the range is $\left(-2\sqrt{3},2\sqrt{3}\right)$ .