Chapter 10.2, Problem 15Q

(a)

To determine

To graph the function and find Domain, Range.

Answer to Problem 15Q

Domain = [ $0,\infty$ )

Range = $[0,\infty )$

Explanation of Solution

Given information: $t=\frac{1}{4}\sqrt{h}$

Formula Used: Square root function cannot be negative.

Calculation:

As the domain of square root function is greater than or equal to zero i.e. cannot be negative.

So,

  $\sqrt{h}\ge 0$

Squaring both sides,

  $h\ge 0$

Hence,

Domain = [ $0,\infty$ )

As,

  $\sqrt{h}\ge 0$

Now, multiply both sides by $\frac{1}{4}$

  $\frac{1}{4}\sqrt{h}\ge 0$

As, $t=\frac{1}{4}\sqrt{h}$

  $t\ge 0$

Range = $[0,\infty )$

Graph of $t=\frac{1}{4}\sqrt{h}$

  $\begin{array}{cccc}h& 0& 1& 2\\ t& 0& 0.25& 0.35\end{array}$

  

(b)

To determine

To find how high is the bridge above the river.

Answer to Problem 15Q

  $h=876.16$ feet

Explanation of Solution

Given information: $t=\frac{1}{4}\sqrt{h}$ and $t=7.4$ seconds

Formula Used: Square root function cannot be negative.

Calculation:

  $t=7.4$ seconds

As, $t=\frac{1}{4}\sqrt{h}$

So,

  $\frac{1}{4}\sqrt{h}=7.4$

Now,

  $\sqrt{h}=7.4\times 4$

So,

  $\sqrt{h}=29.6$

Now, squaring both sides

  $h={\left(29.6\right)}^2$

Hence,

  $h=876.16$ feet