Chapter MPS, Problem 5.2MPS

a.

To determine

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

Answer to Problem 5.2MPS

The domain for the function is all real number and the range is all real number less than or equal to maximum value.

Explanation of Solution

Given information: The function is $h\left(t\right)=-16t^2+75t+150$ .

Calculation:

The domain for the function is all real number and the range is all real number less than or equal to maximum value.

b.

To determine

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

Answer to Problem 5.2MPS

The domain is $h\left(t\right)\le 237.86$ .

Explanation of Solution

Given information: The function is $h\left(t\right)=-16t^2+75t+150$ .

Calculation:

The $x$ intercepts is,

  $t=-\frac{75}{\begin{array}{l}2\left(-16\right)\\ =-2.3\end{array}}$

The $y$ intercepts is,

  $\begin{array}{c}h=-16{\left(2.3\right)}^2+75\left(2.3\right)+150\\ =237.86\end{array}$

c.

To determine

To find: The maximum height reached by the object.

Answer to Problem 5.2MPS

The maximum height reached by the objectis $237.86\text{feet}$ .

Explanation of Solution

Given information: The function is $h\left(t\right)=-16t^2+75t+150$ .

Calculation:

The $x$ intercepts is,

  $x=-\frac{75}{\begin{array}{l}2\left(-16\right)\\ =-2.3\end{array}}$

The $y$ intercepts is,

  $\begin{array}{c}h=-16{\left(2.3\right)}^2+75\left(2.3\right)+150\\ =237.86\end{array}$

d.

To determine

To explain: The meaning of y intercept in context of the problem.

Explanation of Solution

Given information: The function is $h\left(t\right)=-16t^2+75t+150$ .

Calculation:

The y intercepts shows the height gain by bullet after the firing is done.