Chapter 4.6, Problem 20PPS

(a)

To determine

To find:

The domain of $h=-4.9t^2+3t+10$ .

Answer to Problem 20PPS

The domain $\left(-1.155,1.767\right)$ Range = $\left(0,1.767\right)$

Explanation of Solution

Given:

  $h=-4.9t^2+3t+10$

Concept used:

The set of all $x$ - values that a function passes through.also the left coordinate in a coordinate in a coordinate pair.

The set of all $y$ - values that a function passes through.also the right coordinate in a coordinate in a coordinate pair.

Calculation:

The smallest number that the square root of that is still in the real number system, which of course is zero.

Solved the equation $h=-4.9t^2+3t+10$ = 0

This is

  $\begin{array}{l}t=\frac{-30-\sqrt{20500}}{-98}=\frac{15+5\sqrt{205}}{49}=1.767\\ t=\frac{-30+\sqrt{20500}}{-98}=\frac{15-5\sqrt{205}}{49}=-1.155\end{array}$

So, that is the smallest, legal $x$ value which is the lower limit of domain.

domain $\left(-1.155,1.767\right)$

or

Domain = $\left\{x:x\in R\right\}$

Range = $\left(0,1.767\right)$

Or

Range = $\left\{y:y\in R\right\}$

(b)

To determine

To find:

The diver hit the water of $h=-4.9t^2+3t+10$ .

Answer to Problem 20PPS

  $t=\left(-1.155,1.767\right)$

Explanation of Solution

Given:

  $h=-4.9t^2+3t+10$

Concept used:

The set of all $x$ - values that a function passes through.also the left coordinate in a coordinate in a coordinate pair.

The set of all $y$ - values that a function passes through.also the right coordinate in a coordinate in a coordinate pair.

Calculation:

The smallest number that the square root of that is still in the real number system, which of course is zero.

Solved the equation $h=-4.9t^2+3t+10$ = 0

This is

  $\begin{array}{l}t=\frac{-30-\sqrt{20500}}{-98}=\frac{15+5\sqrt{205}}{49}=1.767\\ t=\frac{-30+\sqrt{20500}}{-98}=\frac{15-5\sqrt{205}}{49}=-1.155\end{array}$

So, that is the smallest, legal $x$ value which is the lower limit of domain $t=\left(-1.155,1.767\right)$