Chapter 8.5, Problem 47PPS

a.

To determine

To determine the factored form of the expression for the height of the rock after $t$ seconds.

Answer to Problem 47PPS

  $8t(55-2t)$

Explanation of Solution

Given:

Height of the rock in feet $=440t-16t^2$ , $t$ represents time.

Calculation:

Height of the rock in feet $=440t-16t^2$ , $t$ represents time

The above expression can be written as,

  $\Rightarrow h=440t-16t^2$ where $h$ represents the height,

  $\Rightarrow h=8t(55-2t)$

Conclusion:

Therefore, the factored form of the expression for the height of the rock after $t$ seconds is $h=8t(55-2t)$ feet.

b.

To determine

To determine the rock height after $10$ second.

Answer to Problem 47PPS

  $h=2800$

  $h=81600$

Explanation of Solution

Given:

Height of the rock in feet $=440t-16t^2$ , $t$ represents time

  $t=10$ second

Calculation:

Height of the rock in feet $=440t-16t^2$ , $t$ represents time

  $\Rightarrow h=440t-16t^2$ where $h$ represents the height,

Now, given value of $t=10$ second,

  $\Rightarrow h=440(10)-16{(10)}^2$

  $\Rightarrow h=2800$

Now, given value of $t=20$ second,

  $\Rightarrow h=440(20)-16{(20)}^2$

  $\Rightarrow h=81600$

Conclusion:

Therefore, the rock height after $20$ second is $h=81600$ feet.

c.

To determine

To determine the maximum height of the rock.

Answer to Problem 47PPS

  $h=3025$

Explanation of Solution

Given:

Height of the rock in feet $=440t-16t^2$ , $t$ represents time

  $t=13.75$ second

Concept used:

Placing values of polynomial

Calculation:

Height of the rock in feet $=440t-16t^2$ , $t$ represents time

  $\Rightarrow h=440t-16t^2$ where $h$ represents the height,

Now, given value of $t=13.75$ second,

  $\Rightarrow h=440(13.75)-16{(13.75)}^2$

  $\Rightarrow h=3025$

Conclusion:

Therefore, the spider height after $13.75$ second is $h=3025$ feet.