Question

Please help as soon as possible!!

Answer 1

A) 144 feet

`\textsf{B)} \quad h(t)=16t(6-t)`

Explanation:

Part A

Given polynomial:

`h(t)=96t-16t^2`

where:

• h(t) is the height of the debris (in feet).
• t is the time (in seconds) after the explosion.

To find the height of the debris 3 seconds after the explosion, substitute t = 3 into the polynomial and solve:

`\begin{aligned}\implies h(3)& = 96(3)-16(3)^2\\ & = 288 - 16(9)\\ & =288-144\\ & =144 \sf \:\: ft\end{aligned}`

Part B

To factor the polynomial, rewrite 96 as 6 × 16:

`\implies h(t)=6 \cdot 16t-16t^2`

Rewrite t² as t × t:

`\implies h(t)=6 \cdot 16t-16t \cdot t`

Factor out the common term 16t:

`\implies h(t)=16t(6-t)`

Check

Substitute t = 3 into the factored expression:

`\begin{aligned}h(3) & = 16(3)(6-3)\\& = 16(3)(3)\\& = 48(3)\\& = 144\:\: \sf ft \end{aligned}`

As the height is 144 ft when t = 3 is substituted into the original polynomial and the factored polynomial, this confirms that the factorization is correct.