Question

PLEASE HELP IM FAILING MATH!!!!

A child launches a toy rocket from the top of a slide at the park. Suppose the equation -16t^2 + 28t + 8= 0
Write the equation in factored form.

Use the zero product property to solve the equation. Show all the steps needed to find both answers.

Explain how the solution relates to this situation.

Answer 1

-1) -4 (4t + 1) (t - 2) = 0

2) t = 2 sec

Explanation:

The given equation is:

`-16t^(2)+28t+8=0`

We need to factorize this equation.

Taking -4 as common from left hand side, we get:

`-4(4t^(2)-7t-2)=0`

The term inside the brackets can be further simplified by breaking down -7t as -8t + t:

`-4(4t^(2)-8t+t-2)=0\\\\ -4(4t(t-2)+1(t-2))=0\\\\ -4(4t+1)(t-2)=0`

This is the fully factored form of the given equation.

Using the zero product property,we can write:

4t + 1 = 0 → t =
`-(1)/(4)` → t = -0.25

t - 2 = 0 → t = 2

This means, the rocket touches the ground at time = -0.25 sec and at time = 2 sec. Since, negative time is not possible we neglect this value.

Therefore, we can conclude that the rocket launched by the child reaches/touches the ground after 2 seconds.