solve for t. h(t)=16t^2+60t+30

Answer 1

To solve for t in the equation h(t) = 16t^2 + 60t + 30, we can set h(t) equal to a specific value and solve for t.

Let's solve for h(t) = 0:

0 = 16t^2 + 60t + 30

To simplify the equation, we can divide all terms by 2:

0 = 8t^2 + 30t + 15

Now, let's solve this quadratic equation. We can either factor it or use the quadratic formula.

Since the equation doesn't factor easily, let's use the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 8, b = 30, and c = 15.

t = (-30 ± √(30^2 - 4(8)(15))) / (2(8))

Simplifying further:

t = (-30 ± √(900 - 480)) / 16

t = (-30 ± √420) / 16

Now, we have two possible solutions for t:

t = (-30 + √420) / 16

and

t = (-30 - √420) / 16

These are the solutions for t in the equation h(t) = 16t^2 + 60t + 30.