Question

Solve: h = -16t^2 + 60t + 0. Round to the nearest hundredth.

Answer 1

To solve the equation \( h = -16t^2 + 60t + 0 \), we can factor or use the quadratic formula to find the values of \( t \) when \( h = 0 \).

Thus, we need to solve:
\[
-16t^2 + 60t = 0
\]

We can factor out \( t \):
\[
t(-16t + 60) = 0
\]

Setting each factor to zero gives us:
1. \( t = 0 \)
2. \( -16t + 60 = 0 \)

For the second equation:
\[
-16t + 60 = 0 \\
16t = 60 \\
t = \frac{60}{16} \\
t = \frac{15}{4} \\
t = 3.75
\]

Thus, the solutions to the equation \( h = 0 \) are:
\[
t = 0 \quad \text{and} \quad t = 3.75
\]

Since the initial question asked for the solution to the equation \( h = -16t^2 + 60t + 0 \) with rounding to the nearest hundredth, the roots are:

\[
t = 0.00 \quad \text{and} \quad t = 3.75
\]