MATH SOLVE

5 months ago

Q:
# Eva is jumping on a trampoline. Her height h at time t can be modeled by the equation h=-16t^2+20t+6. Would Eva reach a height of 14 feet?

Accepted Solution

A:

Given the equation modeling Eva's height at time,t. To evaluate if she will reach height of 14 ft, we evaluate maximum height that she will reach.

At maximum height h'(t)=0

but

h(t)=-16t^2+20t+6

h'(t)=-32t+20=0

solving for t we get:

-32t=-20

t=20/32

t=5/8

thus the maximum height reached was:

h(5/8)=-16(5/8)^2+20(5/8)+6

h(5/8)=12.25 ft

Thus we conclude that she won't reach the height of 14 ft because her maximum height was 12.25 ft

At maximum height h'(t)=0

but

h(t)=-16t^2+20t+6

h'(t)=-32t+20=0

solving for t we get:

-32t=-20

t=20/32

t=5/8

thus the maximum height reached was:

h(5/8)=-16(5/8)^2+20(5/8)+6

h(5/8)=12.25 ft

Thus we conclude that she won't reach the height of 14 ft because her maximum height was 12.25 ft