Question

Jesse tossed a paintbrush off her roof. The height of the brush (in meters above the ground) t seconds after Jesse tossed it is modeled by h(t)=−5t²+5t+10. What is the initial height of the paintbrush?

a) 10 meters
b) 5 meters
c) -10 meters
d) -5 meters

Answer 1

The initial height of the paintbrush that Jesse tossed off her roof is 10 meters. This is determined by substituting t = 0 seconds into the height function h(t)=-5t²+5t+10 to get the result of h(0) = 10 meters.

Step-by-step explanation:

The initial height of the paintbrush tossed off the roof can be determined by evaluating the height function h(t)=-5t²+5t+10 at t = 0 seconds. The term 5t represents the initial velocity component of the throw, and the constant term 10 represents the initial height from which the paintbrush was tossed.

To find the initial height, we substitute t = 0 into the equation:
h(0) = -5(0)² + 5(0) + 10
= 0 + 0 + 10
= 10 meters

Therefore, the direct answer to the question is a) 10 meters. This is the initial height of the paintbrush at the moment it was released from Jesse's hand.