The height of a ball kicked in the air is modeled by the equation h(t) = -2t^2 +8t +24, where h is the height of the ball in feet and t is the time in seconds. What is the average rate of change of the function over the intervalt t = 2 to t = 5 A. -3

B. -6

C. 3

D. 6

Step-by-step explanation:

The rate of change in any function is the slope of the line between 2 points. Our points are t = 2 and t = 5. But we know that the slope formula also involves the h's for each of those t's. We need to find them first. The slope formula is

, but for us it will look like this (fittted to our needs):

. So we need to find those h's.

when t = 2, plug in a 2 for t and solve for h.

Therefore, and

h(2) = 32 and in coordinate form, (2, 32).

When t = 5, plug in a 5 for t and solve for h.

Therefore, and

h(5) = 14 and in coordinate form, (5, 14). Now we can plug into our slope formula:

, choice B.

The rate of change is -6 which, in words, means that the ball fell 6 feet every 1 second it fell.

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it