Jack is standing on the roof of his house in kicked a rubber ball in the air for it to land on the ground for his dog Henry to fetch. The ball is launched into the air from a height of 12 feet at time t=0. The function that models the situation is h(f) = -2t^2 + 10t +12, where T is measured in seconds and H is the height in feet

When will the ball hit the ground

t = 6 seconds

Step-by-step explanation:

h(t) = -2t^2 + 10t +12

We want when h(t) =0

0 = -2t^2 + 10t +12

Divide each side by -2

0/-2 = -2/-2t^2 + 10/-2t +12/-2

0 = t^2 -5t -6

Factor

What two numbers multiply to -6 and add to -5

-6*1 = -6

-6+1 = -5

0 = (t-6) (t+1)

Using the zero product property

t-6 =0    t+1 = 0

t = 6      t= -1

We don't have negative time

t=6 seconds

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2