11. While playing basketball Jessica shoots an air-ball. The height h in feet of the ball is given by h(t) = -16t2 + 32t +8, where h(t) represents the height in feet after t seconds. How long will it take the ball to hit the ground?

seconds

Step-by-step explanation:

h(t) = -16t² + 32t +8

0 = -16t² + 32t +8

0 =-0.125(-16t² + 32t+8)

0=2t²-3t-1

0=2t²-2t-t-1

Group

0=(2t²-2t)(-t-1)

0=2t(t-1)-1(t+1)

0=(2t-1)(t-1)(t+1)

0=2t-1                                        0=t-1                             0=t+1

1/2(1)=(2t)1/2                              0+1=t-1+1                        0-1=t+1-1

0.5=t                                            1=t                                 -1=t

t=0.5                                             t=1                                  t=-1

6.63 ft

Step-by-step explanation:

In this case we use pythagora's theorem which is

= +

in this case, the hypotenuse (hyp) is the length of the ladder, the opposite (opp) is the height of the tree house and, the adjacent (adj) is the distance of the ladder's bottom to the base of the tree.

hpy = 12 ft

opp = 10 ft

adj = ?

substituting into the equation above, we have

= +

144 = + 100

144 - 100 = 44 =

the image is shown below

adj = = 6.63 ft