This must be on the moon as the acceleration due to gravity in this equation must be around 1/8 that on earth. :) Anyway...
h=-2t^2+9t+11
A)
dh/dt=-4t+9, when velocity, dh/dt=0, it is the maximum height reached
dh/dt=0 only when 4t=9, t=2.25 seconds
h(2.25)=21.125 ft (21 1/8 ft)
B)
As seen in A), the time of maximum height was 2.25 seconds after the squirrel jumped.
C)
The squirrel reaches the ground when h=0...
0=-2t^2+9t+11
-2t^2-2t+11t+11=0
-2t(t+1)+11(t+1)=0
(-2t+11)(t+1)=0, since t>0 for this problem...
-2t+11=0
-2t=-11
t=5.5 seconds.
The unit rate here is 2 pounds of trash in an hour. If two pounds of trash are picked up in an hour, we can multiply that by 3 and get that there will be 6 pounds picked up in 3 hours.
The quantity 5 more than a number t is labeled as (5+t)
Product of 9 and the quantity is labeled as = 9(5+t) which equals 45+9t
Result is less than 6 so the equation becomes
45+9t < 6
I think the answer is -7/4.
