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Nutka1998 [239]
3 years ago
9

A ball is thrown into the air with an upward velocity of 48 ft/s. Its height h in feet after t seconds is given by the function

h = -16t^2 + 48t + 6. How long does it take the ball to reach its maximum height? What is the ball's maximum height?
Mathematics
1 answer:
Mila [183]3 years ago
6 0
So you have to find the velocity (or first derivative) from the position function of h=-16t^2+48t+6

the velocity is -32t+48 which you then have to set equal to 0 in order to find t
-32t+48=0
-32t=-48
t=1.5

you then take your t value and sub it back into your original position function
-16(1.5)^2+48(1.5)+6 which will give you a maximum height of 42 feet

so the time it takes is 1.5 seconds to reach a maximum height of 42 feet
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The correct format of the question is

At the end of 2006, the population of Riverside was 400 people. The population for this small town can be modeled by the equation below, where t represents the number of years since the end of 2006 and P represents the number of people. P = 400 ( 1.2 )^ t Based on this model, approximately what was the increase in the population of Riverside at the end of 2009 compared to the end of 2006?

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