A baton twirler releases a baton at a height of 5 feet above the ground with the initial velocity of 30 feet per second. The height of the baton , t seconds after it is thrown is given by the function, h(t)=−16t2+30t+5, where h(t) is the height of the baton in feet. How high is the baton after 1.5 second? Round your answer to the nearest hundredth, if applicable.

How long does it take for the baton to reach its maximum height? Round your answer to the nearest hundredth, if applicable.

What is the maximum height of the baton? Round your answer to the nearest hundredth, if applicable.

step-by-step explanation:

18.8cm hope i at all

step-by-step explanation:

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt