A balloon filled with helium is being releases from the ground and is flying 17 points upward at a rate of 20 feet per second. An archer is challenged to shoot an arrow at the ballon and pop it. If the archer fires the arrow at an initial vertical velocity of 48 feet per second from an initial height of 6 feet, it is modeled by the equation h(t)=-16t^2-48t+6. At what time(s) could the arrow pop the ballon? Round to the nearest hundredth: > X = 20 x = 1.94 x = 3.67

the answer is y = 11.54

hope this : )

i think the length is 12 and the width is 17

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

combine all like terms then its just a 2 step equation