The graph below shows the height of a projectile t seconds after it is launched. If acceleration due to gravity is -16 ft/s2
which equation models the height of the projectile correctly?
h(t) = at2 + vt + h0

Correct option: fourth one -> h(t) = -16t2 + 32v + 5

Step-by-step explanation:

To find the equation h(t) we need to find the values of a, v and h0.

The value of a is already given (a = -16).

Now, we just need to use two of the three points given to find the other parameters:

point (1,21): t = 1 and f(t) = 21:

21 = -16 + v + h0

point (0,5): t = 0 and f(t) = 5

5 = 0 + 0 + h0

h0 = 5

Using this value of h0 in the first equation, we have:

21 = -16 + v + 5

v = 21 + 16 - 5 = 32

So the equation is:

h(t) = -16t2 + 32v + 5

Correct option: fourth one.

$649.60

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