L. B. Johnson Middle School held a track and field event during the school year. Miguel took part in a four-person shot put team. Shot put is a track and field event where athletes throw (or “put”) a heavy sphere, called a “shot,” as far as possible. To determine a team score, the distances of all team members are added. The team with the greatest score wins first place. The current winning team’s final score at the shot put is 52.08 ft. Miguel’s teammates threw the shot put the following distances: 12.26 ft., 12.82 ft., and 13.75 ft. Exactly how many feet will Miguel need to throw the shot put in order to tie the current first-place score? Show your work.

11.25 ft

Step-by-step explanation:

To determine a team score, the distances of all team members are added.

The current winning team’s final score at the shot put is 52.08 ft.

So, in order to tie the score Miguel's team must equal the above score.

The total score before Miguel's throw was 12.26+12.82+13.75= 38.83 ft

so , Miguel will have throw 52.08-38.83= 11.25 ft in order to tie the score.

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