A hot air balloon is 10 meters above the ground and rising at a rate of 10.5 meters per minute. Another balloon is 250 meters above the ground and descending at a rate of 14 meters per minute.

a. Define variables for this problem.

x =

y =

b. Write a system of equations to represent the height of the balloons at any given time.

c. Put the equations into a graphing calculator. Use the calculator to solve the system of equations.

d. Explain what the solution means in the context of this problem.

I managed to get the variables down but the rest of the problem has me confused. I would really appreciate any help on this problem.

30005

yes ok                                            

sorry

step-by-step explanation:

sorry, but im pretty sure its a now that i look at it

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