PLEASE I NEED THIS ANSWERED ASAP The density of apple juice is 1.05 grams per cm3. The density of fruit syrup is 1.4 grams per cm3. The density of carbonated water is 0.99 grams per cm3. 25 cm3 of apple juice are mixed with 15 cm3 of fruit syrup and 280 cm3 of carbonated water to make a drink with a volume of 320 cm3. Work out the density of the drink. Give your answer correct to 2 decimal places. (4 marks)

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

c.

step-by-step explanation: