While riding her bike, susan burns 450 calories every ½ hour. based on this

rate, how many calories will susan burn if she rides the bike for 1¾?

1575 calories

Step-by-step explanation:

Every an hour while riding her bike, Susan burns 450 calories.  

If the rate remains constant then within one hour riding her bike Susan will burn ( 450 × 2 ) = 900 calories.  

Now, it is asked to calculate the number of calories that Susan burns in hours bike riding.

Here, hours

Therefore, in hours she will burn calories. (Answer)

we don't have enough info to solve this

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