The path of a race will be drawn on a coordinate grid like the one shown below. The starting point of the race will be at (−5.4, 3). The finishing point will be at (3, −5.4). A four-quadrant coordinate grid is drawn from negative 4 to positive 4. Quadrant I is labeled Quadrant P, Quadrant II is labeled Quadrant Q, Quadrant III is labeled Quadrant R, and Quadrant IV is labeled Quadrant S.

Part A: Use the grid to determine in which quadrants the starting point and the finishing point are located. Explain how you determined the locations. (6 points)

Part B: A checkpoint will be at (5.4, 3). In at least two sentences, describe the difference between the coordinates of the starting point and the checkpoint, and explain how the points are related. (4 points)

The path of a race will be drawn on a coordinate grid like the one shown below. The starting point of the race will be at (−5.5, 2). The finishing point will be at (2, −5.5).

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