1) How many gallons of gasoline are used in the United States in one day? Assume
ID: 1273726 • Letter: 1
Question
1) How many gallons of gasoline are used in the United States in one day? Assume two cars for every three people, that each car is driven an average of 10,000 miper year, and that the average car gets 20 miles per gallon.
A. 8.9 x 10^7 gal/day
B. 4.5 x 10^9 gal/day
C. 1.1 x 10^8 gal/day
D. 2.8 x 10^8 gal/day
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A. For the vectors A? and B? in the figure (Figure 1) , use a scale drawing to find the magnitude of the vector sum A? +B?
express your answer using two significat figures
B. Find the direction of the vector sum A? +B? .
express your answer using two significat figures
C. Find the magnitude of the vector difference A? ?B?
express your answer using two significat figures
D. Find the direction of the vector difference A? ?B? .
express your answer using three significat figures
E. Use your answers to find the magnitude of ?A? ?B? .
Express your answer using two significant figures.
F. Find the direction of ?A? ?B? .
Express your answer using three significant figures.
G. Find the magnitude of B? ?A? .
Express your answer using two significant figures.
Explanation / Answer
1) D. 2.8 x 10^8 gal/day
Population: 300,000,000
Therefore # cars. 2/3 * 300,000,000 = 200,000,000
Avg distance per car = 10,000 miles per year = 10,000/365 =27.39 miles per day
Therefore distance travelled by all cars in USAdaily
= 200,000,000 * 27.39 = 5479452054.79 miles
Given 1 gallon gives 20 miles.
# of gallons used per day in USA = 5479452054.79 / 20 =273972602.7 gallons = 2.8*10^8 gallons/day
2)
A = 0 i - 8 j, B = 15sin(30) i + 15cos(30) j = 7.5 i + 13 j
A) A + B = 7.5 i + (-8 + 13) j = 7.5 i + 5 j
magnitude |A + B| = ?(7.52 + 52) = 9
B) direction: tan-1(5/7.5) = 33.7o
C) A - B = (0 - 7.5) i + (-8 - 13) j = -7.5 i - 21 j
magnitude |A - B| = ?(7.52 + 212) = 22.3
D) direction: 180 + tan-1(21/7.5) = 250o
E) -A - B = -(A+ B) = -(7.5 i + 5 j) = -7.5 i - 5 j
magnitude |-(A + B)| = ?(7.52 + 52) = 9
F) direction: 180 + tan-1(5/7.5) = 213.7o
G) B - A = -(A - B) = -(-7.5 i - 21 j) = 7.5 i + 21 j
magnitude |B - A| = ?(7.52 + 212) = 22.3
direction: tan-1(21/7.5) = 70o
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