Calculus Volume 1

Chapter 5 | Integration

579

0

3.5 21 1.5

19 1.8 40 2.3

1

4.1 22 1.4

20 2.1 41

Table 5.8 Income Distributions Source : http://www.census.gov/ prod/2013pubs/p60-245.pdf a. Estimate the percentage of U.S. households in 2012 with incomes less than $55,000. b. What percentage of households had incomes exceeding $85,000? c. Plot the data and try to fit its shape to that of a graph of the form a ( x + c ) e − b ( x + e ) for suitable a , b , c . 238. Newton’s law of gravity states that the gravitational force exerted by an object of mass M and one of mass m with centers that are separated by a distance r is F = G mM r 2 , with G an empirical constant G =6.67 x 10 −11 m 3 / ⎛ ⎝ kg · s 2 ⎞ ⎠ . The work done by a variable force over an interval ⎡ ⎣ a , b ⎤ ⎦ is defined as W = ∫ a b F ( x ) dx . If Earth has mass 5.97219 × 10 24 and radius 6371 km, compute the amount of work to elevate a polar weather satellite of mass 1400 kg to its orbiting altitude of 850 km above Earth. 239. For a given motor vehicle, the maximum achievable deceleration from braking is approximately 7 m/sec 2 ondry concrete. On wet asphalt, it is approximately 2.5 m/sec 2 . Given that 1 mph corresponds to 0.447 m/sec, find the total distance that a car travels in meters on dry concrete after the brakes are applied until it comes to a complete stop if the initial velocity is 67 mph (30 m/sec) or if the initial braking velocity is 56 mph (25 m/sec). Find the corresponding distances if the surface is slippery wet asphalt. 240. John is a 25-year old man who weighs 160 lb. He burns 500−50 t calories/hr while riding his bike for t hours. If an oatmeal cookie has 55 cal and John eats 4 t cookies during the t th hour, how many net calories has he lost after 3 hours riding his bike? 241. Sandra is a 25-year old woman who weighs 120 lb. She burns 300−50 t cal/hr while walking on her treadmill. Her caloric intake from drinking Gatorade is 100 t calories during the t th hour. What is her net decrease in calories after walking for 3 hours?

2

5.9 23 1.3

3

5.7 24 1.3

4

5.9 25 1.1

5

5.4 26 1.0

6

5.5 27 0.75

7

5.1 28 0.8

8

4.8 29 1.0

9

4.1 30 0.6

10 4.3 31 0.6

11 3.5 32 0.5

12 3.7 33 0.5

13 3.2 34 0.4

14 3.0 35 0.3

15 2.8 36 0.3

16 2.5 37 0.3

17 2.2 38 0.2

18 2.2 39 1.8

Table 5.8 Income Distributions Source : http://www.census.gov/ prod/2013pubs/p60-245.pdf

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