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Math 252 – HomeWork #1 Name ___________________ Due: July 3, 2019

12/ 26/ 15 7:20 PMThe Widths (in Meters) Of A Kidney- shaped Swimming ... | Chegg.com

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The widths (in meters) of a kidney-shaped swimming pool were measured at 5-

meter intervals as indicated in the figure. Use Simpson's Rule to estimate the

area of the pool. (Round your answer to the nearest square meter.)

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1) You want to purchase a heater for your outdoor pool. The salesperson advises that to purchase the correct size heater you must know the (approximate) surface area of your pool. You and a friend take measurements every 3 meters and collect the lengths (in meters) given in the diagram below.

Explain several ways that you could use this information to approximate the surface area of your pool.

2) Annual coal production in the US (in quadrillion BTU per year) is given in the table. This is the rate of coal production and it is always increasing. It is NOT a total amount (note that the rate changes).

a) Draw a graph that represents this information where the t-axis represents the number of years since 1960 and the y-axis represents r(t) the rate of coal production at t years (since 1960). Label the axis! Continued on next page

b) What does the ordered pair (1965, 13.06) represent?

c) Give both an over and under-estimate of the amount of coal produced

between 1970 and 1975. Explain how you arrived at your estimates and what they mean geometrically (as an area). Particularly, show how your area relates to the graph of r(t).

d) Use a Riemann sum to estimate the coal production between 1960 and 1990 and represent the sum geometrically on your graph. Could you use a different Riemann sum to estimate the coal production (this is not simply a yes or no answer, explain)?

3) A bicyclist is pedaling along a straight road for one hour with a velocity v shown in the graph below. She starts out five kilometers from the lake and positive velocities take her toward the lake (negative velocities take her away from the lake). The vertical lines on the graph are at 10 minute (1/6 hour) intervals.

What can you determine about her distance from the lake at various times (be sure to explain how you know your answers)? Answer each of the following questions with short explanations.

a) When is she going the fastest?

b) How fast is she going then?

c) Toward the lake or away?

d) Does the cyclist ever turn around? If so, do you know at what time? Give time and Explain!

e) Do you know when she is closest to the lake? Can you approximate how close to the lake she gets? If so give your approximation. Explain your reasoning!

f) When is she farthest from the lake? Approximately how far from the lake is she then? Explain!