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Advanced Algebra II (H): Variation Functions
1. The arnount of force you must exert on a wrench handle to loosen a rusty bolt dep~ds on how
long the wrench handle is. Suppose that for a particular bolt, a wrench 7 inches long would
require a force of270 pounds, and a wrench 21 inches long would require 90 pounds.
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a. How does force vary with length? Write the general equation.
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b. Wfite the particular equation.
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c. Wh at are the units 0 t e proportiona ity constant.
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needed to loosen the bolt.)
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d. Find the force needed for wrenches with handles 3, 10, 15, 30 and 60 inches long.
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e. How long a wrench would be needed by Sarah Sota, who can exert a force of300 pounds?
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f. How long a wrench would be needed by Sarah's little sister Minnie, who can exert a force of.3i ..
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g. Plot a graph offorce versus handle length in the domain from 3 through 60 inches. Use
answers from above.
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2. The amount of refund you get for returning recyclable aluminum cans varies directly with the
number of cans you collect. The price per pound depends on supply and demand, but may be
assumed to be about 40 cents a pound (23 cans) L -:. $ "b ''''''''''''~
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a. Write the particular equation expressing number of cents of refund in terms of number of cans
you return. ?t:.
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b. How much refund woul
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you get for 100 cans?
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c. If you wanted to earn $100, how many cans would you have to return?
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3. A great white shark was caught off Catalina Island. The shark was
2000 pounds.
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5 feet long, and w*ghed
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a. Assuming that all great white sharks have similar proportions, how should the weight of a great
white shark vary with its length?
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b. Write the particular equation expressing weight in terms of length.
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c. Predict the weight of:
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ii. the shark in the novel Jaws, 25 feet long.
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d. If you caught a shark weighing 250 pounds, how long would you expect it to be?
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e. Fossilized teeth have been found in Florida that resemble those of a great white shark. If this
creature had the same proportions as present-day sharks, it would have been 1OU1'eetlong. How
much would such a shark have weighed?
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4. Tumors are sometimes treated by irradiating them with gamma rays from a radioactive source
such as cobalt-60. The intensity of radiation you receive depends on how fauou are from the
source. Suppose that for a particular source, the intensity is 80 mr/hr at 2 meters and 5 mr/hr at 8
meters. ("mrlhr" stands for "rnilliroentgens per hour." The work "roentgen" iSJJfOnQUDCed
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a. How does the intensity vary with distance? Write the general equation.
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b. Write the particular equation.
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c. Whaf-wot - the intensity be if your distance were
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d. At what distance would the intensity be 0.5 mr/hr?
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e. Plot the graph of this function.
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