College Algebra

7th Edition

ISBN: 9781305115545

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Question

Write an equation that expresses the following relationship.

w varies directly with u

and inversely with d

In your equation, use k

as the constant of proportionality.

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You should be able to complete these vocabulary and concept statements before you proceed to the practice excercises. Fill in the blanks. In the equation y=kx2z,y varies directly with ______ and inversely with _____.

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Find the constant of proportionality. I is inversely proportional to R. If R=20, then I=50.

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The resistance of a copper wire carrying an electrical current is directly proportional to its length and inversely proportional to its cross-sectional area. A copper wire with a diameter of 0.0126inch has a resistance of 64.9ohms per thousand feet. What length of 0.0201-inch-diameter copper wire will produce a resistance of 33.5ohms?

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Find the constant of proportionality. R is inversely proportional to the square of I. If I=25, then R=100.

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Find the unknown value. y varies inversely as the square of x and when x=3,y=2. Find y if x=1.

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Skidding in a Curve A car is traveling on a curve that forms a circular arc. The force F needed to keep the car from skidding is jointly proportional to the weight w of the car and the square of its speed s and is inversely proportional to the radius r of the curve. a Write an equation that expresses this variation. b A car weighing 1600 lb travels around a curve at 60 mi/h. The next car to round this curve weighs 2500 lb and requires the same force as the first car to keep from skidding. How fast is the second car traveling?

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Solve each problem. w is directly proportional to z. If w=-6 when z=2, find w when z=-3.

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A Jet of Water The power P of a jet of water is jointly proportional to the cross-sectional area A of the jet and to the cube of the velocity v. a Write an equation that expresses this variation. b If the velocity is doubled and the cross-sectional area is halved, by what factor is the power changed? c If the velocity is halved and the cross-sectional area is tripled, by what factor is the power changed?

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Filling a Tank The water level in a tank rises 4feet every minute. Write an equation of change that describes the height H, in feet, of the water level at time t in minutes.

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Electrical resistance The resistance of a wire varies directly as the length of the wire and inversely as the square of its diameter. A 1000-foot length of wire, 0.05 inch in diameter, has a resistance of 200 ohms. What would be the resistance of a 1500-foot length of wire that is 0.08 inch in diameter.

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The maximum weight M that can be supported by a beam is jointly proportional to its width w and the square of its height h and inversely proportional to its length L. a Write an equation that expresses this proportionality. b Determine the constant of proportionality if a beam 4 in. wide, 6 in. high, and 12 ft long can support a weight of 4800 lb. c If a 10-ft beam made of the same material is 3 in. wide and 10 in. high, what is the maximum weight it can support?

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