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 _____.
Find the constant of proportionality. I is inversely proportional to R. If R=20, then I=50.
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?
Find the constant of proportionality. R is inversely proportional to the square of I. If I=25, then R=100.
Find the unknown value. y varies inversely as the square of x and when x=3,y=2. Find y if x=1.
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?
Solve each problem. w is directly proportional to z. If w=-6 when z=2, find w when z=-3.
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?
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.
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.
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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