| 1. If your car now gets 21 mpg of gas and you can go 250 miles on a tank of
gasoline, how far could you drive with the same amount of gasoline with a car the
gets 35 mpg?
2. If
y is inversely proportional to the square of x, and y has the value 1.55 when x is
7.38, find y when x is 44.2.
3. If y is
inversely proportional to the cube root of x, by what factor will y change when x is
tripled?
4. The power
needed to drive a ship varies directly as the cube of the speed of the ship and a 77.4hp
engine will drive a certain ship at 11.2 knots, find the horsepower needed to propel that
ship at 18.0 knots.
5. If
y varies jointly as w and x, and y is 3.85 when w is 8.36 and x is 11.6, evaluate the
constant of proportionality and write the complete expression for y in terms of w and x.
Round result to nearest hundredth.
6. The work
(W) done on a spring varies as the square of the distance (d) it is extended beyond rest.
If 2-joules of work extends the spring 2-m beyond rest, find the relationship between W
and d.
7. The
intensity (I) of light varies inversely as the square of its distance (r) from the source.
If the intensity is 20 lumens at 2-ft, what is the intensity at 4-ft?
8. If the
force (F) on an object varies directly as its mass (m) and inversely as the square of the
distance (r) the object is from the point and the force is 200-N when the mass is 4-kg and
its distance is 2-m, find the force when the mass is 2-kg and the distance is 4-m.
9. If y
varies as the square root of x and inversely as the cube of z, what is the effect on y if
x is quadrupled and z is halved?
10. The
power available in a jet of liquid is directly proportional to the cross-sectional area of
the jet and to the cube of the velocity. By what factor will the power increase if the
area and velocity are both increased by 50%.
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