Name______________________________________________ Period______
Date__________
Variation #2
Find the value of K and write a general formula to describe each variation. Solve each problem.
1.
If p varies jointly as q and r squared, and p = 225 when q = 4 and r = 3, find p
when q = 6 and r = 8.
2.
If y varies jointly as x and z, and y = 33 when x = 9 and z = 12, find y when x = 16 and z = 22.
3.
If f varies jointly as g and the cube of h, and f = 200 when g = 5 and h = 4, find f when g = 3
and h = 6.
4.
If p varies directly as the square of q and inversely as the square root of r, and p = 60 when q =
6
and r = 81, find p when q = 8 and r = 144.
5.
If y varies jointly as x and z, and y = 12 when x = 9 and z = 3, find z when y = 6 and x = 15.
6.
If a varies jointly as b and c and inversely as the square of d, and a = 120 when b = 5, c = 2,
and d = 9, find a when b = 12, c = 9 and d = 9.
7.
14.
If a varies jointly as b cubed and c, and a = 36 when b = 4 and c = 6, find a when b = 2 and c =
8.
If a varies jointly as b and the square root of c, and a = 21 when b = 5 and c = 36,
find a when b = 8 and c = 225.
Identify each variable in your problem. Find the value of K and write a general formula to describe
each variation. Solve each problem and round your final answer to the nearest integer. Write a
concluding statement and label your answer with appropriate units.
9.
Wind resistance varies jointly as an object’s surface area and velocity. If an object traveling at
40 mile
per hour with a surface area of 25 square feet experiences a wind resistance of 225 Newtons,
how fast
must a car with 40 square feet of surface area travel in order to experience a wind resistance
of 270
Newtons?
10.
For a given interest rate, simple interest varies jointly as principal and time. If $2000 left in an
account for 4 years earns interest of $320, how much interest would be earned in if you
deposit
$5000 for 7 years?
11.
The volume of a pyramid varies jointly as its height and the area of its base. A pyramid with a
height of
12 feet and a base with area of 23 square feet has a volume of 92 cubic feet. Find the volume
of a
pyramid with a height of 17 feet and a base with an area of 27 square feet.
12.
The volume of a cone varies jointly as its height and the square of its radius. A cone with a
radius of 6
inches and a height of 10 inches has a volume of 120π cubic inches. Find the volume of a
cone having a
radius of 15 inches and a height of 7 inches.
13.
Kinetic energy varies jointly as the mass and the square of the velocity. A mass of 8 grams
and a
velocity of 5 centimeters per second has a kinetic energy of 100 ergs. Find the kinetic energy
for a
mass of 6 grams and a velocity of 9 centimeters per second.
14.
The volume of gas varies directly as the temperature and inversely as the pressure. If the
volume is 230 cubic centimeters when the temperature is 300ºK and the pressure is 20 pounds
per square centimeter, what is the volume when the temperature is 270 ºK and the pressure is
30 pounds per square centimeter?
15.
The maximum load that a cylindrical column with a circular cross section can hold varies
directly as the fourth power of the diameter and inversely as the square of the height. A 9
meter column 2 meters in diameter will support 64 metric tons. How many metric tons can be
supported by a column 9 meters high and 3 meters in diameter?
16.
The electrical resistance of a wire varies directly as its length and inversely as the square of its
diameter. A wire with a length of 200 inches and a diameter of one-quarter of an inch has a
resistance of 20 ohms. Find the electrical resistance in a 500 inch wire with the same
diameter.