If y varies inversely as x, and y = 32 when
x = 3, find x when y = 15.
Complete
Solution
The frequency of a vibrating guitar string
varies inversely as its length. Suppose a
guitar string 0.65 meters long vibrates 4.3
times per second. What frequency would a
string 0.5 meters long have?
Complete
Solution
If r varies inversely as the cube of s, and r
= 17 when s = 3, find r when s = 2.
Complete
Solution
If g varies inversely as the square root of h,
and g = 9 when h = 121, find g when h =
81.
Complete
Solution
The current in a simple electrical circuit is
inversely proportional to the resistance. If
the current is 80 amps when the resistance
is 50 ohms, find the current when the
resistance is 22 ohms.
Complete
Solution
The intensity of light produced by a light
source varies inversely as the square of the
distance from the source. If the intensity of
light produced 3 feet from a light source is
750 foot-candles, find the intensity of light
produced 5 feet from the same source.
Complete
Solution
If y varies directly as x and inversely as z,
and y = 22 when x = 4 and z = 6, find y
when x = 10 and z = 25.
Complete
Solution
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?
Complete
Solution
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.
Complete
Solution
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?
Complete
Solution
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.
Complete
Solution
The centrifugal force of an object moving
in a circle varies jointly with the radius of
the circular path and the mass of the object
and inversely as the square of the time it
takes to move about one full circle. A 6
gram object moving in a circle with a
radius of 75 centimeters at a rate of 1
revolution every 3 seconds has a
centrifugal force of 5000 dynes. Find the
centrifugal force of a 14 gram object
moving in a circle with radius 125
centimeters at a rate of 1 revolution every
2 seconds.
Complete
Solution
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.
Complete
Solution
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.
Complete
Solution
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?
Complete
Solution
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?
Complete
Solution
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 = 9 and c = 225.
Complete
Solution
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.
Complete
Solution
If y varies directly as x and inversely as z,
and y = 22 when x = 4 and z = 6, find y
when x = 10 and z = 25.
Complete
Solution
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?
Complete
Solution
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.
Complete
Solution
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?
Complete
Solution
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.
Complete
Solution
The centrifugal force of an object moving
in a circle varies jointly with the radius of
the circular path and the mass of the object
and inversely as the square of the time it
takes to move about one full circle. A 6
gram object moving in a circle with a
radius of 75 centimeters at a rate of 1
revolution every 3 seconds has a
centrifugal force of 5000 dynes. Find the
centrifugal force of a 14 gram object
moving in a circle with radius 125
centimeters at a rate of 1 revolution every
2 seconds.
Complete
Solution