If x varies as y, and x = 4 when y = 8, find y when x = 15.
If p is directly proportional to q, and p = 5 when q = 30, find q when p = 15.
If s varies as r2, and s = 4 when r = 2, find s when r = 6.
If p is proportional to (r – 2), and p = 18 when r = 8, find p when r = 11.
If a, b, c are positive and, then b is called the mean proportional or the geometric mean.
Work out the geometric mean between each pair of numbers.
4 and 9
10 and 8
Prove that ad= bc when
.
Prove that
Prove
when and c d.
Show a + b varies directly as c when a and b vary directly as c.
Show yz varies directly as y2 + z2 when y and z varies directly as x.
Use the given values to write an equation relating x and y, where x and y vary inversely. Then find y when x = 3.
x = 7, y = –3
x = 5, y = 1
The variable z varies jointly with the product of x and y.
Find an equation that relates the variables x, y, and z.
The given values are
Use the given values to write an equation relating x, y and z, where z varies jointly with x and y. Then find z when x = –3 and y = 5.
x = 3/4, y = (2/9), z = 6
If c varies jointly with m and n, and n varies directly with s, show that c varies jointly with m and s.
Suppose t varies jointly with a and b, and t = 90 when a = 5 and b = 6. Find t when a = 6 and b = 5.
State whether x and y show direct variation, inverse variation, or neither.
xy = 12
y = x – 2
x = 7y
A paycheck varies directly with the number of hours worked.
Suppose the pay for 20 hours of work is $238.25.
What is the pay for 500 hours of work?
A pump empties a swimming pool in 60 minutes at the rate of 1500 L/min.
If the rate of pumping is 2500 L/min, how long does it take to empty the swimming pool?
The curved surface area of a cylinder varies jointly with the radius of its base and its height. Find the constant of variation.
The work W (in joules) done when lifting an object varies jointly with the mass m (in kg) of the object and the height h(in meters) that the object is lifted. The work done when a 140 kg object is lifted 1.6 meters is 2060.8 joules. Write an equation that relates W, m and h. How much work is done when lifting a 100 kg object 1.5 meters?
Suppose a single pane window with an area of 1 sq meter and a temperature difference of 1 Kelvin has a heat loss of 6.4 watts. What is the heat loss through a single–pane window with an area of 2.5 meters and a temperature difference of 20 Kelvin?
The distance that an object falls from rest varies directly as the square of the time it has fallen. If the object fell 2 ft during the first half second, how far did it fall during the next two seconds?
If a,b, c are positive and, then b is called the mean proportional or the geometric mean.
Prove that ad = bc when
Show a+ b varies directly as c when a and b vary directly as c.
Show yzvaries directly as y2 + z2 when y and z varies directly as x.
