Direct, Inverse and Joint Variation.notebook
February 28, 2014
Example of Direct Variation
Sections 8­1 & 8­2
Direct, Inverse & Joint Variation
Name
Direct Variation
Inverse Variation
Equation
Language
y = mx
y varies directly as x
xy = k or y = k
x
Joint Variation
If y varies directly as x, and y = 25 when x = 15, find x when y = 40.
Example: z = kxy
y varies inversely as x or y is inversely proportional to x
Example: z varies jointly as x and y
m and k are called the constant of variation
Example of Inverse Variation
Example of Joint Variation
If y varies inversely as q, and y = 22 when q = 6, find q when y = 15.
If r varies jointly as s and t and inversely as u, and r = 18 when s = 2, t = 3 and u = 4, find s when r = 6, t = 2 and u = 4.
Direct, Inverse and Joint Variation.notebook
Example of Direct Variation (Word Problem)
The amount of hydrogen produced when sodium is added to water varies directly as the amount of sodium added. If 92 grams of sodium produces 4 grams of hydrogen, find the amount of sodium needed to produce 10 grams of hydrogen.
February 28, 2014
Example of Inverse Variation (Word Problem)
For cones of equal volume, the height is inversely proportional to the square of the radius of the base. If the radius of a cone is 10 cm and its height is 15 cm, find the radius of a second cone of equal volume with a height of 60 cm.
Example of Joint Variation (Word Problem)
The surface area of a cylinder varies jointly as the radius and the sum of the radius and the height. A cylinder with height 8 cm and radius 4 cm has a surface area of 96π cm2. Find the surface area of a cylinder with radius 3 cm and height 10 cm.
Assignment #15
Page 354 #2 ­ 8 Even, Problems #4, 8, 10, 12, 16
Page 360 #2 ­ 10 Even, Problems #2, 4, 10, 12