Inverse variation With inverse variation the independent variable

Inverse variation With inverse variation the independent variable, x, appears in the denominator of the equation. An example is where k is the constant of variation. Types of inverse variation include: Linear: Quadratic: Cubic: Square root: y varies inversely as x y varies inversely as the square of x y varies inversely as the cube of x y varies inversely as the square root of x With all types of inverse variation as x increases, y decreases and when x decreases, y increases. y 1/x 2 y 1/x 3 y 1/ x

Example 1 The speed at which a web page downloads is inversely proportional to the number of people connected to the net. A page downloads at 30 kb/s when 6 people are connected. a) What speed would it download the page if 5 people are online? b) How many people were online if the page downloaded at 20 kb/s? write a proportion statement a) s 1/p b) s = 180/p 20 = 180/p k form an equation, s = /p 20 p = 180 add the constant of variation k p = 180 20 k sub in the initial values 30 = /6 p = 9 people solve for k k = 30 × 6 = 180 rewrite the equation s = 180/p answer the question s = 180/5 = 36 kb/s

Example 2 The intensity of the signal sent out by a data projector is inversely proportional to the square of the distance of the projector to the screen. At a distance of 3· 2 m the intensity is 450 candela (C). a) What is the intensity of light 4 m from the projector? b) How far from the screen is the projector if the intensity is 128 C ? write a proportion statement a) I 1/d 2 b) I = 4608/d 2 128 = 4608/d 2 k 2 form an equation, I = /d 128 d 2 = 4608 add the constant of variation k 2 = 4608 128 d sub in the initial values 450 = k/3· 22 d 2 = 36 d = 6 m solve for k k = 450 × 10· 24 = 4608 rewrite the equation I = 4608/d 2 answer the question I = 4608/42 = 288 C

Today’s work Exercise 12 G page 386 Q 1, 2, 8, 9, 11 to 15