In these lessons, we will learn about indirect variation and how to solve applications that involve indirect variation.Related Topics:
There are many situations in our daily lives that involve inverse variation (indirect variation).
For example, the number of days required to build a bridge is varies inversely to the number of workers. As the number of workers increases, the number of days required to build would decrease.
In general, when two variables x and y are such that
xy = k where k is a non-zero constant, we say that y varies inversely with x.
In notation, inverse variation is written as
Suppose that y varies inversely as x and that y = 8 when x = 3.
a) Form an equation connecting x and y.
b) Calculate the value of y when x = 10.
i.e. xy = k where k is a non-zero constant
a) Substitute x = 3 and y = 8 into the equation to obtain k
3 × 8 = k ⇒ k = 24
The equation is xy = 24
b) When x = 10, 10 × y = 24 ⇒ y =
Suppose that y varies inversely as x 2 and that y = 10 when x = .
a) Find the equation connecting x and y .
b) Find the value of y when x = 3.
i.e. yx2 = k
a) Substitute x = and y = 10 into the equation to obtain k
The equation is yx2 =
b) When x = 3,
This video defines inverse variation and shows how to solve some inverse variation problems.
y varies inversely as x. y = 4 when x = 2. Determine the inverse variation equation. Then determine y when x = 16.
The time, t, required to empty a tank varies inversely as the rate, r, of pumping. If a pump can empty a tank in 2.5 hours at a rate of 400 gallons per minute, how long will it take to empty a tank at 500 gallons per minute?
The force, F, needed to break a board varies inversely with the length, L, of the board. If it takes 24 pounds of pressure to break a board 2 feet long, how many pounds of pressure would it take to break a board that is 5 feet long?
y varies inversely as the square root of x. y = 6 when x = 16. Determine the inverse variation equation. Then determine y when x = 4.
This video provides an example of how to solve a basic inverse variation problem.
y varies inversely as x. y = 3 when x = 10. Determine the inverse variation equation. Then determine y when x = 6.
Given m varies inversely as t, and m = 9 when t = 6, find the variation constant and the inverse variation equation. Then determine m when t = 27.
This video provides an example of how to solve a inverse variation problem when k is a fraction
y varies inversely as x. y = 1/2 when x = 2/3. Find the variation constant and the inverse variation equation. Then determine y when x = 2/15.
On a string instrument, the length of a string varies inversely as the frequency of its vibrations. An 11-inch string has a frequency of 400 cycles per second. Find the constant of proportionality and the frequency of a 10-inch string.
The following video gives some practical examples of direct variation and indirect/inverse variation.
This video looks at inverse variation: identifying inverse variations from ordered pairs, writing inverse variation equations, graphing inverse variations, and finding missing values. It includes several examples.