In this lesson, we will learn about indirect variation and how to solve applications that involve indirect variation.
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.
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.
This video looks a inverse variation: identifying inverse variations from ordered pairs, writing inverse variation equations, graphing inverse variations, and finding missing values. It includes several examples.
|Direct Variation||Joint and Combined Variation|
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