Direct, Inverse, Joint Variations

Front

What is direct variation?

Back

Direct variation is a relationship between two variables where one variable is a constant multiple of the other. It can be expressed as y = kx, where k is a non-zero constant.

Front

What is inverse variation?

Back

Inverse variation is a relationship between two variables where the product of the two variables is a constant. It can be expressed as y = k/x, where k is a non-zero constant.

Front

What is joint variation?

Back

Joint variation is a relationship where a variable varies directly as the product of two or more other variables. It can be expressed as z = kxy, where k is a non-zero constant.

Front

If f varies directly as x and f = 20 when x = 4, what is f when x = 10?

Back

f = 50.

Front

If y varies inversely as x and y = 3 when x = 2, what is y when x = 6?

Back

y = 1.

Front

The volume of a cylinder varies directly with its height and the square of its radius. If the volume is 100 cm³ when the height is 5 cm and the radius is 2 cm, what is the volume when the height is 10 cm and the radius is 3 cm?

Back

Volume = 450 cm³.

Front

What is the formula for direct variation?

Back

y = kx, where k is the constant of variation.

Front

What is the formula for inverse variation?

Back

y = k/x, where k is the constant of variation.

Front

What is the formula for joint variation?

Back

z = kxy, where k is the constant of variation.

Front

If the weight of a liquid varies directly as its volume and the weight is 200 g for a volume of 4 L, what is the weight for a volume of 10 L?

Back

Weight = 500 g.