Direct, Inverse, Joint Variations

Front

What is direct variation?

Back

Direct variation is a relationship between two variables where an increase in one variable results in a proportional increase in the other variable. It can be expressed as y = kx, where k is a constant.

Front

What is inverse variation?

Back

Inverse variation is a relationship between two variables where an increase in one variable results in a proportional decrease in the other variable. It can be expressed as xy = k, where k is a constant.

Front

What is joint variation?

Back

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

Front

If y varies directly with x, and y = 10 when x = 2, what is the value of y when x = 5?

Back

y = 25.

Front

If x varies inversely with v, and x = 35 when v = 3, what is the value of x when v = 15?

Back

x = 7.

Front

The weight of a liquid varies directly as its volume. If the weight of the liquid in a cubical container 5 cm on a side is 250 g, what is the weight of the liquid in a cubical container 3 cm on a side?

Back

54 g.

Front

The frequency of a vibrating string varies inversely as its length. If a 3-foot string vibrates at 175 cycles per second, what is the frequency of a 5-foot string?

Back

105 cycles.

Front

What is the formula for direct variation?

Back

y = kx, where k is a constant.

Front

What is the formula for inverse variation?

Back

xy = k, where k is a constant.

Front

What is the formula for joint variation?

Back

z = kxy, where k is a constant.