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 non-zero 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 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 with the product of two or more other variables. It can be expressed as z = kxy, where k is a non-zero constant.

Front

How do you identify Direct Variation from an equation?

Back

An equation represents direct variation if it can be written in the form y = kx, where k is a constant.

Front

How do you identify Inverse Variation from an equation?

Back

An equation represents inverse variation if it can be written in the form y = k/x, where k is a constant.

Front

How do you identify Joint Variation from an equation?

Back

An equation represents joint variation if it can be written in the form z = kxy, where k is a constant.

Front

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

Back

The constant of variation k is 5.

Front

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

Back

The frequency of a 5-foot string is 105 cycles per second.

Front

If the demand for a product varies inversely with its price, and the demand is 1250 when the price is $2.75, what is the demand when the price is raised to $4.00?

Back

The weekly demand is 859.4.

Front

The force of the wind varies jointly with the area and the square of the velocity. If a wind blowing at 50 mph exerts a force of 75 pounds on a surface of 500 ft², how much force will a wind of 75 mph place on a surface of 10 ft²?

Back

The force will be 3.375 pounds.