Inverse Variation Functions & Solving Square Root Equations

Front

What is inverse variation?

Back

Inverse variation is a relationship between two variables where the product of the variables is constant. If x and y vary inversely, then k = xy, where k is a constant.

Front

How do you find the constant k in an inverse variation problem?

Back

To find the constant k in an inverse variation problem, multiply the values of x and y together (k = xy).

Front

If x = 5 and y = 20, what is the constant k?

Back

k = 5 * 20 = 100.

Front

What is the formula for inverse variation?

Back

The formula for inverse variation is y = k/x, where k is the constant.

Front

If y varies inversely with x and k = 48, what is the equation?

Back

The equation is y = 48/x.

Front

How do you solve for y when given x in an inverse variation equation?

Back

Substitute the value of x into the equation y = k/x to find y.

Front

If the time to fly varies inversely with speed, what does this imply?

Back

This implies that as speed increases, the time taken decreases, and vice versa.

Front

Given y = 54/x, what is the value of k?

Back

k = 54.

Front

If x = 7 when y = 4, how do you find x when y = 2?

Back

Use the constant k: k = xy. First, find k (k = 7 * 4 = 28). Then, set up the equation 28 = 2x and solve for x.

Front

What is the relationship between speed and time in inverse variation?

Back

In inverse variation, if one increases, the other decreases, maintaining a constant product.