F. Manipulating Formulas to Solve for a Desired Variable

The formula for the wind speed of a wind turbine is given on page 223, Question 13 in Principles of Mathematics 11.

Example 1 will show how to arrange the formula to isolate D, the density of the air.

Example 1

Given the formula for the wind speed of a wind turbine, isolate the density of the air, D.

, where S is the wind speed and P is the energy generated (in watts).

Step 1: Determine the restrictions on the variables D and P.
Assuming energy is always positive or zero, P ≥ 0. Assuming density is always positive, D > 0 (D cannot be 0 because that would involve division by zero, which is undefined).

Step 2: To 'undo' the cube root, cube both sides of the equation.

Step 3: The D is in the denominator. To 'undo' division by D, multiply both sides by D.

Step 4: To isolate D, multiplication by S3 is 'undone' by dividing both sides by S3 .

Because the formula was simply rearranged and no solution value was determined (or required), verification is not necessary.