7.5 Formulas. Formulas: a formula is an equation that relates one or more quantities to another quantity. Each of these quantities is represented by a.

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Presentation transcript:

7.5 Formulas

Formulas: a formula is an equation that relates one or more quantities to another quantity. Each of these quantities is represented by a variable, often the first letter of the word used to describe that quantity. For example the formula P = 2l + 2w shows how the perimeter (P) of a rectangle is related to the length (l) and width (w).

The relation between the variables is always expressed using mathematical operations. Formulas are extensively used in geometry, physics and business. We can find the value of any variable as long as we are given values of the other variables.

To solve a formula, replace the variables with their known values then solve the resulting equation as you would any equation. Given the formula A = bh, find A if b = 5 and h = 7. A = bh A = (5)(7) A = 35

Solve the formula for the unknown variable given the values for the other variables.

Sometimes it is useful to rewrite a formula by expressing one variable in terms of the others. To solve a formula for a given variable, we isolate that variable on one side of the equation using the same steps for solving equations.

Solve d = rt for r. Since the formula shows r times t we need to undo the multiplication by dividing by t.

Solve P = 2l + 2w for w Since the w involves multiplication and addition, we undo the addition first, then the multiplication.

Solve each formula for the variable indicated.

The length of a cylinder is given by where c is the constant 0.785, d is the diameter of the cylinder, and V is the volume of the cylinder. Find L if V = and d = 3.