An
equation is a mathematical statement indicating that two expressions are equal. The expressions can be numerical or algebraic. The equation is not inherently true or false, but only a proposition. The values that make the equation true, the solutions, are found using the properties of real numbers and other results. For example, the equation
has the unique solution
because when we substitute 3 for
in the equation, we obtain the true statement
A
formula is an equation expressing a relationship between constant and variable quantities. Very often, the equation is a means of finding the value of one quantity (often a single variable) in terms of another or other quantities. One of the most common examples is the formula for finding the area
of a circle in terms of the radius
of the circle:
For any value of
the area
can be found by evaluating the expression
Using a formula
A right circular cylinder with radius
and height
has the surface area
(in square units) given by the formula
See
[link] . Find the surface area of a cylinder with radius 6 in. and height 9 in. Leave the answer in terms of
A photograph with length
L and width
W is placed in a matte of width 8 centimeters (cm). The area of the matte (in square centimeters, or cm
2 ) is found to be
See
[link] . Find the area of a matte for a photograph with length 32 cm and width 24 cm.
Sometimes we can simplify an algebraic expression to make it easier to evaluate or to use in some other way. To do so, we use the properties of real numbers. We can use the same properties in formulas because they contain algebraic expressions.