Math 101 Intermediate Algebra

Chapter 2, Section 2

A formula is a general representation of an equation (or relationship).

A formula will have many variables and few specific numbers in it.

Example:   v = d
is a formula for speed where v is the speed, d is the distance, and t is the time.

Evaluating Formulas
Given:  the formula.
Given:  values for all but one variable.

Goal:  determine the value of the unknown variable for the given variable values.

Example:  evaluate v = d
when d = 300 miles and t = 5 hours.

Answer: v = 300 miles
  5  hours
 = 60 mph.

Solving for One Variable of a Formula
Given:  the formula.

Asked to:  solve for a particular variable.

Goal:  isolate the particular variable on the left hand side with everything else on the right hand side.

Example:  given v = d
solve for t.

Answer: t = d

Subscripts are smaller numbers or letters placed to the lower right of letters.
Formulas often contain variables with subscripts.

x1 is read "x sub 1" and 1 is the subscript.
Rk is read "R sub k" and k is the subscript.

Some Greek Letters (and Common Meanings)
Greek letters are often used in formulas.
Some greek letters have meanings that are usually associated with them.

Letter Meaning
(small pi) a constant (see to 1000 places)
(small theta) an angle
(capital sigma) summation of many
(capital pi) product of many

Some Common Formulas

Formula Use
A = r2 Area of a circle.
r is the radius
C = 2r Circumference of a circle.
r is the radius
A = LW Area of a rectangle.
L is length, W is width
P = 2L + 2W Perimeter of a rectangle.
L is length, W is width
A = 1
Area of a triangle.
B is base length, H is height
a2 + b2 = c2 Pythagoean theorem for a right triangle.
a, b lengths of legs
c length of hypotenuse
A = Prt Simple interest.
A is interest earned,
P is the principal,
r is the interest rate (decimal),
t is time
A = P(1 + r
) nt
Compound interest.
A is interest earned,
P is principal,
r is interest rate (decimal),
n is number of times interest is paid per year,
t is time in years
A = Rt Rates.
A is amount, R is rate, t is time
d = vt Distance and speed.
d is distance, v is speed, t is time
C = 5
(F - 32)
Temperature conversion.
F is degrees Fahrenheit
C is degrees Centigrade