Intermediate Algebra chapter 2 part 2

Formulas
Chapter 2,

Formulas

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 t

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 t

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 t

solve for t.

Answer: t =

d v

Subscripts

Subscripts are smaller numbers or letters placed to the lower right of letters.

Formulas often contain variables with subscripts.

Examples

x₁ is read "x sub 1" and 1 is the subscript.

R_k 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 2 BH	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 n ) 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 9 (F - 32)	Temperature conversion. F is degrees Fahrenheit C is degrees Centigrade