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## Sunday, 24 March 2013

### 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 = dt
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 = dt
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 = dt
solve for t.
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.
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.
LetterMeaning
(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
FormulaUse
A = r2Area of a circle.
C = 2rCircumference of a circle.
A = LWArea of a rectangle.
L is length, W is width
P = 2L + 2WPerimeter of a rectangle.
L is length, W is width
 A = 12 BH
Area of a triangle.
B is base length, H is height
a2 + b2 = c2Pythagoean theorem for a right triangle.
a, b lengths of legs
c length of hypotenuse
A = PrtSimple interest.
A is interest earned,
P is the principal,
r is the interest rate (decimal),
t is time
 A = P(1 + rn ) 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 = RtRates.
A is amount, R is rate, t is time
d = vtDistance and speed.
d is distance, v is speed, t is time
 C = 59 (F - 32)
Temperature conversion.
F is degrees Fahrenheit