Formulas - Easy Mathematics Step-by-Step

Easy Mathematics Step-by-Step (2012)

Chapter 12. Formulas

In this chapter, you evaluate formulas.

Definition of Formula

A formula is a rule that shows the mathematical relationship that connects two or more variables. Formulas are used extensively in mathematics, the natural and social sciences, engineering, and numerous other areas in the real world. You use your skills in evaluating algebraic expressions to evaluate formulas.

Evaluating Formulas

The symbols and/or letters in a formula are variables (except for special constants like π and e). If you are given numerical values for the variables, you evaluate the formula by substituting the given numerical value for each variable and then performing the indicated operations, being sure to follow the order of operations as you proceed.

If units are involved, carry the units term along in the computation, when it makes sense to do so. When you add or subtract units, the sum or difference has the same units. When you square a unit (i.e., unit × unit), you get unit2. When you cube a unit (i.e., unit × unit × unit), you get unit3.

Problem Evaluate the formula to find the value of the indicated variable.

a. Find C when Image using the formula Image.

b. Find P when Image m using the formula Image.

c. Find positive value c when Image and Image using the formula Image.

d. Find A when Image ft and Image ft using the formula Image.

e. Find I when Image, Image per year, and Image yr using the formula Image.

f. Find A when Image yd using the formula Image. Use Image.

g. Find V when Image cm and Image cm using the formula Image. Use Image.

h. Find d when Image mi per hour and Image hr using the formula Image.

Solution

a. Find C when Image using the formula Image

Image Step 1. Substitute 212 for F in the formula Image

Image

Step 2. Evaluate.

Image

b. Find P when Image m using the formula Image.

Image Step 1. Substitute 8 m for s in the formula Image.

Image

Step 2. Evaluate.

Image

c. Find positive value c when Image and Image using the formula Image.

Image Step 1. Substitute 8 for a and 15 for b in the formula Image

Image

Step 2. Evaluate.

Image

To obtain c, you must find the positive square root of 289. From the list of square roots in Chapter 10, you have Image.

Thus, Image.

d. Find A when Image ft and Image ft using the formula Image.

Image Step 1. Substitute 10 ft for l and 4 ft for w in the formula Image.

Image

Step 2. Evaluate.

Image

e. Find I when P = $3000, r = 4% per year, and Image yr using the formula I = Prt.

Image Step 1. Substitute $3000 for P, Image for r, and 5 yr for t in the formula

Image

Put quantities that follow the word per in the denominator of a fraction.

Step 2. Evaluate.

Image

Notice that the “yr” units divide out, leaving “$” as the units for the answer.

f. Find A when Image yd using the formula Image Use Image.

Image Step 1. Substitute 6 yd for r and 3.14 for π in the formula Image.

Image

Step 2. Evaluate.

Image

g. Find V when Image cm and Image cm using the formula Image. Use Image.

Image Step 1. Substitute 2.5 cm for r, 11.5 cm for h, and 3.14 for π in the formula

Image

Step 2. Evaluate.

Image

Image

h. Find d when Image mi per hour and Image hr using the formula Image.

Image Step 1. Substitute Image for r and 5 hr for t in the formula Image.

Image

Step 2. Evaluate.

Image

Notice that the “hr” units divide out, leaving “mi” as the units for the answer.

Image Exercise 12

Evaluate the formula to find the value of the indicated variable.

1. Find C when Image using the formula Image.

2. Find P when Image m using the formula Image.

3. Find positive value c when Image and b = 24 using the formula Image.

4. Find A when Image ft and Image ft using the formula A = lw.

5. Find I when Image, r = 3% per year, and Image yr using the formula I = Prt.

6. Find A when Image yd using the formula Image Use Image.

7. Find V when Image ft and Image ft using the formula Image. Use Image.

8. Find A when Image and Image using the formula Image.

9. Find V when Image cm and Image cm using the formula Image. Use Image.

10. Find F when Image using the formula Image.