MTH 10905Algebra

FORMULAS

CHAPTER 2 SECTION 6

Simple Interest Formula

Formula is an equation commonly used to express a specific relationship mathematically.

Evaluate a formula is to substitute the appropriate numerical values for the variables and perform the operations.

Simple Interest Formula is used in banking

interest = (principal)(rate)(time)

i = prt

r and t are related in that r is given as annual interest rate and t is given in years

Use the Simple Interest Formula

EXP: How much simple interest would be owed on a $12,000 4-year loan at 6% simple interest?

i = prt i = (12,000)(0.06)(4)i = (720)(4)i = 2,880

The interest will be $2,880

Ask yourself is $2,880 realistic. $720 a year for 4 years

What is the total you will pay for the loan?

$12,000 + $2,880 = $14,880

Use the Simple Interest Formula

EXP: What was the principal on a 3-year, 5% loan is the simple interest was $300.00?

i = prt

300 = (p)(0.05)(3)300 = (0.15)(p)300 / 0.15 = p2000 = p

The Principal amount is $2,000

Use the Distance Formula

Distance Formula:

distance = (rate)(time)d = rt

EXP: Find the distance traveled if a car travels 3 hours at 62.5 mph.

d = rt

d = (62.5)(3)d = 187.5

The car traveled 187.5 miles.

Use the Distance Formula

EXP: How fast is a car traveling if it travels 84 miles in 1.5 hours?

d = rt

84 = (r)(1.5)84 / 1.5 = r56 = r

The car is traveling 56 mph.

Use Geometric Formulas

Perimeter is the sum of the lengths of the sides of a figure.Measured in centimeters, inches, or feet

Area is the total surface within the figures boundaries.Measured in square units, square centimeter, square inches, or square feet.

Quadrilateral is the general name for a four-sided figure.

Square s Area = s2 and Perimeter = 4s A = s2 P = 4s

Use Geometric Formulas – page 142

h

Rectangle Area = lw and Perimeter = 2l + 2w w A = lw P = 2l + 2w

l l = length and w = width

Triangle a c Area = ½ bh and Perimeter = a + b + c A = ½ bh P = a + b + c

b b = base and h = height

Circle Area = П r2 and Circumference = 2 П r r A= П r2 C = 2 П r

r = radius and П ≈ 3.14diameter is a line segment through the center of the circle and endpoints lie on the circle and the Circumference is the length of the curve

Use Geometric Formulas

EXP:A rectangle garden is 60 ft long by 15 ft wide.Find the perimeter and area.

w = 15

l = 60

Area = lw Perimeter = 2l + 2wA = (15)(60) P = 2(60) + 2(15)A = 900 ft2 P = 120 + 30

P = 150 ft

The area is in square feet because the formula involves multiplication of 2 linear dimensions. Example: (2ft)(3ft) = (2)(3)(ft)(ft) = 6 ft2

Use Geometric Formulas

EXP:A rectangle table has a perimeter of 216 inches. If the length is 72 inches find the width.

w = ?

l = 72

Perimeter = 2l + 2w 216 = 2(72) + 2(w) 216 = 144 + 2w216 – 144 = 2w 72 = 2w 36 = w

The width is 36 inches.

Use Geometric Formulas

h

A Triangular sign has an area of 6 ft2 Find the base of the sign if its height is 4 ft. a c

b

Area = ½ bh 6 = (½)(b)(4)6 = 2b3 = b The base is 3 ft.

b = base and h = height

Use Geometric Formulas

EXP:

Find the area and circumference of a pizza with a 10 inch diameter.

r ½ (d) = r½ (10) = r5 = r

A= П r2 C = 2 П rA = П (52) C = (2)(П )(5)A = П (25) C = П (10) A ≈ 78.5 C ≈ 31.4

r = radius and П ≈ 3.14

radius is ½ of the diameter.

Use Geometric Formulas – page 145

Volume is considered the space occupied by a figure. Measured in cubic units, cubic centimeter, cubic feet, and cubic inches. Used with three-dimensional figures. Volume is in cubic units because the formula involves multiplication of 3 linear dimensions. Exp: (2ft)(3ft)(4ft) = (2)(3)(4)(ft)(ft)(ft) = 24 ft3

Rectangular Solid: V = l w h Exp: Safe

Right Circular Cylinder: V = П r2 h Exp: Barrel

Right Circular Cone: V = 1/3 П r2 h Exp: Ice cream cone

Sphere: V = 4/3 П r3 Exp: ball

Use Geometric Formulas – page 145

Sphere: Find the volume of a ball with a diameter of 6 inches.

½ (d) = r½ (6) = r3 = r

V = 4/3 П r3 V = (4/3)( П ) ( 33 )V = (4/3)(27)( П ) V = 36 П V ≈ 113.10 in3

Volume is in cubic units because the formula involves multiplication of 3 linear dimensions. Exp: (2inches)(3inches)(4 inches) = (2)(3)(4)(inches)(inches)(inches) = 24 in3

Solving for a Variable in a Formula

To solve for a variable in a formula you treat each variable as it was a constant except for the one that you are solving.

Solve by isolating the variable you are solving to one side of the equation.

Exp: Simple Interest Formula

i = prt solve for p

ip

rt

Solving for a Variable in a Formula

Exp: Solve A = 2b + c for b

Exp: Solve for b

2

2

2

A b c

A c b

a cb

1

3R ab 1

3

33

3

R ab

abR

R ab

Rb

a

Solving for a Variable in a Formula

Slope intercept formy = mx + b

Write the equation 12x – 4y = 20 in slope intercept form

12 4 20

4 12 20

12 20

43 5

x y

y x

xy

y x

Solving for a Variable in a Formula

Write the equation in slope intercept form

1 1( 3)

2 3y x

1 11

2 3

1 11

3 2

1 1

3 2

y x

y x

y x

Remember

Pay attention to the units. Sometimes a unit conversion will be necessary before using a formula

When working with a formula, start with the general form and then substitute in known quantities.

Sometimes drawing a picture, when appropriate, may be helpful. Label all the known and unknown quantities.

HOMEWORK 2.6

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