MTH 10905 Algebra

1. MTH 10905Algebra formulas CHAPTER 2 Section 6

2. 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

3. 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 = 2,880The interest will be $2,880Ask yourself is $2,880 realistic. $720 a year for 4 yearsWhat is the total you will pay for the loan?$12,000 + $2,880 = $14,880

4. 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 = pThe Principal amount is $2,000

5. 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 = 187.5The car traveled 187.5 miles.

6. 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 = rThe car is traveling 56 mph.

7. 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

8. Use Geometric Formulas – page 142 • Rectangle Area = lw and Perimeter = 2l + 2ww A = lw P = 2l + 2wl 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 rr = 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 h

9. 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

10. 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 = 2w72 = 2w 36 = w The width is 36 inches.

11. Use Geometric Formulas • 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 bh6 = (½)(b)(4)6 = 2b3 = b The base is 3 ft. h b = base and h = height

12. Use Geometric Formulas EXP: Find the area and circumference of a pizza with a 10 inch diameter. r ½ (d) = r ½ (10) = r 5 = r A= П r2 C = 2 П r A = П (52) C = (2)(П )(5) A = П (25) C = П (10) A ≈ 78.5 C ≈ 31.4r = radius and П ≈ 3.14radius is ½ of the diameter.

13. 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 = Пr2hExp: Barrel • Right Circular Cone: V = 1/3П r2 h Exp: Ice cream cone • Sphere:V = 4/3П r3 Exp: ball

14. Use Geometric Formulas – page 145 • Sphere: Find the volume of a ball with a diameter of 6 inches. ½ (d) = r ½ (6) = r 3 = r V = 4/3П r3V = (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

15. 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 Formulai = prt solve for p

16. Solving for a Variable in a Formula • Exp: Solve A = 2b + c for b • Exp: Solve for b

17. Solving for a Variable in a Formula • Slope intercept form y = mx + b • Write the equation 12x – 4y = 20 in slope intercept form

18. Solving for a Variable in a Formula • Write the equation in slope intercept form

19. 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.

20. HOMEWORK 2.6 • Page 148 - 150 #11, 13, 14, 19, 24, 28, 47, 49, 51, 52, 57, 60, 64, 67, 73, 85, 99