G9 Math Q2- Week 1- Types of Variation.ppt
- 2. ‘’ illustrates situations that involve the following variations: (a) direct; (b) inverse; (c) joint; (d) combined’’ Objective
- 3. Types of Variation Direct Variation: y varies directly as x. As x increases, y also increases. As x decreases, y also decreases. Equation for Direct Variation: y = kx Inverse Variation: y varies inversely as x. As x increases, y decreases. As x decreases, y increases. The product of x and y is always constant. Equation for Inverse Variation: xy = k Joint Variation: z varies jointly as x and y. As x and y increases, z also increases. As x and y decrease, z also decreases. Equation for Joint Variation: y = kxz
- 6. Determine whether the relation between the quantities involved is direct or inverse variation. 1. The number of workers and the time required to finish an amount of work. 2. The number of workers and the amount of worked finished. 3. The height of a person and his weight. Inverse Direct Direct
- 7. Steps in solving problems involving variations Write the equation or formula Solve for the value of k Give the equation of variation Solve for the unknown value
- 8. EXAMPLE 1. a is directly proportional to b. if a = 10 and b = 2. Find a if b = 4. Formula: a = kb Solve for k: k = 5 Equation of variation: a = 5b Solve for the unknown value: a = 5b a = 5(4) a = 20
- 9. EXAMPLE 2. If y varies inversely as x and y = 10 when x = 2, find y when x = 10. Formula: Solve for k: k = 20 Equation of variation: Solve for the unknown value: y = 2
- 10. EXAMPLE 3. d varies jointly as h and g. if d = 5 when h = 14 and g = 5, find g when h = 3 and d = 84. Formula: d = khg Solve for k: k = 1/14 Equation of variation: d = 1/14hg Solve for the unknown value: d = 1/14hg 84 = 14(3)g g = 2 84 = 42g
- 11. EXAMPLE 4. If z varies directly as x and inversely as y, and z = 9 when x = 6 and y = 2, find z when x = 8 and y = 12. Formula: Solve for k: k = 3 Equation of variation: Solve for the unknown value: z = 2
- 12. EXAMPLE 4. If z varies directly as x and inversely as y, and z = 9 when x = 6 and y = 2, find z when x = 8 and y = 12. Formula: Solve for k: k = 3 Equation of variation: Solve for the unknown value: z = 2
- 13. EXAMPLE 4. If z varies directly as x and inversely as y, and z = 9 when x = 6 and y = 2, find z when x = 8 and y = 12. Formula: Solve for k: k = 3 Equation of variation: Solve for the unknown value: z = 2
- 14. Evaluation Direct Variation: Direct Variation: If the cost of 5 apples is $10, what is the cost of 15 If the cost of 5 apples is $10, what is the cost of 15 apples if the cost varies directly with the number of apples if the cost varies directly with the number of apples purchased? apples purchased? A) $10 A) $10 B) $30 B) $30 C) $15 C) $15 D) $50 D) $50 In a car rental service, the rental fee is $30 per day. In a car rental service, the rental fee is $30 per day. How much will it cost to rent the car for 4 days? How much will it cost to rent the car for 4 days? A) $120 A) $120 B) $60 B) $60 C) $90 C) $90 D) $40 D) $40
- 15. Evaluation Inverse Variation: Inverse Variation: If it takes 8 workers to complete a task in 6 hours, how If it takes 8 workers to complete a task in 6 hours, how many workers are needed to complete the same task in many workers are needed to complete the same task in 4 hours if the variation is inverse? 4 hours if the variation is inverse? A) 12 A) 12 B) 2 B) 2 C) 3 C) 3 D) 16 D) 16 If the speed of a car is inversely proportional to the If the speed of a car is inversely proportional to the time it takes to travel a certain distance, and it takes 4 time it takes to travel a certain distance, and it takes 4 hours to travel 240 miles, what is the speed of the car? hours to travel 240 miles, what is the speed of the car? A) 60 mph A) 60 mph B) 30 mph B) 30 mph C) 120 mph C) 120 mph D) 15 mph D) 15 mph
- 16. Evaluation Joint Variation: Joint Variation: If the volume of a cube is jointly proportional to the length of If the volume of a cube is jointly proportional to the length of one side (edge) and the square of its width, and a cube with a one side (edge) and the square of its width, and a cube with a side length of 4 inches has a volume of 64 cubic inches, what is side length of 4 inches has a volume of 64 cubic inches, what is the volume of a cube with a side length of 6 inches and a width the volume of a cube with a side length of 6 inches and a width of 3 inches? of 3 inches? A) 144 cubic inches A) 144 cubic inches B) 216 cubic inches B) 216 cubic inches C) 256 cubic inches C) 256 cubic inches D) 324 cubic inches D) 324 cubic inches The amount of work done by a group of workers is jointly The amount of work done by a group of workers is jointly proportional to the number of workers and the time they work. proportional to the number of workers and the time they work. If 6 workers can complete a job in 8 hours, how long will it take If 6 workers can complete a job in 8 hours, how long will it take for 9 workers to complete the same job? for 9 workers to complete the same job? A) 4 hours A) 4 hours B) 6 hours B) 6 hours C) 9 hours C) 9 hours D) 12 hours D) 12 hours
- 17. Evaluation Answers: Answers: B) $30 B) $30 A) $120 A) $120 C) 3 C) 3 B) 30 mph B) 30 mph B) 216 cubic inches B) 216 cubic inches B) 6 hours B) 6 hours B) $90 B) $90 C) 240 square feet C) 240 square feet
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