Presentation regarding Variations (Grade 8-9)

A PDF about Variations

1. REVIEW FOR SECOND QUARTER Prepared by: Mr Allan P. Limin

2. Variations Integral Exponents Radicals

3. Variations

4. Direct Variation y = kx or k =   Direct Square Variation y = or k =   Inverse Variation y = or k = xy   Joint Variation y = kxz or k =   Combined Variation y = or k =  

5. Graph

6. Direct Square Variation

7. Graph

8. y = kxz 20 = k (4)(3) 20 = k 12 k =   y = kxz y = ( )(2)(3) y = 10  

9. Problem: A. Write each in equation form. The volume V of a cylinder varies directly as its height h. The area A of a square varies directly as the square of its side s. The length l of a rectangular field varies inversely as its width w. The volume of cylinder V varies jointly as its height h and the square of the radius r. The electrical resistance R of a wire varies directly as its length l and inversely as the square of its diameter d.

10. V = kh 2. A = k   4. V = kh   3. l =   5. R = .   Answers

11. B. Find k and express the equation of variation. y varies directly as x and y=30 when x=8. x varies directly as the square of y, and x=6, when y=8. c varies jointly as a and b, and c=45, a=15 and b=14. x varies directly as y and inversely as z, when x=15, y=20 and z=40.

12. 1. y = kx 30 = k8 = k y = x   2. x = k 6 = k 6 = k64 = k x =   3 . c = kab 45 = k(15)(14) 45 = k 210 = k c = ab   4. x = 15 = 30 = k x =  

13. C . Solve for the indicated variable in each of the ff. If y varies directly as x, and y = -18 when x = 9, find y when x = 7. If y varies directly as the square of x, and y=36 when x=3, find y when x=5. z varies jointly as x and y, and z=60 when x=5, y=6, find z when x=7 and y=6. If r varies directly as s and inversely as the square of u, and r=2 when s=18 and u=2, find r when u=3 and s =27.

14. Answers!!! 1. y = kx -18 = k9 -2 = k y = (-2)(7) y = -14 2. y = k 36 =k 36 =k9 4 = k y = (4) y = 100   3 . z = kxy 60 = k(5)(6) 60 = k 30 2 = k z = (2)(7)(6) z = 84 4. r = 2 = = k r = r = r =  

15. Worded Problems Candies are sold at 50 centavos each. How much will a bag of 420 candies cost? y = kx .50 = k1 .50 = k y = (.50)(420) y = ₱ 210.00 = = = ₱210.00  

16. 2. When a body falls from rest, its distance from the s tarting point is directly proportional to the square o f the time during which it is falling. In 2 seconds, a b ody falls through 19.57 meters. How far will it fall i n 5 seconds? d = k 19.57 = k 19.57 = k4 4.8925 = k d = (4.8925) d = 122.31   = = = 489.25 = 122.31  

17. 3 . The mass of a rectangular sheet of wood varies jointly as the length and the width. When the length is 20 cm and the width is 10 cm, the mass is 200 g. Find the mass when the length is 15 cm and the width is 10 cm. m = klw 200 = k(20)(10) 200 = k200 1 = k m = (1)(15)(10) m = 150 grams = = 200 = 30,000 150 grams  

18. 4 . The current I varies directly as the electromotive force E And inversely as the resistance R. If in a system a current of 20 amperes flows through a resistance of 20 ohms with an Electromotive force of 100 volts, find the current that 150 volts will send through the system. I = 20 = 400 = k100 4 = k   I = I = I = 30   = = 60,000 = 2,000 30 =  

19. Integral Exponent

20. Laws of Exponents 1. Product of Powers:   2. Power of a Power: =   3 . Power of a Product:   4. Power of a Monomial:   5. Quotient of Powers: =  

21. 6. Power of a Fraction: ( =   7. Zero Exponent:   8 . Negative Exponent:   9. Rational Exponent: or =  

22. Evaluate: (   1.   2.   3. 8   4.   5 . 100 6.   7.   8.   9.  

23. Radicals

24. Definition: If a is a nonnegative real number, the nonnegative number b such that = a is the principal square root of a and Is denoted by b = .  

25. Example:

26. Example:

27. Example:

28. Example:

29. The equivalent of Simplify Evaluate Simplify ( Simplify 2 + 3 + 4 + 2 Simplify + + - 10 Multiply (4 (3 ) Find the product of ( )( ) Rationalize the denominator of Divide:   Evaluate:   3     1/16 18 + 14   -41   24     2