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# Integrated Math 2 Section 3-8

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Equations with Squares and Square Roots

Equations with Squares and Square Roots

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• 1. SECTION 3-8 Equations with Squares and Square Roots
• 2. ESSENTIAL QUESTIONS • How do you solve problems involving squares? • How do you solve problems involving square roots? • Where you’ll see this: • Physics, safety, engineering, mechanics
• 3. VOCABULARY 1. Inverse of an Operation:
• 4. VOCABULARY 1. Inverse of an Operation: The opposite of an operation
• 5. VOCABULARY 1. Inverse of an Operation: The opposite of an operation Addition and subtraction
• 6. VOCABULARY 1. Inverse of an Operation: The opposite of an operation Addition and subtraction Multiplication and division
• 7. QUESTION What is the opposite of squaring?
• 8. EXAMPLE 1 Solve each equation. Check the solution. 2 4 a. x = 2 b. x − 225 = 0 9
• 9. EXAMPLE 1 Solve each equation. Check the solution. 2 4 a. x = 2 b. x − 225 = 0 9 2 4 x =± 9
• 10. EXAMPLE 1 Solve each equation. Check the solution. 2 4 a. x = 2 b. x − 225 = 0 9 2 4 x =± 9 2 x=± 3
• 11. EXAMPLE 1 Solve each equation. Check the solution. 2 4 a. x = 2 b. x − 225 = 0 9 +225 +225 2 4 x =± 9 2 x=± 3
• 12. EXAMPLE 1 Solve each equation. Check the solution. 2 4 a. x = 2 b. x − 225 = 0 9 +225 +225 2 2 4 x = 225 x =± 9 2 x=± 3
• 13. EXAMPLE 1 Solve each equation. Check the solution. 2 4 a. x = 2 b. x − 225 = 0 9 +225 +225 2 2 4 x = 225 x =± 9 2 x = ± 225 2 x=± 3
• 14. EXAMPLE 1 Solve each equation. Check the solution. 2 4 a. x = 2 b. x − 225 = 0 9 +225 +225 2 2 4 x = 225 x =± 9 2 x = ± 225 2 x = ±15 x=± 3
• 15. EXAMPLE 1 Solve each equation. Check the solution. 2 c. 3 x +1= 3 d. 24 = v
• 16. EXAMPLE 1 Solve each equation. Check the solution. 2 c. 3 x +1= 3 d. 24 = v −1 −1
• 17. EXAMPLE 1 Solve each equation. Check the solution. 2 c. 3 x +1= 3 d. 24 = v −1 −1 3 x =2
• 18. EXAMPLE 1 Solve each equation. Check the solution. 2 c. 3 x +1= 3 d. 24 = v −1 −1 3 x =2 3 3
• 19. EXAMPLE 1 Solve each equation. Check the solution. 2 c. 3 x +1= 3 d. 24 = v −1 −1 3 x =2 3 3 2 x= 3
• 20. EXAMPLE 1 Solve each equation. Check the solution. 2 c. 3 x +1= 3 d. 24 = v −1 −1 3 x =2 3 3 2 x= 3 2 2  2 ( x) =   3
• 21. EXAMPLE 1 Solve each equation. Check the solution. 2 c. 3 x +1= 3 d. 24 = v −1 −1 3 x =2 3 3 2 x= 3 2 2  2 4 ( x) =   3 x= 9
• 22. EXAMPLE 1 Solve each equation. Check the solution. 2 c. 3 x +1= 3 d. 24 = v −1 −1 2 ± 24 = v 3 x =2 3 3 2 x= 3 2 2  2 4 ( x) =   3 x= 9
• 23. EXAMPLE 1 Solve each equation. Check the solution. 2 c. 3 x +1= 3 d. 24 = v −1 −1 2 ± 24 = v 3 x =2 3 3 v = ± 24 2 x= 3 2 2  2 4 ( x) =   3 x= 9
• 24. EXAMPLE 1 Solve each equation. Check the solution. 2 c. 3 x +1= 3 d. 24 = v −1 −1 2 ± 24 = v 3 x =2 3 3 v = ± 24 2 x= or 3 2 2  2 4 ( x) =   3 x= 9
• 25. EXAMPLE 1 Solve each equation. Check the solution. 2 c. 3 x +1= 3 d. 24 = v −1 −1 2 ± 24 = v 3 x =2 3 3 v = ± 24 2 x= or 3 2  2 2 4 v ≈ ±4.898979486 ( x) =   3 x= 9
• 26. EXAMPLE 1 Solve each equation. Check the solution. 2 e. c = f. 7w −10 = 4 3
• 27. EXAMPLE 1 Solve each equation. Check the solution. 2 e. c = f. 7w −10 = 4 3 2 2  2 ( c) =   3
• 28. EXAMPLE 1 Solve each equation. Check the solution. 2 e. c = f. 7w −10 = 4 3 2 2  2 ( c) =   3 4 c= 9
• 29. EXAMPLE 1 Solve each equation. Check the solution. 2 e. c = f. 7w −10 = 4 3 +10 +10 2 2  2 ( c) =   3 4 c= 9
• 30. EXAMPLE 1 Solve each equation. Check the solution. 2 e. c = f. 7w −10 = 4 3 +10 +10 2 2  2 7w =14 ( c) =   3 4 c= 9
• 31. EXAMPLE 1 Solve each equation. Check the solution. 2 e. c = f. 7w −10 = 4 3 +10 +10 2 2  2 7w =14 ( c) =   3 2 ( 7w ) =14 2 4 c= 9
• 32. EXAMPLE 1 Solve each equation. Check the solution. 2 e. c = f. 7w −10 = 4 3 +10 +10 2 2  2 7w =14 ( c) =   3 2 ( 7w ) =14 2 4 c= 7w =196 9
• 33. EXAMPLE 1 Solve each equation. Check the solution. 2 e. c = f. 7w −10 = 4 3 +10 +10 2 2  2 7w =14 ( c) =   3 2 ( 7w ) =14 2 4 c= 7w =196 9 7 7
• 34. EXAMPLE 1 Solve each equation. Check the solution. 2 e. c = f. 7w −10 = 4 3 +10 +10 2 2  2 7w =14 ( c) =   3 2 ( 7w ) =14 2 4 c= 7w =196 9 7 7 w = 28
• 35. EXAMPLE 2 The velocity v of a satellite moving in a circular orbit near the surface of Earth is given by the formula v = gr , where g represents the force of gravity and r represents the radius of Earth. Given that g = 9.8 m/sec2 and v = 7.91X103 m/sec, determine the radius of Earth to the nearest meter.
• 36. EXAMPLE 2 The velocity v of a satellite moving in a circular orbit near the surface of Earth is given by the formula v = gr , where g represents the force of gravity and r represents the radius of Earth. Given that g = 9.8 m/sec2 and v = 7.91X103 m/sec, determine the radius of Earth to the nearest meter. v = gr
• 37. EXAMPLE 2 The velocity v of a satellite moving in a circular orbit near the surface of Earth is given by the formula v = gr , where g represents the force of gravity and r represents the radius of Earth. Given that g = 9.8 m/sec2 and v = 7.91X103 m/sec, determine the radius of Earth to the nearest meter. v = gr 3 7.91×10 = 9.8r
• 38. EXAMPLE 2 3 7.91×10 = 9.8r
• 39. EXAMPLE 2 3 7.91×10 = 9.8r 7910 = 9.8r
• 40. EXAMPLE 2 3 7.91×10 = 9.8r 7910 = 9.8r 2 2 7910 = ( 9.8r )
• 41. EXAMPLE 2 3 7.91×10 = 9.8r 7910 = 9.8r 2 2 7910 = ( 9.8r ) 62568100 = 9.8r
• 42. EXAMPLE 2 3 7.91×10 = 9.8r 7910 = 9.8r 2 2 7910 = ( 9.8r ) 62568100 = 9.8r 9.8 9.8
• 43. EXAMPLE 2 3 7.91×10 = 9.8r 7910 = 9.8r 2 2 7910 = ( 9.8r ) 62568100 = 9.8r 9.8 9.8 r = 6384500
• 44. EXAMPLE 2 3 7.91×10 = 9.8r 7910 = 9.8r 2 2 7910 = ( 9.8r ) 62568100 = 9.8r 9.8 9.8 r = 6384500 The radius of Earth is about 6384500 meters.
• 45. HOMEWORK
• 46. HOMEWORK p. 138 #1-51 odd “If ﬁfty million people say a foolish thing, it is still a foolish thing.” - Anatole France