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Algebra

Algebra. Upward Bound Math and Science Rahul Raghunathan. Problem 1. You are walking up a 500. meter high hill. The trail has an incline of 12 degrees. How far will you walk to get to the top?. Solution 1.

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Algebra

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  1. Algebra Upward Bound Math and Science RahulRaghunathan

  2. Problem 1 You are walking up a 500. meter high hill. The trail has an incline of 12 degrees. How far will you walk to get to the top?

  3. Solution 1 • We know angle A (12 degrees) and the length of the opposite side (500. m). We want to know the length of the hypotenuse (H), so we will use the formula • Sine = • Substituting in the appropriate values,

  4. Solution 1 Sine 12 = 0.21

  5. Problem 2

  6. Problem 3 • A member on speak series allows people to join for 11$ then pay 1$ for every event attended. What is the maximum events one can attend for a total of 46$?

  7. Solution 3 • We write the equation that shows the cost of speaker series related to number of events attended ( a) 46 = 1. a + 11 46 = a + 11 35 = a

  8. Problem 4 • Find the Discriminant of V + 4V + 9 = 0

  9. Solution 4 • Discriminant formula is b2 – 4 (a)(c) Where a = 1, b = 4 and C = 9 Substituting we get = 42-4(1)(9) = 16-36 = -20

  10. Problem 5 • Add (4j+8) and (8j+3)

  11. Solution 5 • Add the like terms from the quantities above • (4j+8) + (8j+3) = ( 4j+8j) + ( 8+3) = 12j+ 11

  12. Problem 6 • The population of an industrial town is increasing by 5% every year. If the present population is 1 million, estimate the population five years hence.

  13. Solution 6 • C. I = A-P =

  14. Solution 6 • Present population, P = 1 million, rate of increase = 5% per annumHence population after 5 years = = 1000000 (1·05)5                   = 1276280

  15. Problem 7 • What is the center of the circle x2 + y2 -144 = 0 ?

  16. Solution 7 • The standard equation of a circle is ( x-h)2 + (y-k)2 = r2 Now comparing with given equation we get ( x-0)2 + (y-0)2 = (12)2 The Center of the circle is (0,0)

  17. Problem 8 • A wedding planner placed orders with a florist five times in the last year . What is the standard deviaton of the number of flowers needed • 70 Flowers , 90 Flowers , 21 Flowers , 63 Flowers , 91 Flowers

  18. Solution 8 • Mean = = 67.12 Variance = (70-67.12)2 + (91-67.12)2+ (21-67.12)2+ (63-67.12)2+ (91-67.12)2 =3292.8 Varience =

  19. Solution 8 • Variance = 658.56 • Standard Deviation =

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