Algebra
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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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Algebra

Algebra

Upward Bound Math and Science

RahulRaghunathan


Problem 1

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

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,


Solution 11

Solution 1

Sine 12 = 0.21


Problem 2

Problem 2


Problem 3

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$?


Solution 3

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


Problem 4

Problem 4

  • Find the Discriminant of

    V + 4V + 9 = 0


Solution 4

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


Problem 5

Problem 5

  • Add (4j+8) and (8j+3)


Solution 5

Solution 5

  • Add the like terms from the quantities above

  • (4j+8) + (8j+3)

    = ( 4j+8j) + ( 8+3)

    = 12j+ 11


Problem 6

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.


Solution 6

Solution 6

  • C. I = A-P

    =


Solution 61

Solution 6

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


Problem 7

Problem 7

  • What is the center of the circle

    x2 + y2 -144 = 0 ?


Solution 7

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)


Problem 8

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


Solution 8

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 =


Solution 81

Solution 8

  • Variance = 658.56

  • Standard Deviation =


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