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Tuesday, March 10, 2009

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Monday, March 9, 2009

Solving for unknowns

Question














Solve for x: | 4 - x | = 0
Solve for x: | x - 4 | + 3 = 9
Solve for x: | -3x + 4 | = | -x + 2 |
Solve for x: | x + 2 | = | 2 - x |




Solution
Solve for x: | 4 - x | = 0

  1. x=4

  2. Test


  • |4-4|=0
  • |0| = 0
  • 0 = 0

    Solve for x: | x - 4 | + 3 = 9


    1. |x-4|=9-3

    2. |x-4|=6

    3. x=-2

    4. x=10

    5. Test


  • x=-2

  • | -2 - 4 | + 3 = 9
  • | -6 | + 3 = 9
  • 6 + 3 = 9
  • 9 = 9
  • x=10
  • | x - 4 | + 3 = 9
  • | 10 - 4 | + 3 = 9
  • | 6 | + 3 = 9
  • 6 + 3 = 9
  • 9 = 9

    Solve for x: | -3x + 4 | = | -x + 2 |

    1. x=1

    2. Test


  • | -3*1 + 4 | = | -1 + 2 |
  • | -3 + 4 | = | 1 |
  • | 1 | = | 1 |
  • 1 = 1

    Solve for x: | x + 2 | = | 2 - x |

    1. x=0

    2. Test


  • | 0 + 2 | = | 2 - 0 |
  • | 2 | = | 2|
  • 2=2

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    Solving unknowns

    Question
    3-4k+5(k-6)=2
    Solve for k




    Solution

    1. 3-4k+5k-30=2

    2. 5k-4k+3-30=2

    3. k-27=2

    4. k=2+27

    5. k=29

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    Perimeter of a rectangle

    Question
    Rectangular garden is 85 meter long and 57 meter broad. Trees are to be planted around the garden at a distance of 5 meter having a distance of 4 meter the start. How many such trees can be planted




    Solution
    Procedure 1
  • compute for the perimeter of the rectangle that is available for tree planting
  • L: 85 meter - 4 meter = 81 meter
  • W: 57 meter 4 meter = 53 meter
    Procedure 2
  • The perimeter of a rectangle is computed by 2L + 2W
  • 2 (81 meter) + 2 (53 meter)
  • 162 meter + 106 meter = 268 meter
    Procedure 3
  • How many meters can be planted?
  • 268 meter / 5 meter = 53 trees

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  • Interest rate compounded continuous

    Question
    If you invest $6,700 in an account paying 8.5% compounded continuously, how much money will be in the account at the end of 4.5 years?



    Solution
    Solution 1
    Investment (1 + interest rate)time
    $6,700 (1.085)4.5
    $6,700 (1.44356)

    $9,671.83



    Solution 2







































    YearInvestmentInterestBalance
    1$6,700.00$569.501$7,269.50
    2$7,269.50$617.91$7,887.41
    3$7,887.41$670.23$8,557.64
    4$8,557.64$727.40$9,279.04
    4.5$9,279.04$394.36$9,673.40


    NOTE: The difference in the final answers are due to rounding off.
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