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Mathematics: Post your doubts here!

Discussion in 'International A And AS Level' started by XPFMember, Sep 8, 2011.

  1. thestudyguy

    thestudyguy

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    its a sequence question so i dont think they will give marks for this
    btw there is no compound interest in the AS syllabus for maths
     
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  3. AAnsarii

    AAnsarii

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    Assalamu alaikum wa rahmatullah.
    I picked up math again after a long time.

    Pure Mathematics 1, by Hugh Neill and Douglas Quadling, Chapter 1, Miscellaneous exercise 1, questions 4, 20 and 22.
    4. A(7,2) and C(1,4) are two vertices of a square ABCD.
    a. Equation of the diagonal BD.
    b. Coordinates of B and D.

    For part a., I know the product of two diagonals is -1, but I can't get it
    Q 20 is similar, but a rhombus.

    22. Two lines have equations y=m1x+c1 and y=m2x+c2, and m1m2= -1. Prove that the lines are perpendicular.
    (PS for 22, I couldn't type the 1s and 2s in subscript, sorry.)

    Jazakumullahu khayr
     
  4. Hadi Murtaza

    Hadi Murtaza

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    a)
    m(AC) = (y₂ - y₁)/(x₂ - x₁)
    m(AC) = (4 - 2)/(1 - 7)
    m(AC) = 2/-6 = -1/3
    Therefore m(BD) would be = - 1/(-1/3) = 3

    The midpoints of both diagnols will be the same since they intersect.
    Midpoint = (x₁ + x₂)/2 , (y₁ + y₂)/2
    Midpoint = (7 + 1)/2 , (2 + 4)/2
    Midpoint = (4 , 3)

    Using point slope formula
    y - y₁ = m(x - x₁)
    y - 3 = 3(x - 4)
    y - 3 = 3x - 12
    [ y = 3x - 9 ]

    b)
    The distance from the midpoint to points B and D is the same as the distance from the midpoint to A and C.
    d² = (x - 4)² + (y - 3)²
    d² = (7 - 4)² + (2 - 3)²
    d² = 9 + 1
    d² = 10

    10 = (x - 4)² + (y - 3)²
    Substituting y = 3x - 9
    10 = (x - 4)² +(3x - 9 - 3)²
    10 = x² - 8x + 16 + 9x² - 72x + 144
    10x² - 80x + 150 = 0
    x² - 8x + 15 = 0
    (x - 5)(x - 3) = 0
    [ x = 5 , 3 ]

    y = 3x - 9
    y = 3(5) - 9 , 3(3) - 9
    [ y = 6 , 0 ]

    Hence B and D are (3 , 0) and (5 , 6)
     
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  5. Jenessa182

    Jenessa182

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    Hi could someone help me with this question:
    Simplify the following
    (n+1)!/n!
     
  6. Jenessa182

    Jenessa182

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    Hi, could someone help me with this question?
    Use the inductive definition to find the Pascal sequences for (a)n=5 (b) n=6 (c) n=8
     
  7. studyingrobot457

    studyingrobot457

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    will be n+1 , lets say n=3, (3+1)!=4!=24,3!=6,24/6=4
     
  8. Thought blocker

    Thought blocker

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    (n+1)! = (n + 1) * ( n)!
    therefore the answer to this question is (n + 1)
     
  9. krishnapatelzz

    krishnapatelzz

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