Results 1 to 3 of 3

Math Help - proportion and modulus function

  1. #1
    Junior Member
    Joined
    Jun 2008
    Posts
    53

    proportion and modulus function

    1.The braking distance of a car is directly proportional to the square of its speed. When the speed is p metres per second, the braking distance is 6m. When the speed is increased by 300%, find
    a)an expression for the speed of the car
    b)the braking distance
    c)the percentage increase in the braking distance

    2.Solve |x^2+3x-4|=6

    for 1(a), what i tried to do was,
    let braking distance be d, speed be s and constant be k.
    d=ks^2
    6=kp^2
    k=\frac{6}{p^2}
    speed increased by 300%,
    d=ks^2
    s=\sqrt{\frac{d}{\frac{6}{p^2}}}
    this doesn't seem right..........==

    for question2, is there a way to solve it without drawing the graph??
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Sep 2009
    Posts
    32
    for question 2, yes you can solve it with calculations
    it isnt much different to a regular quadratic without the absolute values, you just have to tweak it a little to get rid of them

    |x^2 + 3x - 4| = \sqrt{(x^2 + 3x - 4)^2}

    did you get that far?

    = 6 , so then square both sides

    (x^2 + 3x - 4)^2 = 36 , now root both sides (get consent first, always)

    (x^2 + 3x - 4) = 6 or -6 (you understand that bit?)

    so we now have 2 sets of solutios, which ill split up
    (x^2 + 3x - 4) = 6 , (x^2 + 3x - 4) = -6
    x^2 + 3x - 10 = 0 , x^2 + 3x + 2 = 0
    (x + 5)(x - 2) = 0 , (x + 2)(x + 1) = 0

    so all up

    x = -5 , 2, -2 and -1
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by wintersoltice View Post
    1.The braking distance of a car is directly proportional to the square of its speed. When the speed is p metres per second, the braking distance is 6m. When the speed is increased by 300%, find
    a)an expression for the speed of the car
    b)the braking distance
    c)the percentage increase in the braking distance
    d=kv^2

    So if d_1, d_2 denote two stopping distances corresponding to speeds v_1 and v_2 respectivly:

    \frac{d_1}{d_2}=\frac{v_1^2}{v_2^2}

    We are told that if the speed is p m/s then the breaking distance is 6m and are asked to find the speed when the speed is 3\times 6=18 m.

    So put d_1=6, v_1=p, v_2=3p then:

    \frac{6}{d_2}=\frac{p^2}{9p^2}

    So:

    d_2=\frac{9}{6}

    or:

    ....

    CB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Modulus of function help
    Posted in the Algebra Forum
    Replies: 5
    Last Post: January 9th 2012, 04:19 PM
  2. [SOLVED] Inverse proportion/Direct proportion question
    Posted in the Statistics Forum
    Replies: 3
    Last Post: September 26th 2011, 07:22 AM
  3. help with modulus function
    Posted in the Algebra Forum
    Replies: 1
    Last Post: November 7th 2009, 02:25 PM
  4. modulus and linear function
    Posted in the Algebra Forum
    Replies: 1
    Last Post: November 5th 2009, 06:10 AM
  5. Replies: 3
    Last Post: July 6th 2009, 07:25 PM

Search Tags


/mathhelpforum @mathhelpforum