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Math Help - Yr 10 Maths Level 1:Quadratics Investigation

  1. #1
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    Exclamation Yr 10 Maths Level 1:Quadratics Investigation

    the equation is h=-0.4 d^2 + 2d.

    h=height above water, d=horizontal distance.

    Q1) how high above the water is the dolphin when it has travelled 2 m horizontally from its starting point?

    A1) h=-0.4 (2)^2 + (2)
    h=-1.6 + 2
    h=0.4m
    (im fairly sure that this is correct)

    Q2) what horizontal distance does the dolphin cover when it first reaches a height of 25cm?

    A2) 0.25=-0.4 d^2 + 2
    0.25 + 0.4 = d^2 + d
    0.65=d^2 +2
    square root of 0.65=d + d
    0.81= d+d
    0.81/2=d
    0.405m =d

    Q3) what horizontal distance does the dolphin cover when it next reaches a height of 25cm? explain.

    A3) i am unsure of this answer

    Q4)what horizontal distance does the dolphin cover in one leap? (hint:what is the value of h when the dolphin has completed the leap?)

    A4) i am unsure of this answer

    Q5) can this dolphin reach a height of:
    a)0.5 m
    b)1 during a leap?
    How can you work this out without actually solving the equation?

    A5) i am unsure of this answer

    Q6) find the greatest height that the dolphin reaches during its leap.

    A6) i am unsure of this answer

    CAN YOU PLEASE HELP ME WITH THIS INVESTIGATION!!!!!!!!!I NEED YOUR HELP SOON!!!!!!!!!!!!
    Last edited by CaptainBlack; August 17th 2008 at 06:09 AM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Rhyse View Post
    Q2) what horizontal distance does the dolphin cover when it first reaches a height of 25cm?

    A2) 0.25=-0.4 d^2 + 2
    0.25 + 0.4 = d^2 + d
    0.65=d^2 +2
    square root of 0.65=d + d
    0.81= d+d
    0.81/2=d
    0.405m =d
    You want to find d such that:

    0.25=-0.4d^2+2d

    rearrange:

    0.4d^2-2d+0.25=0

    which is a quadratic which you should solve using either the completing the square method or the quadratic formula, and assuming this has two positive roots you require the smaller of them. Q3 then askes for the other root.

    RonL
    Last edited by CaptainBlack; August 17th 2008 at 06:37 AM.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by Rhyse View Post
    the equation is h=-0.4 d^2 + 2d.

    h=height above water, d=horizontal distance.

    Q4)what horizontal distance does the dolphin cover in one leap? (hint:what is the value of h when the dolphin has completed the leap?)

    A4) i am unsure of this answer
    The question is asking you for the horizontal distance to the point at which the dolphin reenters the water.

    The dolphin enters/leaves the water when h=0, so you need to find d>0 so that:

    -0.4 d^2 + 2d=0

    which may be factorised to give:

    d(-0.4d+2)=0

    so the dolphin leaves the water when d=0 and re-enters the whater when (-0.4d+2)=0

    RonL
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by Rhyse View Post
    the equation is h=-0.4 d^2 + 2d.

    h=height above water, d=horizontal distance.

    Q5) can this dolphin reach a height of:
    a)0.5 m
    b)1 during a leap?
    How can you work this out without actually solving the equation?

    A5) i am unsure of this answer
    How high is the dolphin when d=1?

    RonL
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