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Math Help - Slopes of Secants

  1. #1
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    Slopes of Secants

    Flare is shot up with an upwards velocity of 30m/s
    The height of the flare is given by:
     <br />
h=-5t^{2}+30t+10<br />

    d) Determine the instantaneous velocity of the flare at t = 3 seconds by using the slopes of secants (1 mark for table, 2 marks for slopes)

    I'm not really sure what I'm suppose to do, I know how to get slopes of secants but I dont have any secants..... Can someone just help explain the question....thanks
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  2. #2
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    Quote Originally Posted by lil_cookie View Post
    Flare is shot up with an upwards velocity of 30m/s
    The height of the flare is given by:
     <br />
h=-5t^{2}+30t+10<br />

    d) Determine the instantaneous velocity of the flare at t = 3 seconds by using the slopes of secants (1 mark for table, 2 marks for slopes)

    I'm not really sure what I'm suppose to do, I know how to get slopes of secants but I dont have any secants..... Can someone just help explain the question....thanks
    1. Choose two values of t such that t = 3 is the mean of them. For instance:

    t_1 = 2
    t_2 = 4

    2. Now calculate h(2) = ... and h(4) = ...
    Calculate the slope between P_1(2, h(2)) and P_2(4, h(4)). This slope has the same value as the instantaneous velocity at t = 3.

    3. Remark: This method only works if you are dealing with parabolas

    4. Try if you get the same result if you use
    t_1 = 0
    t_2 = 6

    5. You should have got 0.
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