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Math Help - Quadratic Modelling

  1. #1
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    Exclamation Quadratic Modelling

    Here are some questions that i just don't understand, please show working out. Thanks

    Q1. ) A skateboard manufacturer finds that the cost $C of making X skateboards per day is given by C(x) = x^2-24x+244.
    a)How many skateboards should be made per day to minimise the cost of production?

    Q2) The driver of a car travelling downhill on a road applied the brakes. The speed (s) of the car in kmph, t seconds after the brakes were applied is given by s(t)= -4t^2 +12t+80.
    a) How fast was the car travelling when the driver applied the brakes?
    b) After how many seconds was the speed of the car 88 kmph? Can you explain your answer?
    c) After how many seconds did the car reach its maximum speed?
    d) What was the maximum speed reached?

    Q3.) The hourly profit ($P) obtained from operating a fleet of n taxis is given by P(n) = 84n-45-2n^2.
    a) What number of taxis gives the maximum hourly profit?
    b) What is the maximum hourly profit/
    c) HOw much money is lost per hour if no taxis are on the road?

    Q4.) The temperature T Celsius in a greenhour t hours after susk (7.00 pm) is given by T(t)= 1/4 t^2-5t+30, (t<20)
    a)what was the temperature in the greenhouse at dusk?
    b) At what time was the temperature at a minimum?
    c) What was the minimum temperature?




    Thanks guys, i just really need ot know how to do it pronto.
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  2. #2
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    Quote Originally Posted by Tessarina View Post
    Here are some questions that i just don't understand, please show working out. Thanks

    Q1. ) A skateboard manufacturer finds that the cost $C of making X skateboards per day is given by C(x) = x^2-24x+244.
    a)How many skateboards should be made per day to minimise the cost of production?

    Q2) The driver of a car travelling downhill on a road applied the brakes. The speed (s) of the car in kmph, t seconds after the brakes were applied is given by s(t)= -4t^2 +12t+80.
    a) How fast was the car travelling when the driver applied the brakes? Mr F says: Substitute t = 0.
    b) After how many seconds was the speed of the car 88 kmph? Can you explain your answer? Mr F says: Solve 88 = -4t^2 + 12t + 80.
    c) After how many seconds did the car reach its maximum speed?
    d) What was the maximum speed reached?

    Q3.) The hourly profit ($P) obtained from operating a fleet of n taxis is given by P(n) = 84n-45-2n^2.
    a) What number of taxis gives the maximum hourly profit?
    b) What is the maximum hourly profit/
    c) HOw much money is lost per hour if no taxis are on the road? Mr F says: Substitute n = 0.

    Q4.) The temperature T Celsius in a greenhour t hours after susk (7.00 pm) is given by T(t)= 1/4 t^2-5t+30, (t<20)
    a)what was the temperature in the greenhouse at dusk? Mr F says: Substitute t = 0.
    b) At what time was the temperature at a minimum?
    c) What was the minimum temperature?




    Thanks guys, i just really need ot know how to do it pronto.
    Since you did not post these in the calculus subforum I assume that a non-calculus approach is required to find the various maximums and minimums.

    In each part I left unanswered you're expected to know how to find the coordinates of the turning point of a parabola. Have you been taught how to do that? Where do you get stuck?
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  3. #3
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    The function y= (x-a)^2+ b has minimum value when x= a because if [tex]x\ne a[/itex] then x- a is non-zero and the square of any non-zero number is positive: if [tex]x-a \ne 0[/itex] then (x-a)^2+ b> b.

    Similarly the function [tex]y= -(x-a)^2+ b has maximum value at x= a.

    So for each of these problems complete the square!
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