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Math Help - Please help me with Word Function problem

  1. #1
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    Exclamation Please help me with Word Function problem

    An airplane is flying at a speed of 100 mi/h at an altitude of one mile and passes directly over a radar station at time t = 0.

    (a) Express the horizontal distance d (in miles) that the plane has flown as a function of t.
    d = 100t (I came up with this answer and it is correct)

    (b) Express the distance s between the plane and the radar station as a function of d.
    s = ???

    (c) Use composition to express s as a function of t.
    s = ???

    Please help me with the problems b and c. I don't understand what they are talking about. Like for d shouldn't the answer be 100d but the computer said it was incorrect. Please show your steps and explain how to solve these two problems (b) and (c). Thank you so much!
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  2. #2
    Senior Member Educated's Avatar
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    (b) Express the distance s between the plane and the radar station as a function of d.

    Since the plane has an altitude from the radar station of 1 mile, then you must use the pythagorus theorum:

    s^2 = d^2 + 1^2

    s = \sqrt{d^2 + 1^2}

    The answer would be 100d if the plane was on the same altitude as the radar station, but in this case it isn't.

    (c) Use composition to express s as a function of t.

    Now you know that d = 100t, so you substitute that into equation (b) to express s as a function of t.
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  3. #3
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    Thank you so much Educated for helping me with this problem!
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