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Math Help - one more question

  1. #1
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    one more question

    I have this questions an answer to it would be great.
    .Q.1 At t minutes after an engine starts, the rate of fuel consumption is Rkg per minute. it is given by R=10+ 10/2t+1.
    a) Sketch R as a function of t
    b) find the rate of consumption after 7 mins
    c) find the limiting value of R as t becomes very large
    d) calculate the total consumption in the 1st 7 mins
    not sure how to do it
    Thank You
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  2. #2
    MHF Contributor
    Joined
    Apr 2005
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    Quote Originally Posted by bungy189 View Post
    I have this questions an answer to it would be great.
    .Q.1 At t minutes after an engine starts, the rate of fuel consumption is Rkg per minute. it is given by R=10+ 10/2t+1.
    a) Sketch R as a function of t
    b) find the rate of consumption after 7 mins
    c) find the limiting value of R as t becomes very large
    d) calculate the total consumption in the 1st 7 mins
    not sure how to do it
    Thank You
    R = 10 +[10 /(2t +1)]

    a) Sketch R as a function of t
    So, vertical axis is for R; horizontal axis is for t.
    Ordered pair is (t,R).

    When t = 0, R = 10 +[10/1] = 20, so, (0,20)
    When t = 1, R = 10 +[10/3] = 13.333, so, (1,13.333)
    When t = 2, R = 10 +[10/5] = 12, so, (3,12)
    Umm, it is not linear, because the differences foy R are not the same.
    When t = 10, R = 10 +[10/21] = 10.476, so, (10,10.476)

    I don't know how to draw here, but the the graph is a smooth curve that starts at (0,20) and decreasing as t becomes larger.
    You can do the sketch on paper. Plot all those solved ordered pairs or points, then run a smooth curve through them.
    The limit of the curve as t grows bigger is the horizontal line R = 10.

    b) find the rate of consumption after 7 mins
    R7 = 10 +[10 /(2*7 +1)] = 10 +[10/15] = 10.667 kg/min.

    c) find the limiting value of R as t becomes very large
    As mentioned in part (a), R = 10 kg/min.

    d) calculate the total consumption in the 1st 7 mins
    Umm, integration.

    Consumption, C = R*t
    C7 = INT.(0-->7)[R*dt]
    C7 = INT.(0-->7)[10 +10/(2t +1)] dt
    C7 = (10)INT.(0-->7)[1 +1/(2t +1)]dt
    C7 = 10[t +(1/2)ln(2t +1)]|(0-->7)
    C7 = 10{[7 +(1/2)ln(15)] -[0 +(1/2)ln(0+1)]
    C7 = 10[7 +(1/2)ln(15)]
    C7 = 83.54 kg ---------------answer.
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