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Calculus
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17 Nov 2019

show steps pls how to get this answer

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    10 Feb 2019
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    Normal Probability The mean height of American men between 20 and 29 years old is 69 inches, and the standard deviation is 3 inches. A 20- to 29-year-old man is chosen at random from the population. The probability that he is 6 feet tall or taller is

    (Source: National Center for Health Statistics)

    (a) Use a graphing utility to graph the integrand. Use the graphing utility to convince yourself that the area between the x-axis and the integrand is 1.

    (b) Use a graphing utility to approximate .

    (c) Approximate using a graphing utility. Use the graph in part (a) to explain why this result is the same as the answer in part (b).

    Many airlines restrict the size of carry on item in terms of theircombined length, width and height (L+W+H).
    I am due to fly on an airline that states "The sum of the length,the width and height of your item must be at most 70 inches".
    Suppose I want to take a box (cuboid) on my trip that will allow meto carry on as much as possible, and that I also want this box tohave a square base.
    The questions we will answer using optimization are: Whatdimensions should the box have, and what would be the resultingmaximum volume

    a.If the base of the box is a square whose sides have length x, andthe height of the box is h (both measured in inches), enterexpressions for the volume of the box, V, and the sum of thelength, width and height of the box in terms of x and h.
    V :

    Sum L+W+H :


    b.Since the sum of the length, width and height must be less thanor equal to 70 inches, and it is clearly best to choose this sum toequal 70 inches, write down the constraint equation.
    Rearrange the constraint equation to give the height of the box, h,in terms of the length of the base, x

    h =

    c.What is the objective function for this problem?
    Using the constraint equation, rewrite the objective function interms of x alone

    V =

    d.Differentiate V with respect to x, to find the derivative dV /dx.
    =

    e.Find the values of x for which we have a potential relativeextreme point of V.

    One of these is at x = 0, and the other occurs when x is equal towhat value?

    (Give your answer, and those that follow, correct to two decimalplaces.)

    x =

    For this question, you need not show that this is actually arelative maximum point. (But you should know how you would dothis.)

    f.Now that you know the length of the base of the box, what is itsheight?
    height : inches

    g.What is the maximum volume of the box?
    volume : cubic inches

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