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Math Help - Another function model.

  1. #1
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    Another function model.

    I really can't figure out what this problem is telling me to do. I've tried for the last 20 minutes but I just don't know how to make the function and I don't know where to start. Please help!

    * * *

    A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions W inches by L inches by cutting out equal squares of side x at each corner and then folding up the sides. (W = 14 in. and L = 25 in).



    (a) Find a function that models the volume V of the box.

    (b) Find the values of x for which the volume is greater than 240 in3. (Give each answer correct to three decimal places.)

    (c) Find the largest volume that such a box can have. (Round your answer to three decimal places.)

    * * *

    Thank you in advance for your help!
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  2. #2
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    Re: Another function model.

    Quote Originally Posted by FatimaA View Post
    I really can't figure out what this problem is telling me to do. I've tried for the last 20 minutes but I just don't know how to make the function and I don't know where to start. Please help!

    * * *

    A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions W inches by L inches by cutting out equal squares of side x at each corner and then folding up the sides. (W = 14 in. and L = 25 in).



    (a) Find a function that models the volume V of the box.

    (b) Find the values of x for which the volume is greater than 240 in3. (Give each answer correct to three decimal places.)

    (c) Find the largest volume that such a box can have. (Round your answer to three decimal places.)

    * * *

    Thank you in advance for your help!
    length of the box = 25-2x

    width of the box = 14-2x

    height of the box = x

    Volume of the box = (length of the box)(width of the box)(height of the box)
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  3. #3
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    Re: Another function model.

    Thank you that was so helpful...Why did you subtract 2x from length and width?
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  4. #4
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    Re: Another function model.

    Quote Originally Posted by FatimaA View Post
    Thank you that was so helpful...Why did you subtract 2x from length and width?
    look closely at the sketch of the problem ...
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  5. #5
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    Re: Another function model.

    Oh! Lol, it's kind of obvious. That's why I hate these problems.

    Anyways, thanks. I think I can figure out b and c from here.
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  6. #6
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    Re: Another function model.

    Gah, sorry to bother you again but I really need some help with b and c too.
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  7. #7
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    Re: Another function model.

    Quote Originally Posted by FatimaA View Post
    Gah, sorry to bother you again but I really need some help with b and c too.
    get out your graphing calculator ...

    graph y = x(25-2x)(14-2x) and y = 240 in the window 0 < x < 7 (why?)

    find the interval of x-values where the curve is above y = 240 using the "intersect" feature in the calculate menu

    find the maximum using the "calculate" menu ...
    Attached Thumbnails Attached Thumbnails Another function model.-boxgraph.jpg  
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  8. #8
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    Re: Another function model.

    Thank you.
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