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anonymous

  • 5 years ago

Ok so i have a few questions. When graphing y>x^2 you can only use quadrant one right? Also i have a word problem that goes like this-Suppose you have 80 ft of fence to enclose a rectangular garden. The function A = 40x - x2 gives you the area of the garden in square feet where x is the width in feet. and then it has two parts... a. What width gives you the maximum gardening area? and b. What is the maximum area? Please help because I have no idea what to do. Thanks :)

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  1. amistre64
    • 5 years ago
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    unless the problem restricts it; you can use any quadrant that is available to use

  2. amistre64
    • 5 years ago
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    2l+2w=80 thats your perimeter right?

  3. amistre64
    • 5 years ago
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    and Area = x*y correct?

  4. anonymous
    • 5 years ago
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    yes

  5. amistre64
    • 5 years ago
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    A=l*w..i really should keep my variables consistent

  6. amistre64
    • 5 years ago
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    with the perimeter we can slve for one of the variables... you want l or w?

  7. anonymous
    • 5 years ago
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    sure

  8. amistre64
    • 5 years ago
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    either way its the same....and the max area is a square in the end as you will see...hopefully ;)

  9. amistre64
    • 5 years ago
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    l=(80-2w)/2 = 40-w substitute this 'value' into the area formula A = w(40-w) A = 40w -w^2

  10. amistre64
    • 5 years ago
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    which is what they gave you in the wording; i just went the long way to get to it

  11. amistre64
    • 5 years ago
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    now, do you know what the graph of this thing looks like?

  12. amistre64
    • 5 years ago
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    its an upside down 'U'

  13. amistre64
    • 5 years ago
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    so the highest point gives you the maximum area possible

  14. amistre64
    • 5 years ago
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    what do you know about the graph? i can throw out alot of technical names that might mean nothing to you...

  15. amistre64
    • 5 years ago
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    the highest point is when w=20.. which is the vertex of the graph we know that 2w + 2l = 80 2(20) +2l = 80 40 +2l = 80 2l = 40 l = 40/2 = 20 the width is 20, the length is 20 ..its a square :)

  16. amistre64
    • 5 years ago
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    the max area is 20(20) = 400 square ....feet? yeah, feet

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