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anonymous

  • one year ago

Rectangle R has varying length L and width W but with a constant area of 4 square feet. a)Express the perimeter P as a function of length L. What type of function is P? What is the domain of P? (I only help with parts B and C) b)Describe the asymptotic behavior of P. What can you say about rectangle R because of this behavior? c) For what values of L and W will the perimeter of R be the least? Give a geometric explanation.

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  1. anonymous
    • one year ago
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    I only help with parts B and C

  2. ganeshie8
    • one year ago
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    what do you have for part A ?

  3. ganeshie8
    • one year ago
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    i ask because PartB and C depend on part A

  4. triciaal
    • one year ago
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    |dw:1436241409178:dw|

  5. anonymous
    • one year ago
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    I have P = 2(4+L^2)/L

  6. triciaal
    • one year ago
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    @mahima2558 do you have the same for part A?

  7. triciaal
    • one year ago
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    |dw:1436242085909:dw|

  8. ganeshie8
    • one year ago
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    \[\large P = \dfrac{2(4+L^2)}{L}\] looks good

  9. anonymous
    • one year ago
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    so for part b, is L=0 the only asymptote

  10. anonymous
    • one year ago
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    and I'm not sure what I can say about the rectangle from that

  11. ganeshie8
    • one year ago
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    Look at the graph of P |dw:1436239083007:dw|

  12. ganeshie8
    • one year ago
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    x axis is L y axis is P

  13. ganeshie8
    • one year ago
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    what do you notice in the graph as you increase L ?

  14. anonymous
    • one year ago
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    P increases?

  15. ganeshie8
    • one year ago
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    Yes, what happens if you increase L too much

  16. ganeshie8
    • one year ago
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    P also increases and the rectangle looks as if it is a thin line, yes ? |dw:1436239328327:dw|

  17. anonymous
    • one year ago
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    yes

  18. ganeshie8
    • one year ago
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    just explain that in ur own words for part b

  19. ganeshie8
    • one year ago
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    also explain what happens to P and how the rectangle looks as you make L very low

  20. anonymous
    • one year ago
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    ok that makes sense

  21. anonymous
    • one year ago
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    for part c do i use the graph to find the value of L and W were P would be the least?

  22. ganeshie8
    • one year ago
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    that will do!

  23. anonymous
    • one year ago
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    the minimum value of the graph is (2,8) so that means the length is 2 and the perimeter is 8

  24. anonymous
    • one year ago
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    so the width would be 2 as well?

  25. anonymous
    • one year ago
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    ok great, thank you

  26. ganeshie8
    • one year ago
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    yw!

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