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hugy0212

  • one year ago

A farmer has 120 feet of fencing available to build a rectangular pen for her pygmy goats. She wants to give them as much room as possible to run. 1.Draw a diagram to represent this problem. 2.Write an expression in terms of a single variable that would represent the area of a rectangle in this family. 3.Find the dimensions of the rectangle with maximum area. 4.What is another name for this kind of rectangle?

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  1. freckles
    • one year ago
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    Have you number 1?

  2. hugy0212
    • one year ago
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    no :(

  3. freckles
    • one year ago
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    Hmmm... you should know what a rectangle looks like...

  4. freckles
    • one year ago
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    |dw:1443890804767:dw| opposite sides are equal |dw:1443890824575:dw|

  5. hugy0212
    • one year ago
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    I do not need to apply any numbers to the sides?

  6. freckles
    • one year ago
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    what don't know the numbers....I called the numbers x and y.

  7. freckles
    • one year ago
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    but we do know a relationship between x and y

  8. hugy0212
    • one year ago
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    oh alright

  9. freckles
    • one year ago
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    we know we have 120 feet of fencing

  10. freckles
    • one year ago
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    so you should know the perimeter equals?

  11. hugy0212
    • one year ago
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    yes

  12. freckles
    • one year ago
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    so can you state an equation relating x and y (think perimeter)

  13. hugy0212
    • one year ago
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    x+y?

  14. freckles
    • one year ago
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    x+y is an expression I'm looking for an equation that relates x and y (the hint I gave for this equation was to think perimeter )

  15. freckles
    • one year ago
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    you have 120 feet amount of fencing in terms of x and y you have how much amount of fencing ?

  16. freckles
    • one year ago
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    how many sides have measurement x? how many sides have measurement y?

  17. hugy0212
    • one year ago
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    two sides with x and two sides with y

  18. freckles
    • one year ago
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    right x+x+y+y is how much fencing we have or simplifying 2x+2y is how much fencing we have but we were also given that we had 120 feet of fencing so 2x+2y=120

  19. freckles
    • one year ago
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    Also you guys probably know the formula for finding the perimeter of a rectangle ...

  20. freckles
    • one year ago
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    which is Perimeter=2L+2W

  21. freckles
    • one year ago
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    Anyways to make 2x+2y=120 prettier I would divide both sides by 2 giving x+y=60

  22. freckles
    • one year ago
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    anyways we have started doing number 2 sorta of except we need to mention something about the area of this rectangle

  23. freckles
    • one year ago
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    what is the area of our rectangle

  24. hugy0212
    • one year ago
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    to find area is length times width

  25. freckles
    • one year ago
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    in terms of x and y

  26. freckles
    • one year ago
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    our length is ? and our width is?

  27. hugy0212
    • one year ago
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    so xy?

  28. freckles
    • one year ago
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    yes we have Area=xy I'm just going to use A for area A=xy now number 2 also says write in terms of one variable this is where that perimeter equation we came up with will come in use

  29. freckles
    • one year ago
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    remember we had x+y=60 solve for either x or y (your choice; no need to solve for both though)

  30. hugy0212
    • one year ago
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    x=-y+60

  31. freckles
    • one year ago
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    right good so replace the x in A=xy with x=-y+60 and you will have completed number 2

  32. hugy0212
    • one year ago
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    So A= (-y+60)y?

  33. freckles
    • one year ago
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    awesome

  34. freckles
    • one year ago
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    Now is this a calculus or algebra class?

  35. freckles
    • one year ago
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    if it is calculus we differentiate or you could use algebraic ways because this is a parabola

  36. hugy0212
    • one year ago
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    Pre calculus

  37. freckles
    • one year ago
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    have you differentiated in this class?

  38. freckles
    • one year ago
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    example: like the derivative of 6x^2 is 12x\

  39. freckles
    • one year ago
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    have you done something like that?

  40. hugy0212
    • one year ago
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    no we have not

  41. freckles
    • one year ago
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    ok then this is parabola so you just need to find the vertex of the parabola to find the max

  42. freckles
    • one year ago
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    \[f(x)=ax^2+bx+c \\ f(x)=ax^2+\frac{a}{a}bx+c \\ \text{ I multiply second term by } \frac{a}{a} \\ \text{ so it would be easier for you to see how I'm going to factor out } a \\ \text{ from the first two terms } \\ f(x)=a(x^2+\frac{1}{a}bx)+c \\ \text{ so } \frac{1}{a} \cdot b =\frac{b}{a} \\ f(x)=a(x^2+\frac{b}{a}x)+c \\ \text{ now I'm going to leave a space inside the ( ) } \\ \text{ this space will be for completing the square } \\ \text{ I will also mention whatever we add in } \\ \text{ we must subtract out } \\ f(x)=a(x^2+\frac{b}{a}x+?)+c-a? \] \[\text{ anyways recall } x^2+kx+(\frac{k}{2})^2=(x+\frac{k}{2})^2 \\ \text{ so that means our } k=\frac{b}{a} \\ \text{ so } (x^2+\frac{b}{a}x+(\frac{b}{2a})^2=(x+\frac{b}{2a})^2 \\ \text{ so going back to } f(x) \\ f(x)=a(x^2+\frac{b}{a}x+\frac{b}{2a})^2+c-a(\frac{b}{2a})^2 \\ f(x)=a(x+\frac{b}{2a})^2+c-a(\frac{b}{2a})^2\] You should recall this is the vertex form of a quadratic. Where there vertex is: \[(-\frac{b}{2a},c-a(\frac{b}{2a})^2)\] you try finding the vertex form (or vertex) of your parabola

  43. Directrix
    • one year ago
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    At the link are two versions of a solution. They may be helpful. http://openstudy.com/study#/updates/55035308e4b01982d66287df @hugy0212

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