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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?
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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freckles
 one year ago
Best ResponseYou've already chosen the best response.0Hmmm... you should know what a rectangle looks like...

freckles
 one year ago
Best ResponseYou've already chosen the best response.0dw:1443890804767:dw opposite sides are equal dw:1443890824575:dw

hugy0212
 one year ago
Best ResponseYou've already chosen the best response.0I do not need to apply any numbers to the sides?

freckles
 one year ago
Best ResponseYou've already chosen the best response.0what don't know the numbers....I called the numbers x and y.

freckles
 one year ago
Best ResponseYou've already chosen the best response.0but we do know a relationship between x and y

freckles
 one year ago
Best ResponseYou've already chosen the best response.0we know we have 120 feet of fencing

freckles
 one year ago
Best ResponseYou've already chosen the best response.0so you should know the perimeter equals?

freckles
 one year ago
Best ResponseYou've already chosen the best response.0so can you state an equation relating x and y (think perimeter)

freckles
 one year ago
Best ResponseYou've already chosen the best response.0x+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 )

freckles
 one year ago
Best ResponseYou've already chosen the best response.0you have 120 feet amount of fencing in terms of x and y you have how much amount of fencing ?

freckles
 one year ago
Best ResponseYou've already chosen the best response.0how many sides have measurement x? how many sides have measurement y?

hugy0212
 one year ago
Best ResponseYou've already chosen the best response.0two sides with x and two sides with y

freckles
 one year ago
Best ResponseYou've already chosen the best response.0right 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

freckles
 one year ago
Best ResponseYou've already chosen the best response.0Also you guys probably know the formula for finding the perimeter of a rectangle ...

freckles
 one year ago
Best ResponseYou've already chosen the best response.0which is Perimeter=2L+2W

freckles
 one year ago
Best ResponseYou've already chosen the best response.0Anyways to make 2x+2y=120 prettier I would divide both sides by 2 giving x+y=60

freckles
 one year ago
Best ResponseYou've already chosen the best response.0anyways we have started doing number 2 sorta of except we need to mention something about the area of this rectangle

freckles
 one year ago
Best ResponseYou've already chosen the best response.0what is the area of our rectangle

hugy0212
 one year ago
Best ResponseYou've already chosen the best response.0to find area is length times width

freckles
 one year ago
Best ResponseYou've already chosen the best response.0our length is ? and our width is?

freckles
 one year ago
Best ResponseYou've already chosen the best response.0yes 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

freckles
 one year ago
Best ResponseYou've already chosen the best response.0remember we had x+y=60 solve for either x or y (your choice; no need to solve for both though)

freckles
 one year ago
Best ResponseYou've already chosen the best response.0right good so replace the x in A=xy with x=y+60 and you will have completed number 2

freckles
 one year ago
Best ResponseYou've already chosen the best response.0Now is this a calculus or algebra class?

freckles
 one year ago
Best ResponseYou've already chosen the best response.0if it is calculus we differentiate or you could use algebraic ways because this is a parabola

freckles
 one year ago
Best ResponseYou've already chosen the best response.0have you differentiated in this class?

freckles
 one year ago
Best ResponseYou've already chosen the best response.0example: like the derivative of 6x^2 is 12x\

freckles
 one year ago
Best ResponseYou've already chosen the best response.0have you done something like that?

freckles
 one year ago
Best ResponseYou've already chosen the best response.0ok then this is parabola so you just need to find the vertex of the parabola to find the max

freckles
 one year ago
Best ResponseYou've already chosen the best response.0\[f(x)=ax^2+bx+c \\ f(x)=ax^2+\frac{a}{a}bx+c \\ \text{ I multiply second term by } \frac{a}{a} \\ \text{ so it would be easier for you to see how I'm going to factor out } a \\ \text{ from the first two terms } \\ f(x)=a(x^2+\frac{1}{a}bx)+c \\ \text{ so } \frac{1}{a} \cdot b =\frac{b}{a} \\ f(x)=a(x^2+\frac{b}{a}x)+c \\ \text{ now I'm going to leave a space inside the ( ) } \\ \text{ this space will be for completing the square } \\ \text{ I will also mention whatever we add in } \\ \text{ we must subtract out } \\ f(x)=a(x^2+\frac{b}{a}x+?)+ca? \] \[\text{ anyways recall } x^2+kx+(\frac{k}{2})^2=(x+\frac{k}{2})^2 \\ \text{ so that means our } k=\frac{b}{a} \\ \text{ so } (x^2+\frac{b}{a}x+(\frac{b}{2a})^2=(x+\frac{b}{2a})^2 \\ \text{ so going back to } f(x) \\ f(x)=a(x^2+\frac{b}{a}x+\frac{b}{2a})^2+ca(\frac{b}{2a})^2 \\ f(x)=a(x+\frac{b}{2a})^2+ca(\frac{b}{2a})^2\] You should recall this is the vertex form of a quadratic. Where there vertex is: \[(\frac{b}{2a},ca(\frac{b}{2a})^2)\] you try finding the vertex form (or vertex) of your parabola

Directrix
 one year ago
Best ResponseYou've already chosen the best response.1At the link are two versions of a solution. They may be helpful. http://openstudy.com/study#/updates/55035308e4b01982d66287df @hugy0212
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