Afarmer will build a rectangular pen for some goats. a wall will form one side of the pen. the farmer has 36 m of fencing to form the other three sides. the farmer plans to build the pen so that it has its maximum possible area. what will be the dimensions of the farmer’s goat pen? by

The maximum area is obtained when half the fence (18 m) is used parallel to the wall. Then the remaining half of the fence forms the other two (equal, 9 m) sides.

The dimensions of the pen will be 9 m by 18 m.

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If x represents the width of the pen (two sides out from the wall), then the area is

... area = x·(36 -2x) = 2x(18 -x)

This expression describes a parabola that opens downward and has zeros at x=0 and x=18. The line of symmetry (and vertex) is halfway between these zeros, at x=9. Hence the width of the pen is 9 m and its length is 36-2·9 = 18 m.

  y= -3x is the required function.

step-by-step explanation:

we have been given a table:

x             y

0             0

1             -3

3             -9

-2             6

we can see that the values of y is -3 times the value of x

hence, the function would be: y= -3x.

put the values of x will give the same y as in the table that means function is satisfying the given table.

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.