A farmer is planning a rectangular area for her chickens. the area of the rectangle will be 450 square feet. three sides of the
rectangle will be formed by fencing, which costs $5 per foot. the fourth side of the rectangle will be formed by a portion of the barn wall, which requires no fencing. in order to minimize the cost of the fencing, how long should the fourth side be?
1 answer:
Let x represent the length in feet of the area along the barn wall. Then the width of the area (out from the wall) will be 450/x, and the total cost of fence will be
cost = 5*(x +2*450/x)
A graphing calculator shows the minimum of the cost function is where x=30.
In order to minimize the cost of fencing, the fourth side should be 30 ft long.
cost = 5*(x +2*450/x)
A graphing calculator shows the minimum of the cost function is where x=30.
In order to minimize the cost of fencing, the fourth side should be 30 ft long.
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The two points (0,0) and (4,5) are on the line. The points are marked in blue in the attached image below.
Use the slope formula to get
m = (y2-y1)/(x2-x1)
m = (5-0)/(4-0)
m = 5/4 <----- this is the answer in fraction form
m = 1.25 <----- this is the answer in decimal form
The idea of the slope formula is we're subtracting the y values together, then subtracting the x values together in the same order, finally we divide the two results and reduce if possible to get the fraction form. Use long division or a calculator to find the decimal form of the fraction. In this case, the rise is 5 and the run is 4. Meaning we go up 5 units and over to the left 4 units to go from (0,0) to (4,5).
