Consider the following problem: A farmer with 950 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens?
(a) Draw several diagrams illustrating the situation, some with shallow, wide pens and some with deep, narrow pens. Find the total areas of these configurations. Does it appear that there is a maximum area? If so, estimate it.
(b) Draw a diagram illustrating the general situation. Let x denote the length of each of two sides and three dividers. Let y denote the length of the other two sides.
(c) Write an expression for the total area A in terms of both x and y.
A =
(d) Use the given information to write an equation that relates the variables.
(e) Use part (d) to write the total area as a function of one variable.
A(x) =
(f) Finish solving the problem by finding the largest area. ft2
Consider the following problem: A farmer with 950 ft of fencing wants to enclose a rectangular...
Consider the following problem: A farmer with 750 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens? (a) Draw several diagrams illustrating the situation, some with shallow, wide pens and some with deep, narrow pens. Find the total areas of these configurations. Does it appear that there is a maximum area? If so,...
Consider the following problem: A farmer with 950 ft of fencing wants to enclose a rectangular area and then divide into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four per (a) Draw several diagrams illustrating the situation, some with shallow, wide pens and some with deep, narrow pens. Find the total areas of these configurations. Does it appear that there is a maximum area? If so, estimate...
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A farmer with 700 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens.
Farmer Ed has 950 meters of fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the river, find the length and width of the plot that will maximize the area. What is the largest area that can be enclosed? 950 - 2x The width, labeled x in the figure, is meters. (Type an integer or decimal.) The length, labeled 950 - 2x in the figure, is meters....
Consider the following problem: A breeder of horses wants to fence three rectangular grazing fields along the river with 1800 total feet of fencing as shown below. (Let x denote the vertical length of each of two sides and two dividers. Let y denote the horizontal length for each of the three grazing areas.) What is the largest possible total area (for all three grazing fields together) that she can enclose? What would the dimensions be for each grazing field?...
1a) b) c) You have 120 yards of fencing and you need to enclose a rectangular area as shown. You want two pens to separate your goat and horse. To save money, you decide to use the corner of your house for two sides of the area so you only need fencing for the remaining two sides. You desire to enclose the largest possible area. Wall Wall x (So the fencing is represented by the red lines in the image.)...
Farmer has 800 yards of fencing to enclose rectangular garden. Express the area A of the rectangle as a function of the width X of the rectangle. What is the domain of A?
I have no idea where to start for this optimization problem 1. A farmer with 800ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens?
A farmer with 8000 meters of fencing wants to enclose a rectangular plot that borders on a river. If the farmer does not fence the side along the river, what is the largest area that can be enclosed?Does that mean I have to consider it a triangle?