10. +-12 points SApCalcBr1 4.6.007 My Notes +Ask Your Teacher Consider the follo

Question

10. +-12 points SApCalcBr1 4.6.007 My Notes +Ask Your Teacher Consider the following problem: A farmer with 640 ft of fencing wants to enclose a rectangular area and then divide it into 4 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, A? If so, estimate it. (Round your answer to the nearest thousand.) A= il.2 (b) Draw a diagram illustrating the general situation. Introduce notation and label the diagram with your symbols O Let x denote the length of the dividers. Let y denote the length of the perimeter. O Let x denote the length of each of two sides and three dividers. Let y denote the length of the other two sides O Let x denote the length of the perimeter. Let y denote the length of the dividers O Let y denote the length of each of two sides and three dividers. Let x denote the length of the other two sides. (c) Write an expression for the total area A= ft2 (d) Use the given information to write an equation that relates the variables

Explanation / Answer

a) 10000

b) Let x denote the lenth of two sides, three other divides and y denote length of other 2 sides

c) x*y ---> Area of rectangle with sides x,y

d) 5x + 2y = 640 ----> Perimeter of figure 5 vertical sides of length x and 2 horizontal sides of length y

e) 320*x - 2.5*x^2 -----> xy = x*(320-2.5*x)

f'(x) = 320 - 5x = 0

x = 64

5x + 2y = 640 ==> y = 160

f) 10240 ---> Area = x*y = 64 * 160

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.