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stevetron
 one year ago
Suppose you have 54 feet of fencing to enclose a rectangular dog pen. The function A=27xx^2, where x = width, gives you the area of the dog pen in square feet. What width gives you the maximum area? What is the maximum area? Round to the nearest tenth as necessary.
a.width = 13.5 ft; area = 546.8 ft2
b.width = 27 ft; area = 182.3 ft2
c.width = 13.5 ft; area = 182.3 ft2
d.width = 27 ft; area = 391.5 ft2
stevetron
 one year ago
Suppose you have 54 feet of fencing to enclose a rectangular dog pen. The function A=27xx^2, where x = width, gives you the area of the dog pen in square feet. What width gives you the maximum area? What is the maximum area? Round to the nearest tenth as necessary. a.width = 13.5 ft; area = 546.8 ft2 b.width = 27 ft; area = 182.3 ft2 c.width = 13.5 ft; area = 182.3 ft2 d.width = 27 ft; area = 391.5 ft2

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campbell_st
 one year ago
Best ResponseYou've already chosen the best response.2is this a calculus or algebra question..?

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.2ok... find the line of symmetry, use \[x = \frac{b}{2 \times a}\] so in your question b = 27 and a = 1 substitute them to find the width for the max area

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.2what you have found is the line of symmetry for the parabola. The maximum area lies on the line of symmetry so given a quadratic \[ax^2 + bx + c \] the line of symmetry is \[x = \frac{b}{2a}\] then to find the max area, substitute the value into the original equation

stevetron
 one year ago
Best ResponseYou've already chosen the best response.1so a=27*13.513.5^2?

stevetron
 one year ago
Best ResponseYou've already chosen the best response.1thank you for explaining it
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