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Question 544742: the amount of cloth used to amke four cutains is given by the function A=-4xsquared+40x, where x ia the width of one cutain in feet ad A i sthe total area in square feet. Find the width that maximizes the area of the curtains. What is the maximum area?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! the amount of cloth used to amke four cutains is given by the function A=-4xsquared+40x, where x ia the width of one cutain in feet ad A i sthe total area in square feet. Find the width that maximizes the area of the curtains. What is the maximum area?
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Standard form of equation for parabola that opens downward (parabola has a maximum):
y=-A(x-h)^2+k, (h,k)=(x,y) coordinates of vertex.
..
A=-4x^2+40x
complete the square
A=-4(x^2-10x+25)+100
A=-4(x-5)^2+100
Vertex:(5,100)
ans:
width=5 ft
maximum area=100 sq ft
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