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A rope 16 feet long is cut into two pieces. One piece is used to form a circle and the other used to form a square. Find a function representing the area of both square and circle as a function of the length of one side of the square.

Guest Feb 25, 2015

#1
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length of rope: 16 ft

length of one side of the square: x

area of square: As(x) = x2

length of the "square piece": 4x

length of "circle piece": 16 - 4x

We know that: C = 2 * pi * r   =>    r = C/(2 * pi)

Area of cicle: Ac = pi * r2 = pi * [C/(2 * pi)]2 = pi * (C2/4 * pi2)

Ac = C2/4pi = (16 - 4x)2/4pi = 4(4 - x)2/4pi

Ac = (4 - x)2/pi

Ac(x) = (4 - x)2/pi

Tetration  Feb 25, 2015
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#1
+808
+5

length of rope: 16 ft

length of one side of the square: x

area of square: As(x) = x2

length of the "square piece": 4x

length of "circle piece": 16 - 4x

We know that: C = 2 * pi * r   =>    r = C/(2 * pi)

Area of cicle: Ac = pi * r2 = pi * [C/(2 * pi)]2 = pi * (C2/4 * pi2)

Ac = C2/4pi = (16 - 4x)2/4pi = 4(4 - x)2/4pi

Ac = (4 - x)2/pi

Ac(x) = (4 - x)2/pi

Tetration  Feb 25, 2015

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