SOLUTION: 1)Perimeter.
Write a formula for the perimeter of a square as a function of its area
and
2)
Area of a sign.
A sign is in the shape of a squ
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Question 184037: 1)Perimeter.
Write a formula for the perimeter of a square as a function of its area
and
2)
Area of a sign.
A sign is in the shape of a square with a semicircle of radius x adjoining one side and a semicircle of diameter x removed from the opposite side. If the sides of the square are length 2x, then write the area of the sign as a function of x.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Write a formula for the perimeter of a square as a function of its area:
:
we know the area of a square = side squared
Therefore, one side = square root of the area (a)
Perimeter (P) is the sum of all 4 sides:
so we have:
:
P(a) =
:
:
and
2)
Area of a sign.
A sign is in the shape of a square with a semicircle of radius x adjoining one side and a semicircle of diameter x removed from the opposite side. If the sides of the square are length 2x, then write the area of the sign as a function of x.
:
Write an expression for the area of each part:
:
Attached semi circle: ; (radius=x)
;
the square: ; (side=2x)
:
removed semi circle: ; (radius=.5x)
:
f(x) = area of the sign
Total area = large semi circle + square - small semicircle
:
f(x) = + -
f(x) = + -
get each expression over 2
f(x) = + -
so we have
f(x) =
Factor out x^2
f(x) =
combine the pi's
f(x) =
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