<PRE><B>Question 1203907</B>
a norman windo with a perimeter of 20 units has the shape of rectangle surmounted by a semi-circle. If its base is x units long and the height of the rectangle is y units long, write a mathematical model for its area in terms of x.

*[illustration norman.png].

P=20 , base =x , height = y

base = x so radius of semicicle = x/2

Perimeter P  of semi circle = pi* (x/2) 

Perimeter of window = x+2y++pi*(x/2)

20 - x-(pi x/2 )=2y

divide by 2

10-x/2-(pix)/4=y

10- (2x+pix)/4 =y

Area of window = area of semicircle + area of rectangle

radius of circle = x/2 area of semicircle - pix^2/8

A= pix^2/8+ xy ( after this step it just simplification)

A = pix^2/8 +x*(10- (2x+pix)/4)

pix^2/8 +10x -2x^2/4 -pix^2/4

(pix^2 +80x -4x^2-2pix^2)/8

(80x -4x^2-pix^2)/8

(80x- x^2(4+pi))/8



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