help @@

[Comatose]

a piece of wire 100 cm long is to be cut so that one piece is used to form a square, while the other is used to form a circle. if the edge length of the square is xcm, find, in terms of x,

a. the radius of the circle
b. the area of the circle
THANKS

[brightsky]

so edge length of square is x. so perimeter of square is 4x. that leaves 100 - 4x to form the circumference of the circle. since circumference of the circle = 2pi*r with r = radius, then 100 - 4x = 2pi*r, r = (100 - 4x)/2pi = (50 - 2x)/pi.
area of the circle = pi*r^2 = pi*((50 - 2x)/pi)^2. simplify at your own will.

[Russ]

dammit, efb, etc.

Once we make the square the length of wire left is 100 - 4x
Since the circumference of the circle is given by C = 2 * pi * r, we can rewrite so that r = C/2pi
C = 100 - 4x, substitute in to get r = (50 - 2x)/pi

The area of the circle is pi*r^2
Already established the radius, just square it and multiply by pi

[b^3]

The lenght that will be used for the square will be the perimeter of the square P=x+x+x+x=4x
so the lenght remaining is 100-4x
so that will equal the circumference of the circle
100-4x=2*pi*r
so r=(100-4x)/2*pi
r=(50-2x)/pi cm

Are of the circle will be pi*r^2
so plug r in
A=pi*((50-2x)/pi)^2
=(50-2x)^2 / pi cm²

EDIT: Beaten

[Comatose]

thank you guys

[Comatose]

c. the total area of the two shapes
answer says its (pi+4)x^2-200x+2500/pi? how do i do it haha

[brightsky]

area of square is x^2. area of circle is pi*((50 - 2x)/pi)^2.
so total area is:
x^2 + pi*((50 - 2x)/pi)^2
= x^2 + pi*(50 - 2x)^2/pi^2
= x^2 + (50 - 2x)^2/pi
= x^2 + (2500 - 200x + 4x^2)/pi
= x^2 pi/pi + (2500 - 200x + 4x^2)/pi
= (x^2(pi + 4) - 200x + 2500)/pi as required

[Comatose]

= x^2 pi/pi + (2500 - 200x + 4x^2)/pi <<<i got to that
but how do you get it to this? = (x^2(pi + 4) - 200x + 2500)/pi

[Comatose]

never mind i got it hahaha sorry for the trouble

[brightsky]

= x^2 pi/pi + (2500 - 200x + 4x^2)/pi <<<i got to that
but how do you get it to this? = (x^2(pi + 4) - 200x + 2500)/pi

same denominator. so the numerator is x^2*pi + 2500 - 200x + 4x^2 and the denominator is pi. then we collect like terms. we group the ones with x^2 together, yielding x^2(pi + 4) + 2500 - 200x. remember that this is exactly the same as if you had x + 2x. you group the like terms (1 + 2)x to give 3x.