Question 244876
area of a circle is equal to pi * r^2 where pi is equal to {{{pi}}} is equal to 3.141592654 and r is the radius of the circle.


let A[i] = the area of circle i.


[] means sub as in A[i] means A sub i.


i can be 1, 2, or 3.


let S = A[1] + A[2] + A[3]


A[1] = pi * r[1]^2 because the radius is not known.


A[2] = pi * 3^2 because the radius is 3.


A[3] = pi * 2^2 because the radius is 2.


You get:


S = pi*r[1]^2 + pi*3^2 + pi*2^2


This becomes:


S = pi*r[1]^2 + pi*9 + pi*4


factor out the pi to get:


S = pi * (r[1]^2 + 9 + 4)


combine like terms to get:


S = pi * (r[1]^2 + 13)


I think that's your polynomial in its simplest form.


to solve for r[1], you would need to know S.


to solve for S, you would need to know r[1].


S is the sum of all three areas.


r[1] is the radius for the first circle.