Calculus help??
I need this to be as detailed as possible. I got the final formula…I don’t know if it’s right, or if I have to put it into the y=^#$*&^$^ form. So, if you could answer both of those questions, that would be EXTREMELY helpful.
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let x = wire for the square, y = wire for the circle
thus we can see that x + y = 5.
but we need to represent the final answer as a function of x; so what we can do is express y in terms of x, in which we get y = 5 – x.
we are looking for the total area by the square and the circle, that is:
A(x) = area of square + area of circle, all as functions of x.
to get the area of the square, we have to know the length of its side: since we the wire used for the square as x, therefore one side would be equivalent to x/4; and its square would be (x/4)^2. = x^2/16.
now we have to find the area of the circle. what we have is its circumference, that is, the length of the wire that defines the circle, which is 5 – x.
the formula for a circle’s circumference is C = 2(pi)(radius), while for its area is A = pi(radius)^2.
now we see that to be able to get the area of a circle, we have to find its radius first, and we can only get that by using the formula for the circumference, since it is there which we have the most number of given data:
C = 5 – x = 2pi(radius)
(5 – x)/2pi = radius
then we can plug this value of the radius into the area formula:
A = pi[(5 – x)/2pi]^2
A = pi[(x^2 – 10x + 25)/4pi^2]
A = (x^2 – 10x + 25)/4pi
since we already have both the areas of the square and the circle, we will have:
A(x) = x^2/16 + (x^2 – 10x + 25)/4pi
I see you’ve also asked this question in the Mathematics area, and you’ve already received detailed answers there. No need for me to repeat the same thing here…but as the other answers indicated, it’s not Calculus. (No differentials, no integrals, etc…just ordinary Algebra.)
Now, if you were asked “find the value of X that minimizes (or maximizes) the sum of the area of the square and the circle” then you might have a real Calculus problem.
