Question

The figure below shows a region that consists of a semi-circle on top of a rectangle. Give the value of x that maximizes the area of the region if the circumference of the region is 13.

Answer 1

Here are the choices

a) \[13/(\pi+2)\]
b) \[13\pi/(\pi+4)\]
c) \[26/(\pi +4)\]
d) \[26/(\pi +2)\]
e) \[13\pi/(\pi+2)\]

Answer 2

please somebody reply, I need the answer quickly
thank you in advance

Answer 3

13 = 2L+x+ pi*x
L= (13- x(1+pi))/2


A = pi*x^2 +xL
= pi*x^2 +x(13-x(1+pi))/2
= (pi -(1+pi)/2 )x^2 +13x/2
= ((pi-1)/2)x^2 +13x/2

take the derivative and set equal to zero; solve for x.