While doing my Advanced functions work I came across this question:
Prove that $A=30y-(1/8)\pi y^2$ when the perimeter of a diagram is $2x+(1/2)\pi y = 60$.
I tried to isolate $x$ and got the following answer: $$x=30-(1/4)\pi y$$ But when I try to sub that in the equation for area (which is $ A = xy+[(1/4)\pi y^2]$) I always end up with $30y$ rather than the equation I was trying to prove.
Can someone please tell me what I am doing wrong please? The full question can be viewed at the following link: https://s.yimg.com/hd/answers/i/745d191c9cb64bcc8d1cc9a7c4726dc4_A.png?a=answers&mr=0&x=1472954214&s=1bc69b025169251ff8647a58ae5e2f0c
Your function for the area is incorrect. It should be
$$A=xy+\frac{\pi\left(\frac{y}{2} \right)^2}{2}=xy+\frac{\pi y^2}{8}.$$
Let me know if the problem is still causing you trouble after this.