Let R be the circle centered at (0,0) with radius 10. The lines x=6 and y=5 divide R into four regions R1, R2, R3 , and R4. Let R_i denote the area of region R_i If R1>R2>R3>R4,

then find R1-R2-R3+R4

Thank you so much!!

Noori Oct 11, 2020

#1**+1 **

By calculus,

\([\mathcal{R}_1] = 30 + \frac{1}{4} \cdot \pi \cdot 10^2 + \int_0^5 \sqrt{100 - x^2} \ dx + \int_0^6 \sqrt{100 - x^2} \ dx.\)

We can write out the areas similarly, to get [R_1] - [R_2] - [R_3] + [R_4] = 92.

Guest Oct 11, 2020

#5**+1 **

Use this to help

\(R_1=Pink,\quad R_2=Blue,\quad R_3=Green, \quad R_4=Purple\)

Area of circle is 100pi

Area of rectangle in the middle is 12*10=120

B+B+G+G+Pu-Pu+120 = 100pi

simply to get

B+G=50pi-60

Pink=G+B-Purple +120

Pink+ purple = G+B+120

substitute

Pink+ purple = 50pi-60+120 = 50pi+60

(Pink+Purple) - (Blue+green) = (50pi+60) - ( 50pi-60) = 120 units squared.

**I really did not need to do all this.**

Just looking at the pic I can see that pink - blue - green +Purple = 120

Melody Oct 12, 2020