+68 Let R be the circle centered at (0,0) with radius 10. The lines x=6 and y=4 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
+1557 The lines x=6 and y=4 divide the circle R into four regions, as shown below:
We can see that R1 is the largest region, followed by R2, R3, and R4.
To find the areas of these regions, we can use the following formula for the area of a sector of a circle:
Area of sector = (Central angle / 360 degrees) * Area of circle
The central angles of the four sectors are as follows:
R1: 90∘
R2: 45∘
R3: 45∘
R4: 90∘
The area of the circle is πr2=π⋅102=100π.
Therefore, the areas of the four regions are as follows:
R1=(90∘/360∘)⋅100π=25π
R2=(45∘/360∘)⋅100π=12.5π
R3=(45∘/360∘)⋅100π=12.5π
R4=(90∘/360∘)⋅100π=25π
Therefore, R1>R2>R3>R4, and R1−R2−R3+R4=25π−12.5π−12.5π+25π=25π.
