Question

"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

Answer 1

The area of a sector R1-R2-R3+R4 can be found as (θ/360) * π * r^2, where θ is the central angle in degrees. These regions are calculated by using geometry principles.

Step-by-step explanation:

In order to determine the areas of the four regions and find the expression R1 - R2 - R3 + R4, let's consider the intersections of the circle and the lines x = 6 and y = 5.

The line x = 6 intersects the circle at two points, (6, 8) and (6, -8).

This divides the circle into R1 and R2.

The line y = 5 intersects the circle at two points, (8, 5) and (-8, 5).

This divides R1 into R1a and R1b, and R2 into R2a and R2b.

The points of intersection of the circle with x = 6 and y = 5 create two more regions, R3 and R4.

Now, calculate the areas of these regions using geometry principles.

The area of a sector R1 - R2 - R3 + R4 can be found as (θ/360) * π * r^2, where θ is the central angle in degrees.