The area for a semi circle in Cartesian coordinate system with the flat edge against the x-axis is:A=∫0r2−x2√∫−rrdxdy
Bounding limits for x are from -r to r. And for y, this comes from the equation for a circle:x2+y2=r2
Solve for y:y=±r2−x2−−−−−−√
But since we are only dealing with a semi circle, we can always look at the positive answer.
To convert to a polar coordinate system, we used some equations you have probably seen:x=rcosθy=rsinθdxdy=rdrdθ
The substitute to convert to polar coordinate system:A=∫0π∫0rrdrdθSolve this for the area.A=πr2/2
To find the x coordinate of the centroid:x=1/A∫∫xdxdyorx=1/A∫0π∫0rrcosθ(rdrdθ)Solve and you will find x = 0 which intuitively makes sense.
Similar for the y coordinate of the centroid:y=1/A∫∫ydxdyory=1/A∫0π∫0rrsinθ(rdrdθ)Solve and you will find y=4r/3π
This means the centroid of a semicircle is at: (0,4r/3π)
D , - if the Fed sells bonds, it decreases the money supply by removing cash from the economy in exchange for bonds.
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Answer:
y=2x+6
Step-by-step explanation:
Graph the coordinates
Go up to over one or down two left on
Get your y-intercept
put in y=mx+b
I think the answer is a but I’m not for sure
Answer:
15
Step-by-step explanation:
-75 x-3 is 225
Square root of 225 is 15
