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So you have (hopefully) ? gured out how to use many random numbers to estimate the area of a circle; now let’s use the same technique to estimate the area covered by two partially over-lapping circles. both circles have radii of r = 0.6. one is centered at (xc, yc) = (0.4,0) while the other is centered at (xc, yc) = (? 0.4,0). since they are partially over-lapping, it is not very easy to calculate the area by hand – but your random number technique should work just ? ne. use about 1 random numbers, and give your answer with 5 signi? cant digits.(a) estimate the area a of the two over-lapping circles. note that a should include regions where either circle exists (i. e., the union of the two ) without running any additional random number simulations, can you estimate the area of the intersection between the circles (i. e., the area where they overlap? hint: use your estimated value of a and the known areas of the circles.

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