SOLUTION: Radiation​ machines, used to treat​ tumors, produce an intensity of radiation that varies inversely as the square of the distance from the machine. At 3​ meters,

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Question 1126399: Radiation​ machines, used to treat​ tumors, produce an intensity of radiation that varies inversely as the square of the distance from the machine. At 3​ meters, the radiation intensity is 62.5 milliroentgens per hour. What is the intensity at a distance of 3.2 meters
Found 2 solutions by josmiceli, greenestamps:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +k+ = constant of proportionality
+62.5+=+k%2A%28+1%2F%283%5E2%29+%29+
+62.5+=+k%2A%28+1%2F9+%29+
+k+=+562.5+
-------------------
+I+=+k%2A%28+1%2F%283.2%5E2%29%29+
+I+=+562.5%2A%28+1%2F10.24+%29+
+I+=+54.932+
check the math

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


If you want a formula that you can use to find the radiation intensity at any given distance from the machine, then you can find the constant of proportionality as shown by the other tutor.

If you only need to answer the problem for this one new distance, you don't need to do that much work.

Since the intensity varies inversely as the square of the distance from the machine, the intensity at 3.2 meters will be the intensity at 3 meters, multiplied by the square of the ratio of the two distances:

62.5%2A%283%2F3.2%29%5E2 = 54.932, to 3 decimal places.