Question

The intensity of an x-ray beam at any distance
from the source varies inversely as the square of
that distance. If the intensity of an x-ray beam is
30 R/hour when the object is 2 inches from the
source, determine the level of intensity when an
object is 5 inches from the source. (Note: R/hour
stands for Roentgens/hour. A Roentgen is a unit
for measuring the amount of x-ray or gamma
radiation in the air.)

Answer 1

it varies inversely so I know you divide I think 30 by 15?

Answer 2

k= 60?????????

Answer 3

Let \(i\) represent the intensity and let \(\delta\) represent the distance. So we have:
\[i\propto\frac{1}{\delta^2}\]
That is to say:
\[i=\frac{\chi}{\delta^2}\]
Where \(\chi\) is a constant.

So we know:
\[30=\frac{\chi}{2^2}\to30=\frac{\chi}{4}\to\chi=30(4)\to\chi=120\]
We also know that:
\[i=\frac{\chi}{5}\to i=\frac{120}{5}=24R/hr\]

Answer 4

that's what I thought too but here are my choices: A.
15/
2
B. 15
C. 60
D. 120

Answer 5

OH SHOOT! haha i made a mistake: we have,
\[i=\frac{\chi}{5^2}=\frac{\chi}{25}=\frac{120}{25}=\frac{24}{5}=4.8R/hr\]

Answer 6

does that fall into any of the choices?

Answer 7

Nope...something doesn't make sense.