Question

an x - ray machine is used to eliminate germs in certain food processes. the intensity i, in millirads per hour, of x - rays produced by the machine is inversely proportional to the square of the distance d, in meters, from the machine. for a certain machine, the intensity is 26.5 millirads per hour at a distance of 4 meters. based on this information and using the same machine, what is the intensity, in millirads per hour, at a distance of 3.3 meters?
a 18.037
b 29.176
c 32.121
d 38.935

Explanation:

Step1: Write the inverse - square formula

Since $I$ is inversely proportional to $d^{2}$, we have $I=\frac{k}{d^{2}}$, where $k$ is a constant.

Step2: Find the value of the constant $k$

We know that when $I = 26.5$ and $d = 4$, we substitute into the formula $I=\frac{k}{d^{2}}$: $26.5=\frac{k}{4^{2}}$. Then $k=26.5\times4^{2}=26.5\times16 = 424$.

Step3: Find the intensity at $d = 3.3$

Now that $k = 424$ and $d = 3.3$, we use the formula $I=\frac{k}{d^{2}}$. So $I=\frac{424}{3.3^{2}}=\frac{424}{10.89}\approx38.935$.

Answer:

D. 38.935