radiation machines, used to treat tumors, produce an intensity of radiation that varies inversely as the…

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 1.9 meters? the intensity is milliroentgens per hour. (round to the nearest tenth as needed.)

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 1.9 meters? the intensity is milliroentgens per hour. (round to the nearest tenth as needed.)

Answer

Explanation:

Step1: Establish inverse - square relationship formula

Let $I$ be the intensity of radiation and $d$ be the distance. The relationship is $I=\frac{k}{d^{2}}$, where $k$ is a constant. We know that when $d = 3$ meters, $I=62.5$ milliroentgens per hour. Substitute these values into the formula to find $k$: $62.5=\frac{k}{3^{2}}$.

Step2: Solve for the constant $k$

Multiply both sides of the equation $62.5=\frac{k}{9}$ by 9. So, $k = 62.5\times9=562.5$.

Step3: Find the intensity at a new distance

Now we want to find $I$ when $d = 1.9$ meters. Substitute $k = 562.5$ and $d = 1.9$ into the formula $I=\frac{k}{d^{2}}$. We get $I=\frac{562.5}{1.9^{2}}$.

Step4: Calculate the intensity value

First, calculate $1.9^{2}=3.61$. Then, $I=\frac{562.5}{3.61}\approx155.8$.

Answer:

$155.8$