Question

The intensity of radiation at a distance x meters from a source is modeled by the function r given by r(x)=k/x^2, where k is a positive constant.Which the followig gives the average intensity of radioation between 10 meters and 50 meters from source? a. k/900

b. -k/50 + k/10
c. 1/40 (-k/50 + k/10)
d. 1/2 (k/100 + k/2500)

Answer 1

Explanation:

The average intensity of radiation between 10 meters and 50 meters from the source can be found using the following formula:

Average Intensity = (1 / (50 - 10)) * (Integral of r(x) from x=10 to x=50)

Using the formula for r(x), the integral of r(x) between 10 and 50 can be found as:

Integral of r(x) = -k * ln(x) evaluated at x = 50 and x = 10

Therefore, the average intensity of radiation between 10 and 50 meters from the source is given by:

Average Intensity = (1 / (50 - 10)) * (-k * (ln(50) - ln(10)))

This simplifies to:

Average Intensity = (1 / 40) * (-k * ln(5))

This is equivalent to choice c.

Average Intensity = 1/40 (-k/50 + k/10).