Question

Joe traded Kramer a helmet in exchange for a radio. The strength for the radio signal varies inversely with the square of your distance from the transmitter. If the strength is 1000 units at a distance of 2km, what is the strength at a distance of 10 km from the transmitter?

Answer 1

40 units

Explanation:

Let y be the strength for the radio signal.

Let x be the distance from the transmitter.

If the strength for the radio signal varies inversely with the square of the distance from the transmitter, then:

`\boxed{y \propto (1)/(x^2)\implies y=(k)/(x^2)}`

where k is the constant of proportionality.

Given the strength is 1000 units at a distance of 2km:

• 
  `y = 1000`
• 
  `x = 2`

Substitute the values into the equation and solve for k:

`1000=(k)/(2^2)`

`1000=(k)/(4)`

`k=4000`

Therefore, the equation that links y and x is:

`y=(4000)/(x^2)`

To find the strength (y) at a distance (x) of 10 km from the transmitter, substitute x = 10 into the equation:

`y=(4000)/(10^2)`

`y=(4000)/(100)`

`y=40`

Therefore, the strength of the radio signal at a distance of 10 km from the transmitter is 40 units.