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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?

1 Answer

5 votes

Answer:

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.

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