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The number of telephone calls N between two cities A and B varies directly as...

Mathematics
JAMB 1978

The number of telephone calls N between two cities A and B varies directly as the population P\(_{A}\), P\(_B\) respectively and inversely as the square of the distance D between A and B. Which of the following equations represents this relation?

  • A. N = \(\frac{kp_A}{D^2} + {cp_B}{D^2}\)
  • B. N = \(\frac{k P_{A} P_{B} }{D^2}\)
  • C. N = \(\frac{kD_AP_D}{B^2}\)
  • D. N = \(\frac{kD^2_AP_D}{B}\)
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Correct Answer: Option B
Explanation

\(N \propto P_{A}\); \(N \propto P_{B}\); \(N \propto \frac{1}{D^{2}}\)

\(\therefore N \propto \frac{P_{A} P_{B}}{D^{2}}\)

\(N = \frac{k P_{A} P_{B}}{D^{2}}\)


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