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Phantasy [73]
3 years ago
9

The number of phone calls between two​ cities, N, during a given time period varies directly as the populations p 1 and p 2 of t

he two cities and inversely as the​ distance, d, between them. If 18 comma 000 calls are made between two cities 310 miles apart and the populations of the cities are 15 comma 500 and 180 comma 000​, how many calls are made between two cities with populations of 100 comma 000 and 160 comma 000 that are 435 miles​ apart?
Mathematics
1 answer:
kherson [118]3 years ago
5 0

Answer:

∴73,563 calls are made between two cities with populations of 100,000 and 160,000 that are 435 miles apart.

Step-by-step explanation:

Given that,

The number of phone calls between two cities (N )

  • directly proportional as the value of populations p_1  and p_2  of two cities.
  • Inversely varies as the magnitude of distance (d).

N\propto\frac{p_1p_2}{d}

N=k.\frac{p_1p_2}{d}

Given that,

N=18,000, d=310 miles,  p_1=15,500 and p_2=180,000

18,000=k.\frac{15,500\times 180,000}{310}

\Rightarrow k=\frac{18,000\times310}{15,500\times 180,000}

\Rightarrow k=\frac{31}{15,500}

Now,

N=? , d=435 miles,  p_1=100,500 and p_2=160,000

N=\frac{31}{15,500}.\frac{100,000\times 160,000}{435}

\Rightarrow N\approx 73,563

∴73,563 calls are made between two cities with populations of 100,000 and 160,000 that are 435 miles apart.

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