contestada

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 the 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?

Respuesta :

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 [tex]p_1[/tex]  and [tex]p_2[/tex]  of two cities.
  • Inversely varies as the magnitude of distance (d).

[tex]N\propto\frac{p_1p_2}{d}[/tex]

[tex]N=k.\frac{p_1p_2}{d}[/tex]

Given that,

N=18,000, d=310 miles,  [tex]p_1[/tex]=15,500 and [tex]p_2[/tex]=180,000

[tex]18,000=k.\frac{15,500\times 180,000}{310}[/tex]

[tex]\Rightarrow k=\frac{18,000\times310}{15,500\times 180,000}[/tex]

[tex]\Rightarrow k=\frac{31}{15,500}[/tex]

Now,

N=? , d=435 miles,  [tex]p_1[/tex]=100,500 and [tex]p_2[/tex]=160,000

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

[tex]\Rightarrow N\approx 73,563[/tex]

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