Question

It has been found that the average number of daily phone calls C between two cities is directly proportional to the product of the populations P1 and P2 of the two cities and inversely proportional to the square of the distance d between the cities. That is, C=(kP1P2)/(d^2).

The distance between Albany, New York, and Cleveland, Ohio, is about 480 miles. If the average number of daily phone calls between the cities is 250,000, find the value of k and write the equation of variation. Round to the nearest thousandth. The population of Albany and Cleveland is 95,000 and 2,900,000 respectively.

Answer 1

Hello.

427000 = k(777000)(3695000)/420^2


427000 = k(16275595.24)


k = 427000/16275595.25

k = .0262355996

Have a nice day

Answer 2

k = 0.209

Explanation:

The given expression in the question is C =
`(kP_(1)P_(2))/(d^(2) )`

Where
`P_(1)` and
`P_(2)` are the populations of the two cities and d is the distance between the cities.

If the distance between the cities d is 480 miles

Population of the cities are
`P_(1)` = 95000 and
`P_(2)`=2900000 respectively.

And average number of the daily phone calls is 250000.

Then we have to find the value of k.

C =
`(kP_(1)P_(2))/(d^(2) )`

250000 =
`(k* 95000* 2900000)/((480)^(2) )`

`k=(250000* (480)^(2) )/(95000* 2900000)`

`k=(25* 48* 48)/(9500* 29)`

k = 0.2091 ≈ 0.209

k = 0.209 is the answer.