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

Answer:

k = 0.209

Step-by-step explanation:

The given expression in the question is C = $\frac{kP_{1}P_{2}}{d^{2} }$

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 = $\frac{kP_{1}P_{2}}{d^{2} }$

250000 = $\frac{k\times 95000\times 2900000}{(480)^{2} }$

$k=\frac{250000\times (480)^{2} }{95000\times 2900000}$

$k=\frac{25\times 48\times 48}{9500\times 29}$

k = 0.2091 ≈ 0.209

k = 0.209 is the answer.

Answer 2

Hello.

427000 = k(777000)(3695000)/420^2 


427000 = k(16275595.24) 


k = 427000/16275595.25 

 k = .0262355996

Have a nice day