The rainfall, r, is inversely proportional to the water shortage, s, in a city. If the rainfall in the city is 40 inches, there is a water shortage of 200 million gallons per day.

Question

Mathematics

Adrienne Burch

28 May, 10:58

The rainfall, r, is inversely proportional to the water shortage, s, in a city. If the rainfall in the city is 40 inches, there is a water shortage of 200 million gallons per day.

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Yandel Nunez · Answer 1

We are asked in this problem to look for the constant given the relationship of the variables is in inverse proportion. In this case, rainfall, r is inversely proportional to the water shortage, s. The expression that represents this is r = k/s where k is the constant of proportionality. Given the data on the problem, we substitute

r = k/s

40 in = k / 200 million gal/d

using cross multiplication to find k, the resulting equation is

40 in * 200 million gal/d = k

8000 million gal in / d = k

8000 in scientific notation is 8x10^3 and million is 10^6, thus multiplying both is 8x10^9.

Thus k is equal to 8 x 10 ^9 with the units of gal in / d.