To understand the inverse variation,let is correlate it with our real life of inverse variation examples such as the total time taken with the speed traveled in a trip. Assuming distance of a trip would be fixed, let us say the distance of a trip would be 250 mile.
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Here inverse variation equation will be used as T=250/r , according to the time will be T be time of the trip will be equal to 250 divided by the Rate in miles per hour which will called r .so if rate is 50 miles per hour it would take, 5 hours .
The next of the inverse example is total time taken to spread the soil and the number of people working on a part of land. so let us say if the total time of the job will take 12 hours the total time T to complete the job would be 12 hours divided by n, ( n is the number of workers).
Here the equation will be T= 12/n. so if have 1 worker , we take 12 hours, 3 workers we take 4 hours and so on.
Total amount of cost required by per person for petrol and the number of people in a cab. So if we know that it will cost 45 dollars’ worth of petrol to go for a picnic trip. The cost represents C= 45 dollars divided by number of people in the cab.
That is C= 45/no of people. So if n will increases the total cost decreases.
Here in inverse variation definition is as the ones quantityvalue gets bigger and the others value gets smaller in such that there product remains the same or proportional. Let us understand with one more example, Y varies inversely as X. where Y= 4 and when X=2.
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Find the value of the inverse-variation equation. Then determine Y when X= 16. By performing substitution we can solve this question. Y= k/x. by doing cross multiplication , we get 4= k/2 which is k=8. So our inverse-variation will be Y=K/x that is 8/x. Now we can answer the second query on determining the y when x is 16. So, y= 8/x , substituting the value of x as 16. So y= 8/16. And we get 1/2 . y= ½ and x= 16.