Geometry/Direct and Inverse Variation
QUESTION: Hello sir
Sir below are eg of direct an inverse variation.
direct variation--> An electric pole ,14 meters high, casts a shadow of 10 meters . Find the height of a tree that casts a shadow of 15 meters unders similar condition.
sol let the height of a tree be x meter
Height of tree-- 14 x
lenght of shadow-- 10 15
Note the more the height of object , the more would be its lenght of its shadow
there for it is a case of direct variation
= that is X1 / Y1= X2 / y2
= 14/ 10=x/15
=14/10 x 15 =x
14 x 3/ 2 = x
If 15 workers can buld a wall in 48 hrs , how many workers will be required to do the same work in 30 hrs
Let the no of workers employed to build the wall in 30 hours be y
no. of hours----- 48 30
no. of workers--- 15 y
This is a case of inverse variation. that is x1 y1=x2 y2
48 x 15 30 x y
there fore 48 x 15
------- = y
or y =24
Sir on basis of example please tell me why we do different in both variation and why
ANSWER: Hi Aishwarya,
Direct variation involves a common ratio. This is usually pretty clear to see. As you say in your example, the taller an object, the longer its shadow.
Indirect variation is a bit trickier in that it involves a common product (multiplication). In the example you gave, we have worker-hours, which is a measure of total effort. 15 hours times 48 workers means (15)(48)=720 worker-hours. If you want to do the same work, in 30 hours, we will get (30)y=720 worker-hours, which means that y=24 workers.
You could string it all together like this:
But the 720 in the middle does not matter. We know the left side must equal to the right side, so we can reduce it to:
And that is the format of the equation you provided.
Hope this helps,
---------- FOLLOW-UP ----------
QUESTION: Hello sir
Sir iam extremely sorry t5o irritate you behind direct and inverse variation but sir my question is not cleared. My confusion is what is in the inverse that we do common product but why not in direct variation. If we do direct variation method in inverse why it is wrong . Why do we apply different formula for direct and diferent for inverse.
In general, why do you use multiplication sometimes and division others? Why do you add sometimes, and subtract sometimes?
They are different situations and they call for different operations or different ways of solving them. It is up to you to determine from the formulation of the problem which is the correct way to solve it.