Question

Are there any common tricks with inverse and direct variation? Examples would be very helpful for me.

Answer 1

Let's say I was able to measure productivity \(w\), profit \(p\), and cost of materials \(c\) quantitatively. A reasonable model for an explicitly simple system would be:\[p=\frac{w}{c}\]Now, which variables vary directly, and which vary indirectly? Tell me what you think. Even if it's wrong.

Answer 2

Vary Directly-c Vary indirecly-w

I am not sure.

Answer 3

Alright, so as \(p\) increases in\[p=\frac{w}{c}\]either \(w\) is getting higher, or \(c\) is getting lower, or both. For instance, if \(p=2\), \(w=6\), and \(c=3\), what are possible values of \(w,c\) if I increased \(p=4\)?

Answer 4

6=36/6

Answer 5

Very good. You noticed that \(w\) increased (by a larger margin than \(c\))? Now, returning to the previous question, what if I reduced \(p=1\)?

Answer 6

if reduced by one then 1=infinite no of solutions?

Answer 7

Yes, there are an infinite number of solutions. I'm asking what are possible solutions.

Answer 8

like 6/6

Answer 9

Yup. Noticed now how \(c\) increased by a larger margin than \(w\)? So what do you think: does \(p\) increase and decrease directly or inversely with \(c\) and \(w\)?

Answer 10

inversely

Answer 11

Not both. Which to which? If I increase \(p\), \(w\) generally grows larger and \(c\) smaller, so the number \(w/c\) is larger. If I decrease \(p\), \(w\) generally grows smaller, and \(c\) larger, so \(w/c\) grows smaller. Do you understand?

Answer 12

Yeah! Thanks a lot so much. :-) Now I understand

Answer 13

So, final test. Does \(c\) vary inversely or directly with \(p\)? What about \(w\)?

Answer 14

Hey, I invested time into this. I want to see you actually learned something. :P

Answer 15

Just, Hold on a bit I will get to it...

Answer 16

@myininaya I know you're an actual teacher, you might be better here. :P

Answer 17

inversely

Answer 18

Am I right?