SOLUTION: Id have a question if x varies inversely as y and x=2 when y=8, and i should find x when y=17 then x=12 or does x=11? Another question would be; if y varies directly with x and

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Question 189494: Id have a question if x varies inversely as y and x=2 when y=8, and i should find x when y=17 then x=12 or does x=11?
Another question would be; if y varies directly with x and y=10 when x=15, find y when x=6, so y=1?
My last question would be; could someone explain this to me; if y varies directly as x and inversely as z^2, and y=3 when x=2 and z=4, what is the value of x when y=9 and z=4? how would i solve this?
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

For your first question, neither of your answers are correct.

If y varies inversely as x, then you can say:

where k is called the constant of proportionality. The first task is to determine the constant of proportionality based on the given values of x and y. To do this, substitute the given values and then solve for k.

Multiply both sides by 2:

Now you can create the specific relationship for your problem by substituting this newly discovered value for k:

And finally, if you need to know the value of x when y = 17, you need to substitute this value in place of y and solve for x:

Multiply both sides of the equation by :

And that's your answer.

The other two problems are done the same way, except that a direct variation looks like:

And in your third problem, you have to set up two equations and solve them both.

John