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Inverse variation word problem: string vibration

Sal models a context about lengths of strings and the frequency of their vibrations! with an inverse variation equation. Created by Sal Khan and Monterey Institute for Technology and Education.

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• If we graph this variation we get a negative slope. I worked out the equation of the line and got y=-40x+840. Do we always get a negative slope with inverse variation and a positive slope with direct variation?
• We don't always get a positive slope with direct variation because the slope is the k in the equation Y=kx and that could be anything. If k is negitive than the slope is negitive, if k is positive the slope is positive.
• What is inverse variation?
• The simplest way I think of direct vs inverse variation is this way: in an equation, ask yourself what would the other variable do if one variable went up or down. If the other variable goes in the same direction, then the two variables vary directly. If they go in opposite directions, they vary inversely. 'Neither' applies when there is an addition or subtraction function in the equation, because the word 'proportion' no longer applies.
• given that x varies as y and inversely as zsquared and that x=12 when y=3 and z=3,find
{a}the eguation connecting x,y and z.
{b}the value of x when y=3 andz=4
• 5 machines, when operated for 9 hours each day, can harvest a farm in 16 days. How many days would 8 machines take to harvest the same farm, if each machine is now operated for 10 hours each day?
(1 vote)
• 5 machines working for 9 hours each do 45 machine-hours of work total. If the farm is harvested in 16 increments of 45 machine-hours, that means the farm has 16•45=720 machine-hours of work to be done.

720 machine-hours divided by 8 machines is 90 hours of work. If the work is done for 10 hours a day, that gives 90/10=9 days.
• Doesn't "constant" begin with a c, so why do we use K? () I really do not get it.
• It's arbitrary. There's nothing more to read into it. I've seen c,C,K,constant all used.
• what is 1 to the millionth [pwer
(1 vote)
• 1 to almost any power besides 0 is still equal to 1
• I don't understand how this fits in the with function lessons. Is this an example of how a function can be used? Is it possible to fill in the constant K as the function..or something like that? Any help is appreciated!
(1 vote)
• No, you can't fill in K as the function. Think of K as the slope of a line. In this problem think of l as a function of f, or f as a function of l. it works either way.