Question 376745
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<i>Varies Directly</i>


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ kx]


*[tex \Large k] is called the constant of variation and has to be determined using the initial conditions given.


If *[tex \Large y\ =\ 26] when *[tex \Large x\ =\ 4], substitute:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 26\ =\ 4k]


Then solve for *[tex \Large k]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ k\ =\ 6.5]


Then put *[tex \Large k] back into the original equation.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ 6.5x]


Then for *[tex \Large x\ =\ 7]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ 6.5\,\cdot\,7\ =\ 45.5]


<i>Varies Inversely</i>


Works exactly the same way except that you start with:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ \frac{k}{x}]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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