Question 632189
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Whenever two things are in inverse proportion, when one gets bigger, the other gets smaller -- a lot smaller in this case because yellows vary as the <i><b>cube</b></i> of the greys.  So one would expect that if the number of greys got 3 times larger, then the number of yellows would get 3 cubed or 27 times <i><b>smaller</b></i> rather than 3 times larger.  Make sense?


Here's the algebra to back me up:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ \frac{k}{g^3}]


If *[tex \LARGE 270] yellows *[tex \LARGE \Rightarrow\ 2] greys, then:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 270\ =\ \frac{k}{2^3}\ =\ \frac{k}{8}]


I'll leave it up to you to verify that


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ k\ =\ 2160]


Now we have a formula that we can use for specific cases:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ \frac{2160}{g^3}]


Plug in *[tex \LARGE g\ =\ 6]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ \frac{2160}{216}]


I'll leave the rest of the arithmetic to you.


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