Precalc0105to0107-page27 - , for which corresponding side...

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(Section 1.6: Combining Functions) 1.6.15 • Express any other relationships between variables. The height of the tank is twice its base radius. This proportion must hold for the water cone, as well. h = 2 r This may be thought of as a constraint equation . It expresses h as a function of r . •• This may be shown using similar triangles
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Unformatted text preview: , for which corresponding side lengths are in equal proportion. h 10 = r 5 h = 2 r Combine the key formula with any constraint equations. We will make the substitution h = 2 r ( ) into V = 1 3 r 2 h . V = 1 3 r 2 2 r ( ) V = 2 3 r 3 We are now expressing V as a function of one variable, r ....
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