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I guess it would. usually when solving for a bunch of unknowns I would have just as many equations but this time I only got the one and my brain suddenly didn't know what to do.
I'm doing this chapter on splitting big ugly polynomial divisions into simpler fractions. At one point in the chapter we come to an example that got reduced to:
Anyone have a guess as to how the author got 2C = 16? Did the author simply lift
right out of the equation, throw away , ignored the other stuff, and solved for C?of course you're right. i forgot about the quadratic formula.
... if you solved
you probably got 1/3 R, right?
I didn't get 1/3 R.
Did I make a math error to arrive at a quadratic? Is factoring possible without knowing the true value of R?
Let me revise my last post.
Working with my previous equation
yieldedSo I decided to solve for the cylinder radius instead with
Shouldn't the answer workout correctly regardless of whether I solve for the radius or the height? Why did it work out solving for the radius? How can I know in advance whether to solve for the radius or the height?
Problem:
Inscribe in a given cone, the height of which is equal to the radius of the base, a cylinder whose volume is a maximum.
This is a calculus maxima problem. Having drawn a diagram I noticed that
The generic cylinder volume formula is
After that I did
. Set . Solve for h to get the max volume which does not match the answer of .Was I wrong in the initial observation R = b + h ??
I'm back. I've tried to solve the same problem using an alternate method without all the substituting.
which happens to be the answer. The question: is this a valid method of solving the problem or did it work out by accident?
thanks for the speedy solution. I never would have thought to substitute like that although I should have known swapping directly 1 for 1 is incorrect.
Yes both symbols are y.
In any normal exercise things would be y with respect to x with an equation like
y = f(x) = something involving x
Following the same pattern I tried
I guess that would be too easy because the official text book answer is
Anyone know how they came up with that?
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