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Nov
17
comment related rate problem?
You’re welcome; I hope it helps!
Nov
17
comment related rate problem?
It looks okay; I make it about $492.55$. It’s been a while since I used a regular textbook to teach either of them, so I’m not a good person to ask. You might take a look at the notes available here, though; apart from lacking exercises, they’re really textbooks, not just notes. You’re very welcome.
Nov
17
comment related rate problem?
Yes, apart from the typo (extra $0$); I get a value of $z$ a hair more than $504$.
Nov
17
comment Regular Expression For Set of Strings Not Containing OOO
Looks fine to me.
Nov
17
comment related rate problem?
I didn’t check the arithmetic that gave you your $z$ value, but otherwise it looks okay, yes.
Nov
17
comment related rate problem?
The expression in your last comment is $0$, not $-2\cos\frac{\pi}4$. Where on earth are you getting things like $(900)'$? You’re definitely not doing the same thing that you did in your original attempt (with the wrong formula).
Nov
17
comment related rate problem?
It’s not $\cos z$: it’s $\cos\frac{\pi}4$, which is just a constant. Thus, you’re differentiating something of the form $axy$, where $a=-2\cos\frac{\pi}4$. Just use the product rule in the usual way: the derivative is $$a\left(x\frac{dy}{dt}+y\frac{dx}{dt}\right)\;.$$
Nov
17
answered Proving sets A and B are countable
Nov
17
comment Proving sets A and B are countable
Are you using countable to mean countably infinite, or are you using it as most set theorists do to mean finite or countably infinite?
Nov
17
comment related rate problem?
Yes, exactly. Your method was fine; you were simply using the wrong equation to get a relationship amongst $z,x$, and $y$.
Nov
17
comment related rate problem?
Do you know the cosine law?
Nov
17
comment Predicate logic: “Everybody knows somebody who knows Alice”
@Jacob: You’re welcome.
Nov
17
comment related rate problem?
Because that’s the angle between south and southwest.
Nov
17
answered Predicate logic: “Everybody knows somebody who knows Alice”
Nov
17
comment related rate problem?
If $T$ is Toronto, and $P$ and $Q$ are the planes, then $\angle PTQ=\frac{\pi}4$; now use the cosine law to find $z^2$ in terms of $x$ and $y$.
Nov
17
comment related rate problem?
The triangle whose vertices are Toronto and the two planes is not a right triangle.
Nov
17
answered How big is the set of hyper-naturals?
Nov
17
answered Derivative of $e^{-x} - xe^{-x}$
Nov
17
answered Normal spaces in box and uniform topology
Nov
17
comment Normal spaces in box and uniform topology
Are you asking about the ordinary product topology, or about the box product topology?