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[Jim Groovester]

You have two equations with two unknowns. Welcome to linear algebra.

Let x = time and y = speed. You know the following things:

xy = 4800
(x+2)(y-200) = 4800

Now we solve for stuff and make some substitutions.

(x+2)(y-200) = xy
xy + 2y - 200x - 400 = xy
2y - 200x - 400 = 0
2y = 200x + 400
y = 100x + 200

Now we substitute y back into one of the original equations and solve for x.

x(100x + 200) = 4800
100x² + 200x - 4800 = 0
x² + 2x - 48 = 0
(x + 8)(x - 6) = 0

Giving us x = -8 and x = 6 as solutions for x. However, -8 does not make sense in this context so we discard it. Then we can take our equation for y and substitute x into that.

y = 100*6 + 200 = 800

EDIT: As always, it's important to keep track of what the question is asking. 800 km/h is the jet's speed from Tokyo to Bangkok, but the question asks for the speed from Bangkok to Tokyo, which is 600 km/h.

[Descan]

That is far easier than I expected. Thank you (I was about to punch a hole in the wall)

[Skyrunner]

Doesn't it only have one variable?

time1 - time2 = diff time
4800/x - 4800/(x-200) = 2 where x is the speed from Tokyo to Bangkok, and x> 200.

[Jim Groovester]

Traditional setups of problems of this type use two variables.

One variable can be eliminated from the equations by substitution though. I.E.,

xy = 4800 --> x = 4800/y
(x+2)(y-200) = 4800 --> x+2 = 4800/(y-200)

x + 2 - x = 4800/(y-200) - 4800/y = 2

Which is what you have.

[KingBacon]

So, I'm doing topology stuff with metric spaces. I just want to make sure everything I'm doing is kosher.

Let d1 be the discrete metric and d2 be any arbitrary metric.

So I have two metric spaces, one with integers and the discrete metric and one on the reals and some arbitrary metric.

(Z, d1), (R, d2)
any function
f: Z -> R is continuous, because

For all Y that are open subsets of R, f^-1(Y) is an open subset of Z (because all subsets in Z with the discrete metric are closed and open, i.e. "CLOPEN" .)

Does this make sense?

[Neonivek]

So I have the same problem with the math test I am about to get and here is the problem.

A first principle is basically the (F(x + h))-F(x) / h (Ignore the syntax)

Yet the question specifically asks me not to use any formula for getting derivatives.

Yet first principles is a formula.

[Darvi]

Maybe it wants you to just write down the derivative, without the bits in between?

[Neonivek]

Maybe it wants you to just write down the derivative, without the bits in between?

No, he doesn't want power law or product law.

[Jim Groovester]

So I have the same problem with the math test I am about to get and here is the problem.

A first principle is basically the (F(x + h))-F(x) / h (Ignore the syntax)

Yet the question specifically asks me not to use any formula for getting derivatives.

Yet first principles is a formula.

You're supposed to calculate the derivative the tedious way. You can't use any proven shortcuts. I.E., you have to do:

d/dx x² = lim_h->0 ((x + h)² - x²) / h

And simplify that expression instead of:

d/dx x² = 2x

EDIT: Also, don't be a smartass, you know what the problem means.

[Neonivek]

Also, don't be a smartass, you know what the problem means

No. That made me specifically fail the question last time because it made no sense.

It STILL doesn't make any sense and I wish the teacher wouldn't give questions like that.

[Jim Groovester]

Does this make sense?

I haven't had much topology aside from a smattering in an analysis course, but some quick research leads me to believe that you are correct.

It seems to be a pretty direct result.

Also, don't be a smartass, you know what the problem means

No. That made me specifically fail the question last time because it made no sense.

Have you tried talking to your professor or teacher about what the intended solution of the problem is supposed to be?

[Neonivek]

Let me see....

Finding the limit as X approaches infinity of

The Square root of (9x^6 - X)

Divided by X^3 + 1

How do you do it? I understand the answer (afterall 9x^6's square root is essentically 3x^3... making the question 3/1)

But how do you get rid of the -x? Or does that just not matter for this question?

I am aware you COULD use a conjugate, but that seems needless

[Darvi]

It really doesn't matter. You really just need the highest power to get an infinite limit, since whatever influence the lower limits have on the limit is made negligible by those higher powers.

[Another]

It may get a little more obvious if you divide by x^3 and get to 3*lim(sqrt(1-1/(9*x^5))/(1+1/x^3))).

[Skyrunner]

It's pretty logical if you think about it. Once you get to nine bajillion divided by three bajillion, +500 either way isn't significant enough to matter. Like in the case of, say, (9x^3+x+1)/(3x^3).