Math Is Fun Forum

This is kind of lame, but bear with me.

Lay them on their sides so that they form a square. Two glasses on opposite ends of the square are one glass-length apart.

"Wait," you say, "what about the glasses that are touching? They're much closer to each other than those that aren't!"

Aha, but with logic, I can distort reality. You see, a part of those glasses (the opposite end from the one that's touching) is one glass-length away, so it can be said that all of the glasses are equidistant.

I know, I know...lame. But it's all I've got.

I also think they're well done.

While you're treating order of operations, a bit on the distributive property would also be beneficial to the multiplication page, since it's not readily apparent at first that if you multiply both sides by something, you have to do it to everything on both sides.

I remember having a tough time with the distributive property in 7th grade. Surprisingly, a simple, clear explanation of this concept was not available to me. It seemed like this mysterious thing with a fancy name instead of the simple, intuitive concept that it is.

4) Barbados
8) SCUBA is Self Contained Underwater Breathing Apparatus. ELISA could be (just guessing here) English Language Internationally Standardized Aptitude test.
11) A nautical mile is like 6080 ft as opposed to a mile's 5280. I don't know without looking it up, but I believe it derives from the old (still-used) measure of speed, the "knot". Knots used to be measured by throwing a float attached to a knotted rope out the back of a ship, then counting how fast the knots reeled out.
12a) Dichloro-diphenyl-trichloroethane is a banned pesticide. (Go organic chemistry!)

Darth and Justlooking are correct.

I'm still clueless about g) 1 FBOHZIAG.

These are fun, 23 JLFTM!

n) 8 BIAB

o) 7 DYTHY

p) 1.21 GWTTBTTF

q) 3 ICFIAC

r) 6 SOAD

s) 52 PCPD

Looks like I was wrong on d. It fit the acronym, but I didn't bother to check the number.

As my Calc teacher once said, "Machines sometimes give us some interesting answers..."

Remember that computers have no intuition. I'm sure they've got their algorithms such that if a function can be integrated, they will integrate it somehow. It's doubtless not the best at selecting the proper method for every integral, and for some it probably doesn't have a "best method." But if you have the attention span of a computer, it works just fine.

Or maybe somebody taught the computer about artificial job security...

Anyway, I guess this is a case where a calculator isn't the best tool after all. Though, if you're using computers end to end, then the computer doesn't care how ugly the function you ask it to evaluate is...

\mbox{The first post, mathsy. 8O)}

I'm advanced eh? I guess I'm good at sounding smart or something. I'm pretty sure I'm in the same place (Calculus 2) as you, mikau.

Anyway mikau, my question (which both you and irspow answered the same way) is this, using your example:

xe^x - e^x

Is it:
(3e³ - 2e²) - (e³ - e²)

...or is it:
(3e³ - e³) - (2e² - e²)

...? Actually, working through the two, they both come out the same. Is this always the case, though? Let's see:

Let h(x) = uv and g(x) = ∫u′v, then assert:
[h(b) - h(a)] - [g(b) - g(a)] = [h(b) - g(b)] - [h(a) - g(a)]

h(b) - h(a) - g(b) + g(a) = h(b) - g(b) - h(a) + g(a)

So it is. Ok, dumb question. *smacks self*

Edit: on the plus side, this post made me finally learn LaTeX, or at least enough to write it.