Math Is Fun Forum

To get the velocity and displacement functions, you just integrate twice.

∫ π/8 * cos(π/4 * t) dt = 1/2 sin(π/4 * t)
∫ 1/2 sin(π/4 * t) dt = -2/π cos(π/4 * t)

How can you describe the motion with a sketch? Well, that train oscillates, so that's a start.

Hey Ricky, the three reasons you cite are the same reasons I think Java is good to learn on.

I learned on C, not ++, and got quite frustrated with it. I was young at the time (13), so that may have had something to do with it. But also, I was frustrated when trying to go beyond simple stdin/stdout. The leap of knowledge required is tremendous, and the means was not available to me at the time to make it.

It wasn't until I learned Java that programming started to make sense to me. When forced to adhere to the structure, it became ingrained and I realized the sense of it (especially when learning PHP, which tries hard to be accommodating). Perhaps nobody'd ever explained the finer arts of memory allocation, but it always seemed like voodoo; Java garbage collection was a breath of fresh air. And the extensive, well-documented, platform-neutral library let me experiment with things (like gui programming) that I never could have dreamed of doing in C without, well, going to college.

But, maybe my experience fits into one who was "not learning," since I understood pointers and how to make a linked list. :

(Yes, I just used a dunno. It is jU week, after all.)

Yeah, I saw that! It looks amazing. It looks time consuming. It looks like I'll stay the heck away if I know what's good for me.

Nice pages! I only found one mistake. The comma in this sentence, is superfluous:

Yeah, our calendar drags. It is said that the Mayans had a calendar that required no leap years. I'm sure if we put our minds to it, we could come up with one too.

What would it take to transition our globe to a sane time structure? Would it even be possible/worth the effort?

Well, countries have switched weights and measures before. But time is more integral. Besides reprogramming _everything_, we'd have to reprogram ourselves. Not gonna happen.

"Vicinal" hydrogens are separated by three bonds. So, in this structure: H3--C--C--H3 (ethane), 3 hydrogens are vicinal to three others.

So yes, they're close together, but not so much in space as in bonds (though it usually means in space, too).

"Want proof? Well, YOU try solving it!"

I have nothing of value to add, just my lame sense of humor.

Look at it this way, affirmation. The degree of the denominator is less than that of the numerator. As n-> infinity, the top gets much larger than the bottom, such that the division becomes insignificant, and the sum goes to infinity.

Look, I'll show you. You can do polynomial division on that function to simplify it, and it comes out as:
x² + 5x + 6 + 1/(x² + x)

...Where you see that the fractional bit goes to 0 as n-> inifinity, but there is still a quadratic, with nothing taking away from it, adding to the sum.

Lol, I got a 4/10. Not my thing I guess.

You can find the angle between point B, the center, and point A with the inverse sin function: arcsin 1/2. In radians, this comes out to π/6. This is the amount of the circle that rolls to one side before the point hits the top. You can convert this from radians to distance by dividing by the total number of radians in a circle (2π) and multiplying by the circumference of the circle (2π8). This comes out to 4π/3, which is the horizontal distance the semicircle travels.

The diameter of the semicircle is 16 cm. 4π/3 cm are cut out of one side, and 4π/3 are cut out of the other. So, you can find the distance between the two points thusly:
16 - 2(4π/3) = 7.6224.

If you need more explanation I can post diagrams and such; this was kind of a hurried post.