Recent content by DoubleMike

Pick a random dy/dx and random y. Then solve for x and see if f(x) = y in the original equation.

I don't understand your question... the left side just takes the absolute value of the area under f(x), which could well be negative. As for the right side, it will count a negative f(x) as positive... if it's applied to a velocity function, it would give the total distance traveled rather...

what do they mean by no gaps between layers? Does this mean you can treat the winding as a solid shell?

You could've used the fact that w^2 = (9-l^2) and just subed that directly into the equation.

That question was confunsingly worded, but I think it means the rectangular section you can cut our from the circle. Hence, develop a formula for the dimensions of a circumscribed rectangle, then derive it.

I was thinking about this today, and it would seem that one diagonal has to be in the exact center of one of the larger rectangle's sides in order for it to rotate... It's freedom of rotation is then dictated by its other sides. That's all I got. Is there a book with sample AIME questions...

So I'm getting ready to go to college next fall and I have been worried about my future. I've always figured I'd major in math and do so research or something... But recently I can't help but feel inadequate; I visited my college and met with a math professor and he gave me a bunch of test...

That had been my original guess, thanks :)

Why is the area enclosed by a polar curve equal to \int \frac{1}{2}R^2 d\theta What's the Riemann sum from which this is derived?

I thought that you needed to know in respect to which variable. I've just been mechanically integrating both sides, but I don't know why the left side doesn't need a dy. As far as I'm concerned, the LHS is just an equation which happens to be the differential. It would still need a dy (it...

So where does that leave us? Also, don't you need a dy to integrate the left side?

Correct me if I'm wrong, but \frac{d}{dx}[uy] is just notation for the derivative of uy, the dx isn't really a differential at all. If it was, then in reality you would be dividing by dx... Are you telling me that d[uy] = dy?

But the left side is missing the dy... It seems suspect that you can multiply the dx as a fraction like that, then d[uy] really doesn't mean anything. It's like performing math on notation... I'm sure it's just shorthand =/

My class has recently done an intro to differential equations, and although I understand the method of solving simple equations, I want to know why the method of Linear Factors works. Unfortunately my book hasn't provided a proof for it. Also in the final step where you integrate both...

Rubbish math for a less than serious question... Honestly, stop being so critical. Had the question been asked in earnest, then fine.