Recent content by murshid_islam

I was watching this series of videos of Eddie Woo proving Thales' theorem and its converse. I didn't understand this part (at 2:15) where he considered (x–u)(x–v) = 0. He later used the result he got from considering that. But why consider it in the first place?

I'm not getting how that helps. The problem statement says that 1 cube is to be rearranged into 1 square pyramid. The cube has a volume of 9 cm3

I did not follow that. Can you elaborate a little? Also, is a regular 8th grader supposed to know that?

Since the problem did not specify it's a right square pyramid, I assumed it doesn't necessarily have to be one and that it could be an oblique square pyramid.

I'm not getting why a pyramid with a square base cannot have its apex directly vertically above one of the corners of the square. Can you explain? I can't think of a use of that information. Yes, the problem is from the book "MYP Mathematics 3: A Concept-Based Approach" by David Weber, Talei...

This face: What do you mean by "part"? Do you mean the faces? Or do you mean the 10 smaller pieces the puzzle consists of?

I meant the front face looks vertical to me. I don't know if that is actually the case or not. Can you clarify that a bit? I didn't understand what you wrote there.

TL;DR Summary: It seems like not enough information is given for this 8th grade math problem For the attached problem, let b = the side length of the square base of the pyramid and h = the height of the pyramid 1/3 b2h = 9 b2h = 27 One simple and obvious solution is b = h = 3 (and that's...

Any other alternate set of conditions I can check? Like checking if the opposite sides are parallel and the diagonals are equal?

Yes, coordinates in a plane. Thank you. Edited my original post.

If I'm given the coordinates (edit: in a plane) of 4 vertices of a quadrilateral, which conditions should I check to see if it is a square? Will it be sufficient if I check if - all 4 sides are equal all 4 angles are right angles (or even 2 angles are right angles?) or are there other...

Why are the axes taken as perpendicular to each other rather than at some other angle? Is it just a matter of convention? Is there any mathematical reason behind it? Is there some other reason?

What are some good arguments against mathematics being discovered (or for it being invented)?

The range of sin(x) is the interval [-1, 1], which is also the domain of arccos(x). I'm not being able to figure out how that will affect ##\mathrm{d}u##. What will ##\mathrm{d}u## be if ##u = \arccos(\sin x)##?

Ok, I tried it with integration by parts with ##u = \cos^{−1}(\sin(x))## and ##\mathrm{d}v = \mathrm{d}x##, which gives us ##\mathrm{d}u = \frac{−\cos(x)}{\sqrt{1−\sin^2 x}}\mathrm{d}x = −\mathrm{d}x## and ##v=x##. The integral becomes ##x\cos^{−1}(\sin(x)) + \int x \mathrm{d}x =...