Recent content by ago01

That seems like a teacher hastily writing something on a board and a better question for the teacher to answer. Logs are all related and it would strike me the teacher meant log base 2 and not ln base 2. ln base 2 makes no sense.

Ah yes, this is my computer science coming through and also why I am taking this class to improve my rigor. You don't "index" into sets. Sets either contain something or don't contain something. We can check the set from any point r, s in the sense that no matter what we will always move through...

So then it appears the best way to think about infinite sets is (2). Since we can choose a s and r in each set and produce an equal value for any s and r, then certainly the sets must be equal. The sets may be "out of order" but we can still choose two numbers that make them equal at any point...

I am reading an abstract algebra textbook and enjoying it. I am working through preliminaries some more to refine my knowledge on proofs with sets before really digging in. I understand that if $$X \subseteq Y$$ and $$ Y \subseteq X$$ Then $$ X = Y$$ This makes sense to me. However, the...

I see. Yeah that would do it. e^x has y = 1 at x = 0. My graph is shoddy. It's obvious now that if you go the x-direction you have two different functions. One being x= 0, and then it switches to y = e^x. In this case, you would need extra integration to cover that function switch, so dydx is...

I have the solution for this problem using dydx as the area. Worse yet, I cannot find another solution for it. Everyone seems to just magically pick dydx without thinking and naturally this is frustrating as learning the correct choice is 99.9% of the battle... So, I was curious how one might...

So I suppose then as long as the surface is moving at the same acceleration relative to us we will move with that surface and the normal force provides the acceleration. Your explanation also makes sense, if the elevator suddenly stopped the person in the elevator would keep going due to the...

Earlier I was doing a sample problem for class that involved the work done by an elevator, and the problem gave us the normal force experienced by the person in the elevator (to calculate the acceleration of the elevator-person system). I had done this wrong because I had wrongly assumed...

I see yep. I'm glad I asked. This is a good checkpoint for me on making sure I'm getting force pairs correctly. Thank you!

Sure, I'll diagram what's going on in my brain This was my original post diagrammed. However, it appears I forgot a very important condition... I'm not sure if this is totally correct...but it feels closer. So because the puck is spinning a circle, the changing velocity is generating a...

For practice I did the following problem: Solving this problem mechanically was simple enough using the following force diagrams: Then $$F_{net_M} = T - Mg = 0$$ Due to the stationary condition $$T = mg$$ and $$F_{net_m} = T = ma_c$$ $$T = ma_c$$ Because centripedal acceleration is...

I see so I think I see my mistake. To be clear: When the man pulls on the rope he induces a tension in the rope, which by Newton's 3rd law induces a tension on the other side lifting the chair. There's no extra force, just tension. The extra tension force comes from the rope also pulling up on...

I had a homework question recently where I had gotten a bosun chair question wrong. It is the exact question found in this youtube video (with the values changed). I am struggling to understand the way 2T is arrived at here (though I do understand this is an example of mechanical advantage)...

I was doing a practice quiz and got the following integral: ##\int \frac{1}{\sqrt{x^2-49}}dx## Following normal trig sub. Using ##b^2 = c^2 - a^2## we find ##\sec{\theta} = \frac{x}{5}## and so ##x = 5\sec{\theta}## and ##dx = 5\sec{\theta}\tan{\theta}d\theta## Then ## \int...

Interesting...I suppose this makes it clear why you should simplify as much as possible to get to the meat of the integral. The graphs are only equal at the "peaks". Fascinating.