Recent content by verty

I recommend this blue book partnered with https://ocw.mit.edu/courses/mathematics/18-01-single-variable-calculus-fall-2006/video-lectures/ to get you out of your schtuck. I think you need solidly good teaching to get past whatever your issue is.

The idea is that ##{\Delta V \over \Delta r} \approx {dV \over dr}##. So if you know ##dV \over dr##, you can find ##\Delta V## approximately given ##\Delta r##. Definitely the height is remaining constant. The only change is the radius. See if you can work it out.

Here is another shortening: $$S_{m-n} = {m - n \over 2} (2a + (m - n - 1)d) \\ = {m \over 2} (2a + (m-1)d - nd) - {n \over 2} (2a + (n-1)d - (2n - m)d) \\ = (n - m) + {d \over 2} (n(2n - m) - mn) \\ = (n - m) + {d \over 2} 2n (n - m) \\ = (n - m) (1 + nd)$$

This first thing you have to do is differentiate between philosophy and science. If you study this as philosophy, I think that is a mistake. You should have a philosophy that is not based on phenomena but you should think of phenomena as things you might want to study in a scientific way. For...

I think I forgot to make a clear summary. 1. No one can learn everything. 2. You have to choose what you want to learn. 3. Success is important. There, done.

CuriousCarrot, I used to think exactly like you. I thought to myself, the first thing to learn is to learn how to learn, so that it is more efficient. It's a kind of fixed point. One should learn how to learn, and then learn how to learn, and then learn how to learn, until two of these steps...

I am quite a learned person actually. If it demonstrates anything, it shows this to be paucious: that one should learn everything. Not everybody has the same opportunity. How do I know who will read these threads? It may be someone from a poor family without access to good books, etc. My...

Sorry @Alexanddros81, I forgot about question b. I was thinking it was just a and then c.

I think it would be a mistake for CuriousCarrot to study Encyclopedia Britannica because it is too broad to learn arbitrary facts like that. Or take Astroman707 for example, he was a teacher, becoming a theoretical physicist, thinking about coding, he should keep his focus which I think he is...

Why do you want to learn everything? You should not want to learn everything, you should want to learn only what you need to succeed. Success should drive you to want to learn. How old are you? Have you chosen what you want to study after school?

Try to find a formula for the graph. Use the turning point form: ##y = a(x - b)^2 + c## PS. All the help I can give.

I wonder if fish intake has something to do with it. We know that eating fish is good for older people. At high incomes, $200k versus $300k, they are unlikely to be buying fish from their local chippy. Rather, they either cook it which is unlikely or choose it in restaurants. Those eating...

Okay, two different views. You'll have to decide which to take. I don't know that much about physics tuition so take that into account.

That sounds like a good idea, MisterAvocadoMan. That way, you can focus on the physics without also trying to understand the math. After all, calc 3 is a very difficult subject, IMHO. Normally I wouldn't suggest it but since you have been struggling in physics 1, I think it is a good idea.

I will show that ##I_1## is negative: $$50 I_1 + 40 I_2 = 10;\ 40 I_1 + 60 I_2 = 20 \\ 5 I_1 + 4 I_2 = 1; 2 I_1 + 3 I_2 = 1\\ 3 I_1 + I_2 = 0$$ Note that ##I_1## and ##I_2## have different signs and that ##I_3 = -2 I_1##, so ##I_3## and ##I_1## have different signs. And since ##I_2## is clearly...