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    Question of Rotational motion

    Thank you everyone, this problem has been solved.
  2. P

    Question of Rotational motion

    Got it! Since their is no translational motion, the normal reaction from ground+ frictional on the left wall= mg. And, friction on ground = Normal reaction from the left wall. Done!
  3. P

    Question of Rotational motion

    Oh wait, maybe the normal reaction at ground isn't mg. I have had an idea, let me try it out first.
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    Question of Rotational motion

    Ignore the minus sign behind mgk. Their has to be some involvement of centripetal force in friction, but I am not sure how, because it is directed towards the center, and not towards the ground. I know I have probably done it very wrong. I'm sorry if it's too bad.
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    Question of Rotational motion

    I am unable to find the frictional force on the left wall.
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    Question of Rotational motion

    Hello, I'm stuck in this rotational motion problem (advanced high school level). Source: Problems in General Physics- IE Irodov My attempt(s): First I tried using work done by the moment of friction (mgkR) and equated it with change in KE. I got the answer as ## \frac{R (\omega_0)^2}{8 \pi...
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    Challenge Math Challenge - February 2020

    You can simplify the formulas of n=odd. For n and m both odd the formula can be simplified to ## \frac{mn+1}{2} ## . For n odd, m even, the formula can be simplified to ## \frac{mn}{2} ## . This way both the cases of n feel interconnected.
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    Challenge Math Challenge - February 2020

    So much better than what I was going to post. I just expanded ## e^x ## upto first 3 terms to get the second greater than first.
  9. P

    Challenge Math Challenge - August 2019

    Sorry for late reply. I was not able to come online a lot since a long time. Anyway, I tried to prove it, but I couldn't. Hence my proof is wrong. Sorry.
  10. P

    Challenge Math Challenge - August 2019

    Sorry, I thought it was sufficient to leave it at that. EDIT: I made one more mistake, I didn't mention that z is not equal to 0. If z=0, then the answers come to be (0,0,0) which is excluded.
  11. P

    Challenge Math Challenge - August 2019

    One wrong assumption, x=a is not the global maximal for all a. If a is negative or an even natural number, then it is just a critical point. But the answer is correct because it is the global maxima of ##e^{-2}##.
  12. P

    Challenge Math Challenge - August 2019

    In this method, ##a^2=9x^2, b^2=9y^2## . This implies ##c^2## is a multiple of 3. Then you can continue with the same method I did. Using contradiction to prove that solutions don't exist. However, I'm not sure how to prove that d divides c (if I'm not wrong, d is the gcd of a,b).
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    Challenge Math Challenge - August 2019

    I didn't write the answer for this one, because I didn't really come up with the solution. It was an example question in my physics textbook, and it had 2 methods of solving it. One of them was similar to yours and the other was similar to that of @nuuskur gave.
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    Challenge Math Challenge - August 2019

    I'm sorry. I advised it because when I came to this site, I learned that copy pasting latex causes some problems in this website. So I found out alternative ways. It also had the replace function, so I would type shortcuts, and then find and replace them. It also preserved the formatting. You...
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    Challenge Math Challenge - August 2019

    I don't know a lot about ##\LaTeX## on this site, but writing the entire answer in a word and then copy pasting helps me a lot. And @fresh_42 advised me to use windows hot keys. That helps a lot. Best part of word is that formatting is preserved.
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    Challenge Math Challenge - August 2019

    Sure. First I'll explain why x is even. Since l is less than equal to m and n, we can divide both the sides by ##2^{2l}## . That in any scenario gives either x is even or x and y are even or all x,y,z are even (when l=m=n) by taking mod 4 both sides. A similar reasoning is followed for z. As to...
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    Challenge Math Challenge - August 2019

    Most of my solution is correct, except I forgot to write 3 behind z. Should I retype it (it won't be very difficult, I will quote my answer, edit it and then remove the quote brackets at the end), or is it okay? Edit: @Math_QED I have edited my answer. I have made an additional change, I...
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    Challenge Math Challenge - August 2019

    You're right :headbang: . But that doesn't affect the solution luckily. That's because three is not an even number. If the question had 6 instead, then my solution would have been wrong. I got lucky.
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    Challenge Math Challenge - August 2019

    You are correct. It holds true for all real functions. It is a proved and standard result.
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    Challenge Math Challenge - August 2019

    I am neither referring to the real part, nor the imaginary part. I am taking it as a whole. My function is differentiable at all points, f(1)=f(0) and f'(x) is not 0 between 1 and 0.
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    Challenge Math Challenge - August 2019

    It is not differentiable at ##x=\frac{1}{2}##
  22. P

    Challenge Math Challenge - August 2019

    Even I think that. He must have misquoted.
  23. P

    Challenge Math Challenge - August 2019

    Q8 is number theory 🙃
  24. P

    Challenge Math Challenge - August 2019

    Yeah. Sorry, for some reason I read that as f'(a)=f'(b).
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    B Why is the distributive law correct in algebra, like in arithmetic?

    That second video stressed me out for some reason.
  26. P

    Challenge Math Challenge - July 2019

    I think that's just a typo.
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