chwala's latest activity
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chwala reacted to anuttarasammyak's post in the thread Problem involving ordinary differential equation with
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$$\ln 10 e^{y\ln 10 }dy = \frac{dx}{x}$$ $$e^{y\ln 10 } = \ln |x |+ C$$ $$y= \frac{\ln(\ln |x| + C)}{\ln 10}$$defined for $$|x|... -
chwala posted the thread Problem involving ordinary differential equation in Calculus and Beyond Homework Help.##10^y dy = \dfrac{dx}{x\ln 10}## ##\int 10^y dy = \int \dfrac{dx}{x\ln 10}## ... ##10^y = \ln x +C## ##10^y = \ln (ax)##...
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chwala reacted to neilparker62's post in the thread Solve the quadratic equation involving sum and product with Like.
The roots of the equation in part (i) are the same as the roots in part (ii). Since in both cases we have equations of the form ax^2 +...
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It is good to see how problem-solving by humans can be enriched by artificial intelligence. It can also be seen that problem-solving by...
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chwala reacted to Greg Bernhardt's post in the thread Insights AI Enriched Problem Solving with Like.
https://www.physicsforums.com/insights/ai-enriched-problem-solving/ Author: @neilparker62
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chwala reacted to Gavran's post in the thread Solve the quadratic equation involving sum and product with Like.
This can also be shown in the following way. ## \begin{align} &\arctan\frac\alpha c+\arctan\alpha=\arctan c\nonumber\\...
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chwala replied to the thread Prove that ## 4\tan^{-1}\left[\dfrac{1}{5}\right]- \tan^{-1}\left[\dfrac{1}{239}\right]= \dfrac{π}{4}##.With complex numbers, it makes it even easier,...
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chwala reacted to MatinSAR's post in the thread Prove that ## 4\tan^{-1}\left[\dfrac{1}{5}\right]- \tan^{-1}\left[\dfrac{1}{239}\right]= \dfrac{π}{4}## with Like.
According to you ##\dfrac{tan\beta} {4}=tan\dfrac{\beta} {4} ## but it's not correct. Fore example : ##\dfrac{1} {4} tan \pi =0## But...
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I finished - and printed - my collection of short stories! There Be Monsters A collection of fantastical maritime-themed short stories...
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chwala reacted to neilparker62's post in the thread Prove that ## 4\tan^{-1}\left[\dfrac{1}{5}\right]- \tan^{-1}\left[\dfrac{1}{239}\right]= \dfrac{π}{4}## with
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"All in one" derivation of compound angle formulae - based on the video construction. -
chwala replied to the thread Solve the quadratic equation involving sum and product.done.
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chwala replied to the thread Solve the quadratic equation involving sum and product.for part i. i guess the quadratic equation was not indicated. I will go ahead and finish on that; The quadratic equation will be ##x^2...
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chwala reacted to Mark44's post in the thread Find the smallest value of angle ##α + β ## with Like.
The given equations are ##\tan(\alpha) = \frac a {a + 1}## and ##\tan(\beta) = \frac 1 {2a + 1}##. These lead to the equation...
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chwala reacted to Mark44's post in the thread Find the smallest value of angle ##α + β ## with Like.
The wording of the problem isn't clear, IMO. The smallest positive value for ##\alpha + \beta## is ##\frac \pi 4##. There are smaller...
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chwala reacted to DrClaude's post in the thread How to apply BODMAS correctly in the given problem with Like.
I'm getting tired of being these in my social media. This is mathematically ambiguous and there is no right answer.