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Category: Probability and Statistics

Calculate-5-i-4-239-i-Then-Prove-the-Machin-formula-4arctan-1-5-arctan-1-239-pi-4-

Question Number 216746 by sniper237 last updated on 17/Feb/25 $${Calculate}\:\frac{\left(\mathrm{5}+{i}\right)^{\mathrm{4}} }{\mathrm{239}+{i}}\:{Then}\: \\ $$$${Prove}\:{the}\:{Machin}\:{formula} \\ $$$$\mathrm{4}{arctan}\left(\frac{\mathrm{1}}{\mathrm{5}}\right)−{arctan}\left(\frac{\mathrm{1}}{\mathrm{239}}\right)=\frac{\pi}{\mathrm{4}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

find-integers-x-y-such-that-x-x-3-4-y-2-45-1-100-

Question Number 212926 by efronzo1 last updated on 27/Oct/24 $$\:\mathrm{find}\:\mathrm{integers}\:\mathrm{x},\mathrm{y}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\:\:\:\frac{\mathrm{x}}{\mathrm{x}−\mathrm{3}}\:−\frac{\mathrm{4}}{\mathrm{y}^{\mathrm{2}} −\mathrm{45}}\:=\:\frac{\mathrm{1}}{\mathrm{100}} \\ $$ Answered by Frix last updated on 27/Oct/24 $$\Leftrightarrow \\ $$$${x}=\frac{\mathrm{3}\left({y}^{\mathrm{2}}…

The-expected-number-of-values-drawn-fromthe-interval-0-1-at-random-if-the-sum-ofthe-values-drawn-so-far-is-less-than-1-is-too-cntinue-drawing-what-is-the-expectede-numbr-of-draws-

Question Number 212918 by MrGaster last updated on 26/Oct/24 $$\mathrm{The}\:\mathrm{expected}\:\mathrm{number}\:\mathrm{of}\:\mathrm{values}\:\mathrm{drawn}\: \\ $$$$\mathrm{fromthe}\:\mathrm{interval}\left[\:\mathrm{0}\:,\mathrm{1}\right]\:\mathrm{at}\:\mathrm{random}\:\mathrm{if}\:\mathrm{the}\:\mathrm{sum}\: \\ $$$$\mathrm{ofthe}\:\mathrm{values}\:\mathrm{drawn}\:\mathrm{so}\:\mathrm{far}\:\mathrm{is}\:\mathrm{less}\:\mathrm{than}\:\mathrm{1},\:\mathrm{is}\:\mathrm{too} \\ $$$$\mathrm{cntinue}\:\mathrm{drawing}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{expectede} \\ $$$$\mathrm{numbr}\:\mathrm{of}\:\mathrm{draws} \\ $$ Terms of Service Privacy Policy…