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Author: Tinku Tara

Solve-1-x-1-x-3-1-2-1-x-2-1-x-3-1-2-1-

Question Number 201991 by MATHEMATICSAM last updated on 18/Dec/23 $$\boldsymbol{\mathrm{Solve}} \\ $$$$\left(\frac{\mathrm{1}}{{x}}\:−\:\frac{\mathrm{1}}{{x}^{\mathrm{3}} }\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \:+\:\left(\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\:−\:\frac{\mathrm{1}}{{x}^{\mathrm{3}} }\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \:=\:\mathrm{1} \\ $$ Answered by mr W last updated…

Question-202016

Question Number 202016 by sonukgindia last updated on 18/Dec/23 Answered by MM42 last updated on 18/Dec/23 $${x}^{\mathrm{55}} −\mathrm{1}=\mathrm{253}×\mathrm{8}{k}\Rightarrow“{x}''\:{is}\:{odd} \\ $$$$\left({x}−\mathrm{1}\right)\left({x}^{\mathrm{54}} +{x}^{\mathrm{53}} +…+\mathrm{1}\right)=\mathrm{253}×\mathrm{8}{k} \\ $$$${x}−\mathrm{1}=\mathrm{8}{k}'\Rightarrow{x}\overset{\mathrm{8}} {\equiv}\mathrm{1}…

Question-202017

Question Number 202017 by sonukgindia last updated on 18/Dec/23 Answered by Mathspace last updated on 18/Dec/23 $${f}\left({x}\right)=\sum_{{n}=\mathrm{1}} ^{\infty} \frac{{sin}\left({nx}\right)}{\mathrm{2}^{{n}} }\:\Rightarrow \\ $$$$\int_{\mathrm{0}} ^{\pi} {f}\left({x}\right){dx}=\int_{\mathrm{0}} ^{\pi}…

If-and-are-the-roots-of-the-ax-2-2bx-c-0-and-and-are-the-roots-of-Ax-2-2Bx-C-0-for-some-constant-then-prove-that-b-2-ac-a-2-B-2-AC-A-2-

Question Number 202019 by MATHEMATICSAM last updated on 18/Dec/23 $$\mathrm{If}\:\alpha\:\mathrm{and}\:\beta\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\: \\ $$$${ax}^{\mathrm{2}} \:+\:\mathrm{2}{bx}\:+\:{c}\:=\:\mathrm{0}\:\mathrm{and}\:\alpha\:+\:\delta\:\mathrm{and}\:\beta\:+\:\delta\:\mathrm{are} \\ $$$$\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:{Ax}^{\mathrm{2}} \:+\:\mathrm{2}{Bx}\:+\:{C}\:=\:\mathrm{0}\:\mathrm{for}\:\mathrm{some}\: \\ $$$$\mathrm{constant}\:\delta\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\frac{{b}^{\mathrm{2}} \:−\:{ac}}{{a}^{\mathrm{2}} }\:=\:\frac{{B}^{\mathrm{2}} \:−\:{AC}}{{A}^{\mathrm{2}} }\:. \\…

Question-201972

Question Number 201972 by Lekhraj last updated on 17/Dec/23 Answered by mr W last updated on 18/Dec/23 $$\boldsymbol{\Phi}_{\leqslant\boldsymbol{{x}}} =\frac{\mathrm{1}}{\mathrm{2}}\left[\mathrm{1}+\boldsymbol{{erf}}\left(\frac{\boldsymbol{{x}}−\boldsymbol{\mu}}{\:\sqrt{\mathrm{2}}\:\boldsymbol{\sigma}}\right)\right] \\ $$$$\boldsymbol{{with}}\:\boldsymbol{{erf}}\left(\boldsymbol{{x}}\right)=\frac{\mathrm{2}}{\:\sqrt{\boldsymbol{\pi}}}\int_{\mathrm{0}} ^{\boldsymbol{{x}}} \boldsymbol{{e}}^{−\boldsymbol{{t}}^{\mathrm{2}} } \boldsymbol{{dt}}…

A-dice-is-cast-twice-and-the-sum-of-the-appearing-numbers-is-10-The-probability-that-the-number-5-has-appeared-at-least-once-is-

Question Number 201969 by BaliramKumar last updated on 17/Dec/23 $$\mathrm{A}\:\mathrm{dice}\:\mathrm{is}\:\mathrm{cast}\:\mathrm{twice},\:\mathrm{and}\:\mathrm{the}\:\mathrm{sum}\: \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{appearing}\:\mathrm{numbers}\:\mathrm{is}\:\mathrm{10}. \\ $$$$\mathrm{The}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{the}\:\mathrm{number}\:\mathrm{5}\:\mathrm{has}\: \\ $$$$\mathrm{appeared}\:\mathrm{at}\:\mathrm{least}\:\mathrm{once}\:\mathrm{is}. \\ $$ Answered by Frix last updated on 17/Dec/23…