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Author: Tinku Tara

sin-sin-pi-sin-2pi-sin-npi-when-n-is-an-odd-integer-

Question Number 220390 by MATHEMATICSAM last updated on 12/May/25 $$\mathrm{sin}\theta\:+\:\mathrm{sin}\left(\pi\:+\:\theta\right)\:+\:\mathrm{sin}\left(\mathrm{2}\pi\:+\:\theta\right)\:+\:…\: \\ $$$$+\:\mathrm{sin}\left({n}\pi\:+\:\theta\right)\:=\:?\:\mathrm{when}\:{n}\:\mathrm{is}\:\mathrm{an}\:\mathrm{odd} \\ $$$$\mathrm{integer}. \\ $$ Answered by mr W last updated on 12/May/25 $$\mathrm{sin}\:\left({k}\pi+\theta\right)=\mathrm{sin}\:{k}\pi\:\mathrm{cos}\:\theta+\mathrm{cos}\:{k}\pi\:\mathrm{sin}\:\theta…

lim-n-tan-pi-4-1-n-n-

Question Number 220380 by MrGaster last updated on 12/May/25 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}tan}\left[\frac{\pi}{\mathrm{4}}+\frac{\mathrm{1}}{{n}}\right]^{{n}} =? \\ $$ Answered by SdC355 last updated on 12/May/25 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\:\mathrm{tan}\left(\left(\frac{\pi}{\mathrm{4}}+\frac{\mathrm{1}}{{n}}\right)^{{n}} \right)=\mathrm{tan}\left(\mathrm{0}\right)=\mathrm{0} \\…

Prove-equation-0-f-u-g-u-e-u-du-1-2pii-i-i-F-u-G-u-du-F-u-0-f-t-e-ut-dt-G-u-0-g-t-e-ut-dt-

Question Number 220377 by SdC355 last updated on 12/May/25 $$\mathrm{Prove}\:\mathrm{equation} \\ $$$$\int_{\mathrm{0}} ^{\:\infty} \:{f}\left({u}\right)\mathrm{g}\left({u}\right){e}^{−{u}\rho} \mathrm{d}{u}=\frac{\mathrm{1}}{\mathrm{2}\pi\boldsymbol{{i}}}\:\int_{−\infty\boldsymbol{{i}}+\boldsymbol{\gamma}} ^{\:+\infty\boldsymbol{{i}}+\boldsymbol{\gamma}} \:\:{F}\left({u}\right){G}\left({u}−\rho\right)\mathrm{d}{u} \\ $$$${F}\left({u}\right)=\int_{\mathrm{0}} ^{\:\infty} \:{f}\left({t}\right){e}^{−{ut}} \mathrm{d}{t} \\ $$$${G}\left({u}\right)=\int_{\mathrm{0}} ^{\:\infty}…

Question-220375

Question Number 220375 by Tawa11 last updated on 12/May/25 Commented by Tawa11 last updated on 12/May/25 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{and}\:\mathrm{perimeter}. \\ $$$$\mathrm{Please},\:\mathrm{is}\:\mathrm{the}\:\mathrm{question}\:\mathrm{correct}? \\ $$ Commented by AntonCWX8 last…

Question-220340

Question Number 220340 by Noorzai last updated on 11/May/25 Answered by som(math1967) last updated on 11/May/25 $$\:{b}^{\mathrm{2}} {a}−{a}^{\mathrm{2}} {b}+{c}^{\mathrm{2}} {b}−{c}^{\mathrm{2}} {a}+{b}^{\mathrm{2}} {c}−{a}^{\mathrm{2}} {c} \\ $$$$={ba}\left({b}−{a}\right)+{c}^{\mathrm{2}}…

solve-the-system-of-equation-using-gaussian-elimination-method-x-2y-3z-10-2x-3y-z-1-3x-y-2z-9-

Question Number 220366 by klipto last updated on 11/May/25 $$\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{system}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{equation}} \\ $$$$\boldsymbol{\mathrm{using}}\:\boldsymbol{\mathrm{gaussian}}\:\boldsymbol{\mathrm{elimination}}\:\boldsymbol{\mathrm{method}} \\ $$$$\boldsymbol{\mathrm{x}}+\mathrm{2}\boldsymbol{\mathrm{y}}+\mathrm{3}\boldsymbol{\mathrm{z}}=\mathrm{10} \\ $$$$\mathrm{2}\boldsymbol{\mathrm{x}}−\mathrm{3}\boldsymbol{\mathrm{y}}+\boldsymbol{\mathrm{z}}=\mathrm{1} \\ $$$$\mathrm{3}\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}−\mathrm{2}\boldsymbol{\mathrm{z}}=\mathrm{9} \\ $$ Answered by Frix last updated…