Question Number 201091 by MrGHK last updated on 29/Nov/23 Commented by Frix last updated on 29/Nov/23 $$\mathrm{Look}\:\mathrm{at}\:\mathrm{the}\:\mathrm{first}\:\mathrm{few}\:\mathrm{summands}: \\ $$$${i}=\mathrm{0}\:\rightarrow\:\mathrm{1} \\ $$$${i}=\mathrm{1}\:\rightarrow\:\frac{{n}}{\mathrm{2}{n}+\mathrm{4}} \\ $$$${i}=\mathrm{2}\:\rightarrow\:\frac{{n}^{\mathrm{2}} −{n}}{\mathrm{6}{n}+\mathrm{24}{n}+\mathrm{24}} \\…
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Question Number 201011 by Calculusboy last updated on 28/Nov/23 $$\boldsymbol{{Prove}}\:\boldsymbol{{that}} \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{2}\boldsymbol{{arctan}}\left(\frac{\boldsymbol{{t}}}{\boldsymbol{{x}}}\right)}{\boldsymbol{{e}}^{\mathrm{2}\boldsymbol{\pi{t}}} −\mathrm{1}}\boldsymbol{{dt}}=\boldsymbol{{In}\Gamma}\left(\boldsymbol{{x}}\right)−\boldsymbol{{xIn}}\left(\boldsymbol{{x}}\right)+\boldsymbol{{x}}−\frac{\mathrm{1}}{\mathrm{2}}\boldsymbol{{In}}\left(\frac{\mathrm{2}\boldsymbol{\pi}}{\boldsymbol{{x}}}\right) \\ $$$$\boldsymbol{{Michael}}\:\boldsymbol{{faraday}} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 201065 by mr W last updated on 28/Nov/23 Commented by mr W last updated on 28/Nov/23 $${find}\:{the}\:{side}\:{length}\:\boldsymbol{{a}}\:{of}\:{the}\:{square} \\ $$$${in}\:{terms}\:{of}\:\boldsymbol{{r}}. \\ $$ Answered by…
Question Number 201044 by mnjuly1970 last updated on 28/Nov/23 $$ \\ $$$$\:\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\:\mathrm{1}} \left({x}−{y}\:\right)^{\mathrm{2}} {sin}^{\:\mathrm{2}} \:\left(\:{x}+{y}\:\right){dxdy}=? \\ $$ Answered by mathematicsmagic last updated…
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Question Number 201041 by hardmath last updated on 28/Nov/23 $$\mathrm{4}\left(\mathrm{33}\right)\mathrm{7} \\ $$$$\mathrm{4}\left(\mathrm{24}\right)\mathrm{6} \\ $$$$\mathrm{5}\left(\:?\:\right)\mathrm{4} \\ $$$$ \\ $$$$\left.{a}\left.\right)\left.\mathrm{9}\left.\:\:\:\:\:{b}\right)\mathrm{18}\:\:\:\:\:{c}\right)\mathrm{27}\:\:\:\:\:{d}\right)\mathrm{36} \\ $$ Answered by Frix last updated…
Question Number 201037 by mr W last updated on 28/Nov/23 Commented by mr W last updated on 28/Nov/23 $${a}\:{triangle}\:{has}\:{sides}\:{a},\:{b},\:{c}.\:{find}\:{the} \\ $$$${fraction}\:{of}\:{its}\:{area}\:{covered}\:{by}\:{all} \\ $$$$\left({infinite}\right)\:{inscribed}\:{circles}\:{as}\:{shown}. \\ $$…
Question Number 201033 by Mingma last updated on 28/Nov/23 Answered by Frix last updated on 28/Nov/23 $$\mathrm{sin}\:\frac{\pi}{\mathrm{14}}\:\mathrm{sin}\:\frac{\mathrm{3}\pi}{\mathrm{14}}\:\mathrm{sin}\:\frac{\mathrm{9}\pi}{\mathrm{14}}\:={x} \\ $$$$\mathrm{0}<{x}<\mathrm{1} \\ $$$$\mathrm{Using}\:\mathrm{trigonometric}\:\mathrm{formulas}\:\Rightarrow \\ $$$$\frac{\mathrm{1}}{\mathrm{4}}\left(\mathrm{1}−\mathrm{cos}\:\frac{\pi}{\mathrm{7}}\:+\mathrm{sin}\:\frac{\mathrm{3}\pi}{\mathrm{14}}\:−\mathrm{sin}\:\frac{\pi}{\mathrm{14}}\right)={x}\:\bigstar \\ $$$$\mathrm{cos}\:\frac{\pi}{\mathrm{7}}\:−\mathrm{sin}\:\frac{\mathrm{3}\pi}{\mathrm{14}}\:+\mathrm{sin}\:\frac{\pi}{\mathrm{14}}\:=\mathrm{1}−\mathrm{4}{x}…
Question Number 201034 by Mingma last updated on 28/Nov/23 Terms of Service Privacy Policy Contact: info@tinkutara.com