Question Number 227016 by Spillover last updated on 25/Dec/25 $${If}\:\alpha\:{and}\:.\beta\:\:{are}\:{root}\:{of}\:{the}\:{equation} \\ $$$${x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{4}=\mathrm{0}\:{and}\:{for}\:{n}\in\mathbb{N} \\ $$$${Show}\:{that}\: \\ $$$$\alpha^{{n}} +\beta^{{n}} =\mathrm{2}^{{n}+\mathrm{1}} \mathrm{cos}\:\left(\frac{{n}\pi}{\mathrm{3}}\right) \\ $$ Answered by Frix…
Question Number 227011 by fantastic2 last updated on 25/Dec/25 $${in}\:{a}\:{cup}\:{filled}\:{with}\:{a}\:{liquid}\:{of}\:{density}\:\rho,{a} \\ $$$${bubble}\:{rests}\:{in}\:{the}\:{liquid}\:{in}\:{h}\:{deepness}. \\ $$$${radius}\:{initial}\:{of}\:{the}\:{bubble}={r}_{{i}} \\ $$$$\:{initial}\:{density}\:{of}\:{the}\:{bubble}=\sigma_{{i}} \\ $$$$\left(\:{mass\&temparature}\:{is}\:{constant}\right) \\ $$$${a}\:{small}\:{jerk}\:{is}\:{given}\:{to}\:{the}\:{cup}\:{and}\:{the} \\ $$$${bubble}\:{starts}\:{to}\:{go}\:{upwards}. \\ $$$${find}: \\…
Question Number 226991 by Spillover last updated on 24/Dec/25 Answered by Spillover last updated on 25/Dec/25 Answered by Spillover last updated on 25/Dec/25 Answered by…
Question Number 226975 by AlexandreVachon last updated on 24/Dec/25 $$ \\ $$Where are the sans serif letters? Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 227002 by fantastic2 last updated on 24/Dec/25 $${merry}\:{christmas}\:{to}\:{all}\:{of}\:{you}\:{guys}! \\ $$ Commented by AgniMath last updated on 25/Dec/25 $${merry}\:{christmas} \\ $$ Commented by Kassista…
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Question Number 226983 by hardmath last updated on 24/Dec/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 226994 by Spillover last updated on 24/Dec/25 Answered by Spillover last updated on 25/Dec/25 Answered by Spillover last updated on 25/Dec/25 Answered by…
Question Number 226995 by Spillover last updated on 24/Dec/25 Answered by Ghisom_ last updated on 24/Dec/25 $$\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\frac{\mathrm{sin}^{\mathrm{3}} \:{x}\:\mathrm{cos}^{\mathrm{5}} \:{x}}{\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin}^{\mathrm{2}} \:{x}\right)^{\mathrm{3}} }{dx}=\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\frac{\left(\mathrm{1}+\mathrm{cos}\:\mathrm{2}{x}\right)\mathrm{sin}^{\mathrm{3}}…
Question Number 226973 by CrispyXYZ last updated on 23/Dec/25 $$\underset{{n}\rightarrow+\infty} {\mathrm{lim}}\left(\frac{\mathrm{sin}\:\frac{\mathrm{1}}{{n}}}{{n}+\frac{\mathrm{1}}{\mathrm{1}}}\:+\:\frac{\mathrm{sin}\:\frac{\mathrm{2}}{{n}}}{{n}+\frac{\mathrm{1}}{\mathrm{2}}}\:+\:…\:+\:\frac{\mathrm{sin}\:\frac{{n}}{{n}}}{{n}+\frac{\mathrm{1}}{{n}}}\right)=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com