Question Number 73789 by liki last updated on 15/Nov/19 Commented by liki last updated on 15/Nov/19 $$..{Sory}\:{sir};\:{Mr}\:{mind}\:{is}\:{power}\:{plz}\:{help}\: \\ $$$$\:\:{that}\:{qn}\:\mathrm{5}\:\left({a}\right),\left({b}\right),\left({c}\right)\:{and}\:\left({d}\right).\:{or}\:{anyone} \\ $$$$\:{to}\:{assist}\:{me}\:{this}\:{qn} \\ $$ Commented by…
Question Number 8252 by 8168 last updated on 04/Oct/16 Answered by Yozzias last updated on 04/Oct/16 $$\mathrm{6}+\mathrm{4}+\frac{\mathrm{8}}{\mathrm{3}}+\frac{\mathrm{16}}{\mathrm{9}}+… \\ $$$$=\mathrm{6}+\left(\frac{\mathrm{2}^{\mathrm{2}} }{\mathrm{3}^{\mathrm{0}} }+\frac{\mathrm{2}^{\mathrm{3}} }{\mathrm{3}^{\mathrm{1}} }+\frac{\mathrm{2}^{\mathrm{4}} }{\mathrm{3}^{\mathrm{2}} }+…+\frac{\mathrm{2}^{\mathrm{n}+\mathrm{1}}…
Question Number 73787 by Rio Michael last updated on 15/Nov/19 $${sin}\:\mathrm{50}\:+\:{sin}\:\mathrm{40}=\:?\:{without}\:{tables}\:{or}\:{calculators} \\ $$ Commented by mind is power last updated on 15/Nov/19 $$\mathrm{i}\:\mathrm{see}\:\mathrm{just}\:\mathrm{cardan}\:\mathrm{Methode} \\ $$$$\mathrm{sin}\left(\mathrm{50}\right)=\mathrm{sin}\left(\mathrm{90}−\mathrm{40}\right)=\mathrm{cos}\left(\mathrm{40}\right)…
Question Number 139323 by snipers237 last updated on 25/Apr/21 $$\:{Let}\:{f}\:{define}\:{such}\:{as}\:\:{f}\left(\mathrm{1}\right)=\mathrm{1},{f}\left(\mathrm{3}\right)=\mathrm{3} \\ $$$$\forall\:{n}\geqslant\mathrm{2}\:\:,\:{f}\left(\mathrm{2}{n}\right)={f}\left({n}\right)\: \\ $$$${f}\left(\mathrm{4}{n}+\mathrm{1}\right)=\mathrm{2}{f}\left(\mathrm{2}{n}+\mathrm{1}\right)−{f}\left({n}\right) \\ $$$${f}\left(\mathrm{4}{n}+\mathrm{3}\right)=\mathrm{3}{f}\left(\mathrm{2}{n}+\mathrm{1}\right)−\mathrm{2}{f}\left({n}\right) \\ $$$$ \\ $$$$\left.\mathrm{1}\right){Prove}\:{that}\:\forall\:{n}\:,\:{f}\left({n}\right)\:{is}\:{odd} \\ $$$$\left.\mathrm{2}\right){Prove}\:{that}\:{if}\:\:\:{f}\left({a}_{{n}} \right)={a}_{{n}} \:, \\…
Question Number 73782 by liki last updated on 15/Nov/19 Commented by liki last updated on 15/Nov/19 $${I}\:{need}\:{help}\:{plz}\:{that}\:{question}\:{vector}…. \\ $$ Commented by liki last updated on…
Question Number 139319 by mathsuji last updated on 25/Apr/21 $${prove}\:{that}\:{are}\:{axactly}\:\mathrm{1729}\:{positive} \\ $$$${integer}\:{solutions}\:{to}\:{the}\:{below}\:{equation} \\ $$$$\mathrm{4}{x}^{\mathrm{4}} +\mathrm{3}{y}^{\mathrm{3}} +\mathrm{2}{z}^{\mathrm{2}} +{t}=\mathrm{4311} \\ $$ Commented by Rasheed.Sindhi last updated on…
Question Number 8244 by lepan last updated on 04/Oct/16 $${Show}\:{that}\:{the}\:{curve}\:{y}={ln}\left(\frac{\mathrm{5}−\mathrm{7}{x}}{\mathrm{8}+{x}}\right)\:{has} \\ $$$${no}\:{stationary}\:{point}\:{for}\:{all}\:{real}\:{values} \\ $$$${of}\:{x}. \\ $$ Answered by 123456 last updated on 06/Oct/16 $${y}=\mathrm{ln}\:\frac{\mathrm{5}−\mathrm{7}{x}}{\mathrm{8}+{x}} \\…
Question Number 139313 by Dwaipayan Shikari last updated on 25/Apr/21 $$\int_{\mathrm{0}} ^{\infty} \frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{5}} \right)^{\mathrm{5}} }=\frac{\mathrm{798}\sqrt{\mathrm{2}}}{\mathrm{5}^{\mathrm{5}} \sqrt{\mathrm{5}−\sqrt{\mathrm{5}}}}\pi \\ $$ Answered by Ar Brandon last updated on…
Find-the-equation-of-the-perpendicular-bisector-of-the-line-joining-the-points-5-4-to-the-point-9-3-
Question Number 8243 by lepan last updated on 04/Oct/16 $${Find}\:{the}\:{equation}\:{of}\:{the}\:{perpendicular}\:{bisector}\:{of}\:{the}\:{line}\:{joining}\:{the}\:{points}\:\left(−\mathrm{5},\mathrm{4}\right)\:{to}\:{the}\:{point}\:\left(\mathrm{9},−\mathrm{3}\right) \\ $$$$ \\ $$ Answered by sandy_suhendra last updated on 04/Oct/16 $$\mathrm{let}\:\mathrm{A}\left(−\mathrm{5},\mathrm{4}\right)\:\mathrm{and}\:\mathrm{B}\left(\mathrm{9},−\mathrm{3}\right) \\ $$$$\mathrm{P}\:\mathrm{is}\:\mathrm{midpoint}\:\mathrm{of}\:\mathrm{AB}\:\mathrm{so}\:\mathrm{P}\left(\frac{−\mathrm{5}+\mathrm{9}}{\mathrm{2}}\:,\:\frac{\mathrm{4}−\mathrm{3}}{\mathrm{2}}\:\right)=\mathrm{P}\left(\mathrm{2},\frac{\mathrm{1}}{\mathrm{2}}\right) \\…
Question Number 73774 by mind is power last updated on 15/Nov/19 $$\mathrm{hello}\:,\mathrm{show}\:\mathrm{that} \\ $$$$\underset{\mathrm{n}\geqslant\mathrm{1}} {\sum}\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} \mathrm{nsin}\left(\mathrm{n}\right)}{\mathrm{1}+\mathrm{n}^{\mathrm{2}} }=\frac{\pi\mathrm{e}^{\mathrm{1}} −\pi\mathrm{e}^{−\mathrm{1}} }{−\mathrm{2e}^{\pi} +\mathrm{2e}^{−\pi} } \\ $$$$\mathrm{indication}\:,\mathrm{Residus}\:\mathrm{Theorem}\:\mathrm{let} \\ $$$$\mathrm{f}\left(\mathrm{z}\right)=\frac{\mathrm{zsin}\left(\mathrm{z}\right)}{\left(\mathrm{1}+\mathrm{z}^{\mathrm{2}}…