Question Number 131167 by 676597498 last updated on 02/Feb/21 Answered by SEKRET last updated on 02/Feb/21 $$\boldsymbol{\mathrm{U}}_{\boldsymbol{\mathrm{n}}} =\left(\mathrm{1}+\frac{\mathrm{1}}{\boldsymbol{\mathrm{n}}^{\mathrm{2}} }\right)\left(\mathrm{1}+\frac{\mathrm{2}}{\boldsymbol{\mathrm{n}}^{\mathrm{2}} }\right)….\left(\mathrm{1}+\frac{\boldsymbol{\mathrm{n}}}{\boldsymbol{\mathrm{n}}^{\mathrm{2}} }\right) \\ $$$$\boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{U}}_{\boldsymbol{\mathrm{n}}} \right)=\:\boldsymbol{\mathrm{ln}}\left(\mathrm{1}+\frac{\mathrm{1}}{\boldsymbol{\mathrm{n}}^{\mathrm{2}} }\right)+\boldsymbol{\mathrm{ln}}\left(\mathrm{1}+\frac{\mathrm{2}}{\:\:\boldsymbol{\mathrm{n}}^{\mathrm{2}}…
Question Number 93 by mreddy last updated on 25/Jan/15 $$\mathrm{Fnd}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{expression} \\ $$$$\:\:\:\:\:\:\:\:\frac{\mathrm{2}^{\mathrm{n}+\mathrm{3}} −\mathrm{2}^{\mathrm{n}+\mathrm{1}} ×\mathrm{10}}{\mathrm{2}^{\mathrm{n}+\mathrm{1}} ×\mathrm{6}} \\ $$ Answered by sushmitak last updated on 28/Nov/14 $$\frac{\mathrm{2}^{{n}+\mathrm{1}}…
Question Number 131166 by SEKRET last updated on 02/Feb/21 $$\:\int_{\mathrm{0}} ^{+\infty} \frac{\mathrm{1}}{\boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{x}}} \centerdot\boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{x}}\right)}\boldsymbol{\mathrm{dx}}=? \\ $$$$ \\ $$ Commented by Dwaipayan Shikari last updated on 02/Feb/21…
Six-friends-have-an-average-height-of-167-cm-Mike-with-height-162-cm-leaves-What-is-the-new-average-
Question Number 92 by michelle last updated on 25/Jan/15 $$\mathrm{Six}\:\mathrm{friends}\:\mathrm{have}\:\mathrm{an}\:\mathrm{average}\:\mathrm{height}\:\mathrm{of}\:\mathrm{167}\:\mathrm{cm} \\ $$$$\mathrm{Mike}\:\mathrm{with}\:\mathrm{height}\:\mathrm{162}\:\mathrm{cm}\:\mathrm{leaves}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{new}\:\mathrm{average}? \\ $$ Commented by Rasheed Soomro last updated on 09/Jun/16 $$\mathcal{T}{otal}\:{of}\:{six}\:{friends}'\:{heights}=\mathrm{167}×\mathrm{6}…
Question Number 91 by vkulkarni last updated on 25/Jan/15 $$\mathrm{A}\:\mathrm{line}\:\mathrm{passes}\:\mathrm{through}\:\mathrm{the}\:\mathrm{mid}−\mathrm{point}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{line}\:\mathrm{joining}\:\mathrm{the}\:\mathrm{points}\:\left(−\mathrm{3},−\mathrm{4}\right)\:\mathrm{and}\:\:\left(−\mathrm{5},\mathrm{6}\right) \\ $$$$\mathrm{and}\:\mathrm{has}\:\mathrm{a}\:\mathrm{slope}\:\mathrm{of}\:\frac{\mathrm{3}}{\mathrm{4}}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}. \\ $$ Answered by ssahoo last updated on 04/Dec/14 $$\mathrm{slope}\:{m}=\frac{\mathrm{3}}{\mathrm{4}} \\…
Question Number 131162 by EDWIN88 last updated on 02/Feb/21 $${Five}\:{children}\:{sitting}\:{one}\:{behind} \\ $$$${the}\:{other}\:{in}\:{a}\:{five}\:{seater}\:{merry}−{go}−{round} \\ $$$$,{decide}\:{to}\:{switch}\:{seats}\:{so}\:{that}\:{each} \\ $$$${child}\:{has}\:{new}\:{companion}\:{in}\:{front}. \\ $$$${In}\:{how}\:{many}\:{ways}\:{can}\:{this}\:{be}\:{done}? \\ $$ Commented by mr W last…
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Question Number 131156 by EDWIN88 last updated on 02/Feb/21 $$\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{{x}^{\mathrm{2}} \mathrm{cot}\:\left(\frac{\mathrm{1}}{{x}}\right)+\mathrm{4cot}\:\left(\frac{\mathrm{1}}{{x}}\right)}{\mathrm{3}{x}^{\mathrm{2}} +\mathrm{2}{x}}\:? \\ $$ Answered by john_santu last updated on 02/Feb/21 $$\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{{x}^{\mathrm{2}} +\mathrm{4}}{{x}\left(\mathrm{3}{x}+\mathrm{2}\right).\mathrm{tan}\:\left(\frac{\mathrm{1}}{{x}}\right)}\:=\:…
Question Number 131159 by mohammad17 last updated on 02/Feb/21 Commented by mohammad17 last updated on 02/Feb/21 $${who}\:{can}\:{solve}\:{this}\:? \\ $$ Commented by mohammad17 last updated on…
Question Number 131158 by EDWIN88 last updated on 02/Feb/21 $${If}\:\mathrm{4}{a}_{{n}} +\mathrm{2}{a}_{−{n}} =\mathrm{3}{n}^{\mathrm{2}} +\mathrm{2}{n}−\mathrm{3} \\ $$$${find}\:{a}_{{n}} \:=? \\ $$ Answered by mr W last updated on…