Question Number 201947 by Mingma last updated on 16/Dec/23 Answered by Frix last updated on 18/Dec/23 $$\mathrm{sin}\:\alpha\:\mathrm{sin}\:\beta\:\mathrm{cos}\:\left(\pi−\alpha−\beta\right)\:+ \\ $$$$\:\:\:\:\:+\mathrm{sin}\:\beta\:\mathrm{sin}\:\left(\pi−\alpha−\beta\right)\:\mathrm{cos}\:\alpha\:+ \\ $$$$\:\:\:\:\:+\mathrm{sin}\:\left(\pi−\alpha−\beta\right)\:\mathrm{sin}\:\alpha\:\mathrm{cos}\:\beta\:= \\ $$$$=\frac{\mathrm{3}−\left(\mathrm{cos}\:\mathrm{2}\alpha\:+\mathrm{cos}\:\mathrm{2}\beta\:+\mathrm{cos}\:\mathrm{2}\left(\alpha+\beta\right)\right.}{\mathrm{4}}= \\ $$$$\:\:\:\:\:\left[\mathrm{Let}\:\alpha={u}−{v}\wedge\beta={u}+{v}\right]…
Question Number 201144 by sts313 last updated on 30/Nov/23 $$\left(\frac{\mathrm{14}}{\mathrm{15}}\right)^{\mathrm{6}} ×\left(\frac{\mathrm{45}}{\mathrm{28}}\right)^{\mathrm{6}} = \\ $$ Answered by mathlove last updated on 01/Dec/23 $$\left(\frac{\mathrm{14}}{\mathrm{15}}\right)^{\mathrm{6}} ×\left(\frac{\mathrm{3}×\mathrm{15}}{\mathrm{2}×\mathrm{14}}\right)^{\mathrm{6}} =\frac{\cancel{\mathrm{14}^{\mathrm{6}} }}{\cancel{\mathrm{15}^{\mathrm{6}}…
Question Number 200929 by Akira181 last updated on 26/Nov/23 $$\mathrm{A}\:\mathrm{ball}\:\mathrm{lies}\:\mathrm{on}\:\mathrm{the}\:\mathrm{function}\:{z}={xy}\:\mathrm{at} \\ $$$$\mathrm{the}\:\mathrm{point}\:\left(\mathrm{1},\mathrm{2},\mathrm{2}\right).\:\mathrm{Find}\:\mathrm{the}\:\mathrm{point}\:\mathrm{in} \\ $$$$\mathrm{the}\:{xy}−\mathrm{plane}\:\mathrm{where}\:\mathrm{the}\:\mathrm{ball}\:\mathrm{will} \\ $$$$\mathrm{touch}\:\mathrm{it}. \\ $$$$\mathrm{Calculus}\:\mathrm{2}\:\mathrm{problem}. \\ $$ Commented by Akira181 last updated…
Question Number 196918 by cortano12 last updated on 03/Sep/23 Answered by MM42 last updated on 03/Sep/23 $${a}_{{n}} =\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{5}×\mathrm{3}^{{n}−\mathrm{1}} −\mathrm{1}\right)\:\checkmark \\ $$ Terms of Service Privacy…
Question Number 196412 by Erico last updated on 25/Aug/23 $$\mathrm{Prove}\:\mathrm{that}\:\underset{\:{i}} {\int}^{\:+\infty} \left(\mathrm{cos2t}+\mathrm{isin2t}\right)\mathrm{e}^{−\mathrm{t}^{\mathrm{2}} } \mathrm{dt}=\:\frac{\sqrt{\pi}}{\mathrm{2e}} \\ $$ Commented by JDamian last updated on 24/Aug/23 $${is}\:\boldsymbol{\mathrm{t}}\:{real}\:{or}\:{complex}? \\…
Question Number 193204 by Mingma last updated on 07/Jun/23 Answered by witcher3 last updated on 08/Jun/23 $$\mathrm{H}_{\mathrm{n}} =\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{1}}{\mathrm{k}}=\overset{\mathrm{1}} {\int}_{\mathrm{0}} \underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mathrm{x}^{\mathrm{k}−\mathrm{1}} \mathrm{dx}…
Question Number 65261 by shalinu last updated on 27/Jul/19 $${solve}\mathrm{4}−{xy}+{yz}−{xz} \\ $$ Commented by mr W last updated on 27/Jul/19 $${sir},\:{please}\:{explain}\:{your}\:{question}\:{a}\:{little}! \\ $$$${at}\:{the}\:{moment}\:{it}'{s}\:{not}\:{clear}\:{what} \\ $$$${your}\:{question}\:{is}.…
Question Number 64456 by ner0i last updated on 18/Jul/19 Commented by Tony Lin last updated on 18/Jul/19 $$\overset{\rightharpoonup} {{r}}'\left({t}\right)=\hat {{i}}−\frac{\mathrm{2}}{{t}^{\mathrm{2}} }\hat {{j}}−\frac{\mathrm{1}}{{t}^{\mathrm{2}} }\hat {{k}} \\…
Question Number 64011 by Prithwish sen last updated on 12/Jul/19 $$\mathrm{li}\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{m}}\frac{\mathrm{x}^{\mathrm{x}} −\mathrm{1}}{\mathrm{xlnx}} \\ $$ Commented by kaivan.ahmadi last updated on 12/Jul/19 $${y}={x}^{{x}} \Rightarrow{lny}={xlnx}\Rightarrow\frac{{y}'}{{y}}={lnx}+{x}×\frac{\mathrm{1}}{{x}}=\mathrm{1}+{lnx}\Rightarrow \\…
Question Number 128837 by BHOOPENDRA last updated on 10/Jan/21 Commented by BHOOPENDRA last updated on 10/Jan/21 $${without}\:{using}\:{gauss}\:{divergence}\:{theorm}\: \\ $$$${calculate}\:{surface}\:{integral}? \\ $$$${help}\:{me}\:{out}\:{this}? \\ $$ Terms of…