Question Number 132434 by Dwaipayan Shikari last updated on 14/Feb/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{cos}\left({n}\right)}{{n}^{\mathrm{2}} } \\ $$ Answered by mnjuly1970 last updated on 14/Feb/21 $$\:\:{solution}: \\…
Question Number 66895 by Kunal12588 last updated on 20/Aug/19 $${x}+{y}+{z}=−{B} \\ $$$${xy}+{yz}+{zx}={C} \\ $$$${xyz}=−{D} \\ $$$${find}\:{x},{y}\:{and}\:{z}\:{in}\:{terms}\:{of}\:{B},{C}\:{and}\:{D} \\ $$ Answered by mr W last updated on…
Question Number 1358 by tabrez8590@gmail last updated on 25/Jul/15 $${solve} \\ $$$${x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{6} \\ $$ Commented by Rasheed Soomro last updated on 25/Jul/15 $${x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{6}=?…
Question Number 66890 by hmamarques1994@gmail.com last updated on 20/Aug/19 $$\: \\ $$$$\:\:\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{x}}} \:+\:\boldsymbol{\mathrm{x}}^{\mathrm{2}\boldsymbol{\mathrm{x}}} \:=\:\mathrm{20} \\ $$$$\: \\ $$$$\:\:\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{x}}} \:=\:? \\ $$$$\: \\ $$ Answered by…
Question Number 1355 by Rasheed Ahmad last updated on 25/Jul/15 $$\mathrm{8}^{{log}\:\left(\mathrm{12}{x}+\mathrm{1}\right)} =\mathrm{4}^{{log}\:\mathrm{27}} \:\:\:,{solve}\:{for}\:{x}. \\ $$ Answered by Yugi last updated on 25/Jul/15 $${Rewriting}\:{the}\:{above}\:{equation}\:{in}\:{base}\:\mathrm{2}\:{gives} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}^{\mathrm{3}{log}\left(\mathrm{12}{x}+\mathrm{1}\right)}…
Question Number 1354 by Rasheed Ahmad last updated on 25/Jul/15 $${Slightly}\:{modified}\:{form}\:{of}\:{Q}\:\mathrm{1343}. \\ $$$$\mathrm{3}^{{log}\left(\mathrm{3}{x}+\mathrm{4}\right)} =\mathrm{4}^{{log}\left(\mathrm{4}{x}+\mathrm{3}\right)} ,{solve}\:{for}\:{x}. \\ $$ Commented by prakash jain last updated on 25/Jul/15…
Question Number 1352 by 112358 last updated on 24/Jul/15 $${Solve}\:{the}\:{following}\:{DE}\:: \\ $$$${y}\frac{{dy}}{{dx}}+\mathrm{6}{x}+\mathrm{5}{y}=\mathrm{0}\:\:\:\:\:\left({x}\neq\mathrm{0},{y}\neq\mathrm{0}\right) \\ $$ Answered by imhunter last updated on 27/Jul/15 $${q}.{no}.\mathrm{1352}\:\:\:\:\:\:\:\:\:\:\:{y}\:{dy}/{dx}=−\mathrm{6}{x}−\mathrm{5}{y} \\ $$$$ \\…
Question Number 1351 by 123456 last updated on 24/Jul/15 $$\mathcal{W}\left\{{f}\left({x}\right)\right\}\left({t}\right)=\underset{\mathrm{0}} {\overset{\mathrm{1}/{t}} {\int}}{f}\left({x}\right)\mathrm{ln}\left({xt}\right){dx},{t}>\mathrm{0} \\ $$$$\mathcal{W}\left\{{f}\left({x}\right)+{g}\left({x}\right)\right\}\left({t}\right)\overset{?} {=}\mathcal{W}\left\{{f}\left({x}\right)\right\}\left({t}\right)+\mathcal{W}\left\{{g}\left({x}\right)\right\}\left({t}\right) \\ $$$$\mathcal{W}\left\{{cf}\left({x}\right)\right\}\left({t}\right)\overset{?} {=}{c}\mathcal{W}\left\{{f}\left({x}\right)\right\}\left({t}\right) \\ $$$$\mathcal{W}\left\{\mathrm{1}\right\}\left({t}\right)=? \\ $$$$\mathcal{W}\left\{{x}\right\}\left({t}\right)=? \\ $$$$\mathcal{W}\left\{{x}^{{n}} \right\}\left({t}\right)=?,{n}\in\mathbb{N}…
Question Number 1350 by 112358 last updated on 24/Jul/15 $${Evaluate}\:{the}\:{following}\:{integral}: \\ $$$${I}=\int_{\pi/\mathrm{4}} ^{\:\pi/\mathrm{2}} \left({cos}\mathrm{2}{x}+{sin}\mathrm{2}{x}\right){ln}\left({cosx}+{sinx}\right)\:{dx} \\ $$ Commented by prakash jain last updated on 25/Jul/15 $$\int\mathrm{sin}\:\mathrm{2}{x}\mathrm{ln}\:\left(\mathrm{cos}\:{x}+\mathrm{sin}\:{x}\right){dx}…
Question Number 132422 by john_santu last updated on 14/Feb/21 $$\mathrm{Given}\:\mathrm{P}\left(\mathrm{x}\right)\:\mathrm{is}\:\mathrm{polynomial}. \\ $$$$\:\mathrm{If}\:\mathrm{P}\left(\mathrm{x}+\mathrm{1}\right)\:+\:\frac{\mathrm{P}\left(\mathrm{x}\right)}{\mathrm{x}}\:=\:\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} −\mathrm{2} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\frac{\mathrm{P}\left(\mathrm{x}\right)}{\mathrm{x}} \\ $$ Answered by bemath last updated on 14/Feb/21 Terms…