Question Number 132032 by mohammad17 last updated on 10/Feb/21 $${we}\:{say}\:{that}\:{Log}\left({z}_{\mathrm{1}} {z}_{\mathrm{2}} \right)={Log}\left({z}_{\mathrm{1}} \right)+{Log}\left({z}_{\mathrm{2}} \right) \\ $$$${when}:\:{Re}\left({z}_{\mathrm{1}} \right)\leqslant\mathrm{0}\:{and}\:{Re}\left({z}_{\mathrm{2}} \right)\leqslant\mathrm{0} \\ $$$${prove}\:{this}\:? \\ $$ Commented by mohammad17…
Question Number 961 by Madan pd gupta last updated on 08/May/15 $$\left[\left\{\mathrm{8}+\mathrm{4}×\mathrm{3}+\left(\mathrm{7}\boldsymbol{\div}\mathrm{7}×\mathrm{3}\right)\right\}\right]_{} \\ $$ Answered by rpatle69@gmail.com last updated on 08/May/15 $$\mathrm{23} \\ $$ Terms…
Question Number 66497 by ketto2 last updated on 16/Aug/19 Answered by MJS last updated on 16/Aug/19 $$\mathrm{all}\:\mathrm{the}\:\mathrm{money}\:=\mathrm{1} \\ $$$$\mathrm{1}−\frac{\mathrm{5}}{\mathrm{11}}−\frac{\mathrm{7}}{\mathrm{12}}×\left(\mathrm{1}−\frac{\mathrm{5}}{\mathrm{11}}\right)=\frac{\mathrm{6}}{\mathrm{11}}−\frac{\mathrm{7}}{\mathrm{12}}×\frac{\mathrm{6}}{\mathrm{11}}=\frac{\mathrm{6}}{\mathrm{11}}−\frac{\mathrm{7}}{\mathrm{22}}=\frac{\mathrm{5}}{\mathrm{22}} \\ $$ Terms of Service Privacy…
Question Number 132031 by mathlove last updated on 10/Feb/21 Commented by kaivan.ahmadi last updated on 10/Feb/21 $${p}\left({x}\right)={f}\left({x}\right)\left({x}−\mathrm{1}\right)+\mathrm{3}={g}\left({x}\right)\left({x}+\mathrm{1}\right)+\mathrm{7} \\ $$$${p}\left(\mathrm{1}\right)=\mathrm{3},{p}\left(−\mathrm{1}\right)=\mathrm{7} \\ $$$${p}\left({x}\right)={t}\left({x}\right)\left({x}^{\mathrm{2}} −\mathrm{1}\right)+{k}\left({x}\right) \\ $$$${p}\left(\mathrm{1}\right)={k}\left(\mathrm{1}\right)\Rightarrow{k}\left(\mathrm{1}\right)=\mathrm{3}\Rightarrow\left(\mathrm{1},\mathrm{3}\right)\in{k} \\…
Question Number 956 by 123456 last updated on 07/May/15 $$\mathrm{compute}\:\underset{\gamma} {\int}\boldsymbol{{v}}\centerdot{d}\boldsymbol{{r}}\:\mathrm{where} \\ $$$$\boldsymbol{{v}}={yz}\boldsymbol{{i}}+{xz}\boldsymbol{{j}}+{xy}\boldsymbol{{k}} \\ $$$$\mathrm{and}\:\gamma\:\mathrm{is}\:\mathrm{intersection}\:\mathrm{of}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{1}\:\mathrm{with} \\ $$$${z}={xy}\:\mathrm{orinted}\:\mathrm{in}\:\mathrm{the}\:\mathrm{way}\:\mathrm{that}\:\mathrm{the} \\ $$$$\mathrm{prpjection}\:\mathrm{on}\:{xy}\:\mathrm{travel}\:\mathrm{by}\:\circlearrowleft \\ $$ Terms of…
Question Number 66489 by rajesh4661kumar@gmail.com last updated on 16/Aug/19 Answered by $@ty@m123 last updated on 16/Aug/19 $${x}=\mathrm{4} \\ $$$${y}=\mathrm{9} \\ $$ Commented by rajesh4661kumar@gmail.com last…
Question Number 950 by 123456 last updated on 06/May/15 $${f}:\mathbb{R}\rightarrow\mathbb{R},\mathrm{continuous}\:\mathrm{such}\:\mathrm{that}\:\forall{x}\in\mathbb{R},{f}\left({x}\right){f}\left[{f}\left({x}\right)\right]=\mathrm{1},{f}\left(\mathrm{2004}\right)=\mathrm{2003},{f}\left(\mathrm{1999}\right)=? \\ $$ Commented by 123456 last updated on 06/May/15 $${f}\left(\mathrm{2004}\right){f}\left[{f}\left(\mathrm{2004}\right)\right]=\mathrm{2003}{f}\left(\mathrm{2003}\right)=\mathrm{1}\Leftrightarrow{f}\left(\mathrm{2003}\right)=\frac{\mathrm{1}}{\mathrm{2003}} \\ $$$${f}\left(\mathrm{2003}\right){f}\left[{f}\left(\mathrm{2003}\right)\right]=\frac{\mathrm{1}}{\mathrm{2003}}{f}\left(\frac{\mathrm{1}}{\mathrm{2003}}\right)=\mathrm{1}\Leftrightarrow{f}\left(\frac{\mathrm{1}}{\mathrm{2003}}\right)=\mathrm{2003}={f}\left(\mathrm{2004}\right) \\ $$$${f}\left(\frac{\mathrm{1}}{\mathrm{2003}}\right){f}\left[{f}\left(\frac{\mathrm{1}}{\mathrm{2003}}\right)\right]=\mathrm{2003}{f}\left(\mathrm{2003}\right)=\mathrm{1} \\…
Question Number 132023 by mnjuly1970 last updated on 10/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…..{nice}\:\:{calculus}….. \\ $$$${prove}\:{that}::: \\ $$$$\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{{cos}\left(\mathrm{2}{x}\right)}{{cosh}\left({x}\right)}\:{dx}\overset{?} {=}\frac{\pi}{\mathrm{2}{cosh}\left(\pi\right)} \\ $$$$ \\ $$ Answered by mindispower last…
Question Number 949 by 123456 last updated on 04/May/15 $${f}:\mathbb{N}\rightarrow\mathbb{R} \\ $$$${g}:\mathbb{N}\rightarrow\mathbb{R} \\ $$$${f}\left({n}\right)=\underset{\mathrm{0}} {\overset{\mathrm{2}\pi} {\int}}{x}^{{n}} \mathrm{sin}\:{xdx} \\ $$$${g}\left({n}\right)=\underset{\mathrm{0}} {\overset{\mathrm{2}\pi} {\int}}{x}^{{n}} \mathrm{cos}\:{xdx} \\ $$$$\frac{{f}\left({n}+\mathrm{1}\right)−{f}\left({n}\right)}{{g}\left({n}+\mathrm{1}\right)−{g}\left({n}\right)}=? \\…
Question Number 132016 by bramlexs22 last updated on 10/Feb/21 $$\mathrm{Trigonometry} \\ $$$$\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of} \\ $$$$\:\sqrt{\left(\mathrm{3sin}\:\mathrm{x}−\mathrm{4cos}\:\mathrm{x}−\mathrm{10}\right)\left(\mathrm{3sin}\:\mathrm{x}+\mathrm{4cos}\:\mathrm{x}−\mathrm{10}\right)}\:. \\ $$ Answered by EDWIN88 last updated on 11/Feb/21 $$\:\mathrm{consider}\:\left(\left(\mathrm{3sin}\:\mathrm{x}−\mathrm{10}\right)−\mathrm{4cos}\:\mathrm{x}\right)\left(\left(\mathrm{3sin}\:\mathrm{x}−\mathrm{10}\right)+\mathrm{4cos}\:\mathrm{x}\right)= \\…