Question Number 73766 by mathocean1 last updated on 15/Nov/19 $$\begin{cases}{\frac{\mathrm{1}}{\mathrm{x}−\mathrm{1}}=\frac{\mathrm{2}}{\mathrm{y}−\mathrm{2}}=\frac{\mathrm{3}}{\mathrm{z}−\mathrm{3}}}\\{\mathrm{x}+\mathrm{2y}+\mathrm{3z}=\mathrm{56}}\end{cases} \\ $$$$ \\ $$$$\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{it}\:\mathrm{in}\:\mathbb{R}^{\mathrm{3}} \\ $$ Answered by MJS last updated on 15/Nov/19 $$ \\…
Question Number 139290 by mathdanisur last updated on 25/Apr/21 $$\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\:\frac{{sin}\left({x}^{\mathrm{2}} −{arctan}\left(\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)\right)}{\:\sqrt{\mathrm{1}\:+\:{x}^{\mathrm{4}} }}\:{dx} \\ $$ Answered by Ar Brandon last updated on 25/Apr/21…
Question Number 8217 by tawakalitu last updated on 02/Oct/16 $$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{x}^{\mathrm{3}} \:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion} \\ $$$$\mathrm{of}\:\left(\mathrm{1}\:+\:\mathrm{x}\:+\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{x}^{\mathrm{4}} \:+\:\mathrm{x}^{\mathrm{5}} \right)^{\mathrm{6}} \\ $$ Commented by 123456 last updated on…
Question Number 8148 by Rasheed Soomro last updated on 02/Oct/16 $$\mathrm{Determine}\:\mathrm{x}^{\mathrm{4}} −\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{4}} }\:,\:\mathrm{if}\:\mathrm{x}^{\mathrm{2}} +\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }=\mathrm{34}\:. \\ $$ Commented by sou1618 last updated on 02/Oct/16 $${set}\:{X}={x}^{\mathrm{2}}…
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Question Number 73679 by Tinku Tara last updated on 14/Nov/19 $$\mathrm{We}\:\mathrm{have}\:\mathrm{updated}\:\mathrm{backend}\:\mathrm{code}\:\mathrm{to}\: \\ $$$$\mathrm{disallow}\:\mathrm{delete}\:\mathrm{of}\:\mathrm{question}\:\mathrm{which}\:\mathrm{are} \\ $$$$\mathrm{already}\:\mathrm{answered}\:\mathrm{or}\:\mathrm{commented}. \\ $$$$ \\ $$ Commented by malwaan last updated on…
Question Number 8134 by 314159 last updated on 01/Oct/16 Answered by prakash jain last updated on 01/Oct/16 $$\mathrm{See}\:\mathrm{question}\:\mathrm{8025}. \\ $$ Terms of Service Privacy Policy…
Question Number 73665 by aliesam last updated on 14/Nov/19 $${if} \\ $$$$ \\ $$$${cos}^{\mathrm{2}} \left(\theta\right)=\frac{{m}^{\mathrm{2}} −\mathrm{1}}{\mathrm{3}}\:\:,\:\:{tan}^{\mathrm{3}} \left(\frac{\theta}{\mathrm{2}}\right)={tan}\left({a}\right) \\ $$$$ \\ $$$${prove}\:{that} \\ $$$$ \\ $$$$\sqrt[{\mathrm{3}}]{{cos}^{\mathrm{2}}…
Question Number 139193 by EnterUsername last updated on 23/Apr/21 $$\underset{{m}=\mathrm{1}} {\overset{\mathrm{32}} {\sum}}\left(\mathrm{3}{m}+\mathrm{2}\right)\left(\underset{{n}=\mathrm{1}} {\overset{\mathrm{10}} {\sum}}\left(\mathrm{sin}\left(\frac{\mathrm{2}{n}\pi}{\mathrm{11}}\right)−\mathrm{icos}\left(\frac{\mathrm{2}{n}\pi}{\mathrm{11}}\right)\right)\right)^{{m}} = \\ $$$$\left(\mathrm{A}\right)\:\mathrm{4}\left(\mathrm{1}−{i}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{B}\right)\:\mathrm{12}\left(\mathrm{1}+{i}\right) \\ $$$$\left(\mathrm{C}\right)\:\mathrm{12}\left(\mathrm{1}−{i}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{D}\right)\:\mathrm{48}\left(\mathrm{1}−{i}\right) \\ $$ Answered by qaz last…
Question Number 139190 by mathdanisur last updated on 23/Apr/21 $${a};{b}\in\mathbb{R}\:,\:\frac{\mid{ax}+{b}\mid}{\mathrm{1}+{x}^{\mathrm{2}} }\:\leqslant\:\mathrm{1}\:,\:\forall{x}\in\mathbb{R} \\ $$$${prove}:\:\:\mid{a}\mid\leqslant\mathrm{2}\:;\:\mid{b}\mid\leqslant\mathrm{1} \\ $$ Answered by mitica last updated on 24/Apr/21 $${x}=\mathrm{0}\Rightarrow\mid{b}\mid\leqslant\mathrm{1} \\ $$$${x}=\mathrm{1}\Rightarrow\mid{a}+{b}\mid\leqslant\mathrm{2}…
Question Number 139192 by EnterUsername last updated on 23/Apr/21 $$\mathrm{If}\:{z}_{\mathrm{1}\:} \:\mathrm{and}\:{z}_{\mathrm{2}} \:\mathrm{are}\:\mathrm{complex}\:{n}\mathrm{th}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{unity}\:\mathrm{which}\:\mathrm{sub}- \\ $$$$\mathrm{tend}\:\mathrm{right}\:\mathrm{angle}\:\mathrm{at}\:\mathrm{the}\:\mathrm{origin},\:\mathrm{then}\:{n}\:\mathrm{must}\:\mathrm{be}\:\mathrm{of}\:\mathrm{the}\:\mathrm{form} \\ $$$$\left(\mathrm{A}\right)\:\mathrm{4K}+\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{B}\right)\:\mathrm{4K}+\mathrm{2} \\ $$$$\left(\mathrm{C}\right)\:\mathrm{4K}+\mathrm{3}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{D}\right)\:\mathrm{4K} \\ $$ Answered by mr W last…