Question Number 68591 by TawaTawa last updated on 14/Sep/19 Commented by kaivan.ahmadi last updated on 14/Sep/19 $$\mathrm{102}+\mathrm{2}{p}+\mathrm{3}{q}=\mathrm{0} \\ $$$$\mathrm{17}+\mathrm{3}{p}−\mathrm{4}{q}=\mathrm{0} \\ $$$$\Rightarrow \\ $$$$\begin{cases}{\mathrm{2}{p}+\mathrm{3}{q}=−\mathrm{102}}\\{\mathrm{3}{p}−\mathrm{4}{q}=−\mathrm{17}}\end{cases}\Rightarrow\begin{cases}{−\mathrm{6}{p}−\mathrm{9}{q}=\mathrm{306}}\\{\mathrm{6}{p}−\mathrm{8}{q}=−\mathrm{34}}\end{cases}\Rightarrow \\ $$$$−\mathrm{17}{q}=\mathrm{272}\Rightarrow{q}=−\mathrm{16}…
Question Number 133925 by bemath last updated on 25/Feb/21 $$\:\mathrm{Given}\:\mathrm{vector}\:\overset{\rightarrow} {{a}}\:=\:\hat {\mathrm{i}}−\mathrm{2}\hat {\mathrm{j}}+\hat {\mathrm{k}}\:,\: \\ $$$$\overset{\rightarrow} {{b}}=\:\mathrm{2}\hat {\mathrm{i}}+\hat {\mathrm{j}}−\mathrm{2}\hat {\mathrm{k}}\:,\:\overset{\rightarrow} {{c}}=−\hat {\mathrm{i}}+\mathrm{3}\hat {\mathrm{j}}−\hat {\mathrm{k}} \\…
Question Number 133857 by mnjuly1970 last updated on 24/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:…..#{advanced}\:\:\:\:……………\:\:\:{calculus}#….. \\ $$$$\:\:\:\:{prove}\:\:{that}\::::\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}^{\mathrm{2}} \left(\mathrm{1}−{x}\right)}{{x}}{dx}\overset{?} {=}\mathrm{2}\zeta\left(\mathrm{3}\right) \\ $$$$\:\:\:\:\:\:\:\:\overset{\mathrm{1}−{x}={t}} {=}\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}^{\mathrm{2}} \left({t}\right)}{\mathrm{1}−{t}}{dt}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \underset{{n}=\mathrm{0}} {\overset{\infty}…
Question Number 68315 by 9102176137086 last updated on 08/Sep/19 $$\int\left(\frac{{x}^{−\mathrm{3}} +\mathrm{2}{x}−\mathrm{4}}{{x}}\right) \\ $$ Commented by mathmax by abdo last updated on 10/Sep/19 $$=\int\:\left({x}^{−\mathrm{4}} \:+\mathrm{2}\:−\frac{\mathrm{4}}{{x}}\right){dx}\:=\frac{\mathrm{1}}{−\mathrm{4}+\mathrm{1}}{x}^{−\mathrm{4}+\mathrm{1}} \:+\mathrm{2}{x}−\mathrm{4}{ln}\mid{x}\mid\:+{c}…
Question Number 2163 by Filup last updated on 06/Nov/15 $$\mathrm{For}:\:{y}={f}\left({x}\right)\:\rightarrow\:{x}={g}\left({y}\right) \\ $$$$\mathrm{Therefore}: \\ $$$$\begin{cases}{{x}\left({t}\right)={t}}\\{{y}\left({t}\right)={f}\left({t}\right)}\end{cases} \\ $$$$\mathrm{let}\:\boldsymbol{{r}}\left({t}\right)=\langle{x}\left({t}\right),\:{y}\left({t}\right)\rangle \\ $$$$ \\ $$$$\therefore\int\boldsymbol{{r}}{dt}=\langle\int{tdt},\:\int{f}\left({t}\right){dt}\rangle \\ $$$$ \\ $$$$\mathrm{Does}: \\…
Question Number 2130 by Yozzi last updated on 03/Nov/15 $${Find}\:\boldsymbol{{r}}=\begin{pmatrix}{{x}\left({t}\right)}\\{{y}\left({t}\right)}\end{pmatrix}\:\:\:{satisfying}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{{d}\boldsymbol{{r}}}{{dt}}+\boldsymbol{{Ar}}=\mathrm{0} \\ $$$${where}\:\boldsymbol{{A}}=\begin{bmatrix}{−\mathrm{3}\:\:\:\:−\mathrm{1}}\\{\mathrm{8}\:\:\:\:\:\:\:\:\:\:\mathrm{3}}\end{bmatrix}\:{by}\:{using} \\ $$$${a}\:{matrix}\:{integrating}\:{factor}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 133199 by rexford last updated on 19/Feb/21 Answered by mr W last updated on 20/Feb/21 $$\overset{\rightarrow} {\boldsymbol{{AB}}}=\left(−\mathrm{1},\mathrm{5},−\mathrm{3}\right) \\ $$$$\overset{\rightarrow} {\boldsymbol{{AC}}}=\left(−\mathrm{4},\mathrm{3},\mathrm{3}\right) \\ $$$$\overset{\rightarrow} {\boldsymbol{{AD}}}=\left(\mathrm{1},\mathrm{7},\lambda+\mathrm{1}\right)…
Question Number 2092 by Filup last updated on 02/Nov/15 $$\mathrm{If}\:\boldsymbol{{A}}=\langle{p}_{{x}} ,\:{p}_{{y}} ,\:{p}_{{z}} \rangle\:\mathrm{is}\:\mathrm{a}\:\mathrm{position}\:\mathrm{vector}\: \\ $$$$\mathrm{in}\:\mathrm{standard}\:\mathrm{position},\:\mathrm{vector}\:\boldsymbol{{r}}=\langle{r}_{{x}} ,\:{r}_{{y}} ,\:{r}_{{z}} \rangle \\ $$$$\mathrm{is}\:\mathrm{the}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{a}\:\mathrm{3}\:\mathrm{dimensional}\:\mathrm{circle} \\ $$$$\mathrm{with}\:\mathrm{focal}\:\mathrm{point}\:\mathrm{at}\:\boldsymbol{{A}},\:\mathrm{Solve}\:\mathrm{for}\:\mathrm{the} \\ $$$$\mathrm{vector}\:\mathrm{equation}\:\boldsymbol{{r}}\left(\theta\right)\:\mathrm{such}\:\mathrm{that}\:\mathrm{it}\:\mathrm{is}\:\mathrm{the} \\…
Question Number 132972 by rexford last updated on 17/Feb/21 Answered by Ar Brandon last updated on 17/Feb/21 $$\begin{vmatrix}{\mathrm{i}}&{\mathrm{j}}&{\mathrm{k}}\\{\mathrm{1}}&{−\mathrm{2}}&{\mathrm{3}}\\{\mathrm{1}}&{−\mathrm{1}}&{−\mathrm{2}}\end{vmatrix}=\mathrm{7i}+\mathrm{5j}+\mathrm{k} \\ $$ Commented by rexford last updated…
Question Number 1851 by 112358 last updated on 14/Oct/15 $${A}\:{plane}\:{has}\:{equation}\:{x}−{z}=\mathrm{4}\sqrt{\mathrm{3}}. \\ $$$${The}\:{line}\:{l}\:{has}\:{vector}\:{equation} \\ $$$$\boldsymbol{{r}}=\lambda\left[\left({cos}\theta+\sqrt{\mathrm{3}}\right)\boldsymbol{{i}}+\left(\sqrt{\mathrm{2}}{sin}\theta\right)\boldsymbol{{j}}+\left({cos}\theta−\sqrt{\mathrm{3}}\right)\boldsymbol{{k}}\right] \\ $$$${where}\:\lambda\:{is}\:{a}\:{scalar}\:{parameter}. \\ $$$${If}\:{l}\:{meets}\:{the}\:{plane}\:{at}\:{P},\:{show}\:{that}, \\ $$$${as}\:\theta\:{varies},\:{P}\:\:{describes}\:{a}\:{circle}.\: \\ $$ Answered by 123456…