Question Number 67672 by Abdo msup. last updated on 30/Aug/19 $${decompose}\:{the}\:{folowing}\:\:{fraction}\:{at}\:{R}\left({x}\right) \\ $$$$\left.\mathrm{1}\right){F}\left({x}\right)=\frac{{x}^{\mathrm{3}} }{\mathrm{1}−{x}^{\mathrm{6}} } \\ $$$$\left.\mathrm{2}\right)\:{G}\left({x}\right)\:=\frac{{x}^{\mathrm{2}} +\mathrm{1}}{{x}^{\mathrm{3}} \left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Commented by…
Question Number 67673 by Abdo msup. last updated on 30/Aug/19 $${calculate}\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} \:+{x}+\mathrm{1}\right)} \\ $$ Commented by Abdo msup. last updated on 30/Aug/19…
Question Number 2135 by Rasheed Soomro last updated on 04/Nov/15 $${Solve}\:{the}\:{following}\:{system}\:{of}\:{inequalities} \\ $$$${b}^{\mathrm{2}} {x}^{\mathrm{2}} +{a}^{\mathrm{2}} {y}^{\mathrm{2}} \:\leqslant{a}^{\mathrm{2}} {b}^{\mathrm{2}} \:\:\wedge\:\:\:{a}^{\mathrm{2}} {x}^{\mathrm{2}} +{b}^{\mathrm{2}} {y}^{\mathrm{2}} \:\leqslant{a}^{\mathrm{2}} {b}^{\mathrm{2}\:} \:\:;\:\:\:{a},{b}\neq\mathrm{0}…
Question Number 2134 by Rasheed Soomro last updated on 04/Nov/15 $${Factorize} \\ $$$$−\mathrm{2}+\frac{\mathrm{1}}{{x}^{\mathrm{3}} }+{x}^{\mathrm{3}} \\ $$$$\left({Stepwise}\:{process}\:{is}\:{required}\right) \\ $$ Answered by sudhanshur last updated on 04/Nov/15…
Question Number 133206 by rexford last updated on 20/Feb/21 Answered by EDWIN88 last updated on 20/Feb/21 $$\mathrm{i}+\mathrm{j}+\mathrm{3k}=\begin{pmatrix}{\mathrm{1}}\\{\mathrm{1}}\\{\mathrm{3}}\end{pmatrix}\:;\:\mathrm{3i}−\mathrm{3j}+\mathrm{k}\:=\:\begin{pmatrix}{\:\:\:\mathrm{3}}\\{−\mathrm{3}}\\{\:\:\:\mathrm{1}}\end{pmatrix} \\ $$$$−\mathrm{4i}+\mathrm{5j}\:=\:\begin{pmatrix}{−\mathrm{4}}\\{\:\:\:\mathrm{5}}\\{\:\:\:\mathrm{0}}\end{pmatrix} \\ $$$$\Leftrightarrow\:\begin{pmatrix}{\mathrm{1}}\\{\mathrm{1}}\\{\mathrm{3}}\end{pmatrix}\:\mathrm{x}\:+\begin{pmatrix}{\:\:\:\mathrm{3}}\\{−\mathrm{3}}\\{\:\:\:\mathrm{1}}\end{pmatrix}\:\mathrm{y}\:+\begin{pmatrix}{−\mathrm{4}}\\{\:\:\:\mathrm{5}}\\{\:\:\:\mathrm{0}}\end{pmatrix}\:\mathrm{z}\:=\:\lambda\:\begin{pmatrix}{\mathrm{x}}\\{\mathrm{y}}\\{\mathrm{z}}\end{pmatrix} \\ $$$$\Leftrightarrow\:\begin{pmatrix}{\mathrm{x}+\mathrm{3y}−\mathrm{4z}}\\{\mathrm{x}−\mathrm{3y}+\mathrm{5z}}\\{\mathrm{3x}+\mathrm{y}+\mathrm{0z}}\end{pmatrix}\:=\:\lambda\begin{pmatrix}{\mathrm{x}}\\{\mathrm{y}}\\{\mathrm{z}}\end{pmatrix} \\ $$$$\Leftrightarrow\:\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:\mathrm{3}\:\:\:\:\:\:−\mathrm{4}}\\{\mathrm{1}\:\:\:−\mathrm{3}\:\:\:\:\:\:\:\:\mathrm{5}}\\{\mathrm{3}\:\:\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\:\:\mathrm{0}}\end{pmatrix}\:\begin{pmatrix}{\mathrm{x}}\\{\mathrm{y}}\\{\mathrm{z}}\end{pmatrix}\:=\:\lambda\:\begin{pmatrix}{\mathrm{x}}\\{\mathrm{y}}\\{\mathrm{z}}\end{pmatrix}…
Question Number 133201 by Tojiboyeva Kamolahon last updated on 19/Feb/21 $$\sqrt{\mathrm{81}} \\ $$ Answered by MJS_new last updated on 20/Feb/21 $$−\mathrm{3}^{\mathrm{2}} \mathrm{e}^{\mathrm{i}\pi} \\ $$ Commented…
Question Number 2130 by Yozzi last updated on 03/Nov/15 $${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 67664 by Rio Michael last updated on 29/Aug/19 $${show}\:{that}\:\:\exists\:{n}\:\in\:{N}^{+\:} \::\:\:{sin}^{{n}} {x}\:+\:{cos}^{{n}} {x}\:=\:\mathrm{1}\:{and}\:\:{cosh}^{{n}} {x}\:−\:{sinh}^{{n}} {x}\:=\:\mathrm{1}. \\ $$$$ \\ $$$${Hint}:\:{use}\:{Induction}\:{method}. \\ $$$$ \\ $$ Commented…
Question Number 2129 by Yozzi last updated on 03/Nov/15 $${A}\:{mirror}\:{is}\:{designed}\:{so}\:{that}\:{any}\:{ray} \\ $$$${of}\:{light}\:{which}\:{hits}\:{one}\:{side}\:{of}\:{the} \\ $$$${mirror}\:{and}\:{which}\:{is}\:{parallel}\:{to}\:{a}\: \\ $$$${certain}\:{fixed}\:{line}\:{L}\:{is}\:{reflected}\:{through} \\ $$$${a}\:{fixed}\:{point}\:{O}.\:{Prove}\:{that}\:{the}\:{mirror} \\ $$$${intersects}\:{any}\:{plane}\:{containing}\:{L}\:{in} \\ $$$${a}\:{parabola}. \\ $$$${I}\:{would}\:{appreciate}\:{a}\:{formal}\:{proof}. \\…
Question Number 67662 by Rio Michael last updated on 29/Aug/19 $${please}\:{explain}\:{the}\:{fact}\:{that}\: \\ $$$$\int\frac{\mathrm{1}}{{x}}{dx}\:=\:{ln}\:{x}\:+\:{k} \\ $$ Commented by malwaan last updated on 29/Aug/19 $$\int\frac{{f}\:'\left({x}\right)}{{f}\left({x}\right)}{dx}\:={ln}\:\mid{f}\left({x}\right)\mid+\:{c} \\ $$$$\left({x}\right)'=\mathrm{1}…