Question Number 204218 by mnjuly1970 last updated on 08/Feb/24 Answered by AST last updated on 08/Feb/24 $$\begin{pmatrix}{\mathrm{3}}&{\mathrm{2}}\\{\mathrm{4}}&{\mathrm{1}}\end{pmatrix}\begin{pmatrix}{{a}}&{{b}}\\{{c}}&{{d}}\end{pmatrix}\begin{pmatrix}{\:{x}}\\{\:{y}}\end{pmatrix}=\begin{pmatrix}{\mathrm{1}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{1}}\end{pmatrix} \\ $$$$\Rightarrow\begin{pmatrix}{\mathrm{3}}&{\mathrm{2}}\\{\mathrm{4}}&{\mathrm{1}}\end{pmatrix}\begin{pmatrix}{{ax}+{by}}\\{{cx}+{dy}}\end{pmatrix}=\begin{pmatrix}{\left(\mathrm{3}{a}+\mathrm{2}{c}\right){x}+\left(\mathrm{3}{b}+\mathrm{2}{d}\right){y}}\\{\left(\mathrm{4}{a}+{c}\right){x}+\left(\mathrm{4}{b}+{d}\right){y}}\end{pmatrix} \\ $$$$\Rightarrow\begin{pmatrix}{\mathrm{3}{a}+\mathrm{2}{c}}&{\mathrm{3}{b}+\mathrm{2}{d}}\\{\mathrm{4}{a}+{c}}&{\mathrm{4}{b}+{d}}\end{pmatrix}=\begin{pmatrix}{\mathrm{1}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{1}}\end{pmatrix}\Rightarrow\begin{pmatrix}{{a}}&{{b}}\\{{c}}&{{d}}\end{pmatrix}=\begin{pmatrix}{\frac{−\mathrm{1}}{\mathrm{5}}}&{\frac{\mathrm{2}}{\mathrm{5}}}\\{\frac{\mathrm{4}}{\mathrm{5}}}&{\frac{−\mathrm{3}}{\mathrm{5}}}\end{pmatrix} \\ $$$$\Rightarrow{A}^{−\mathrm{1}} =\mathrm{5}^{−\mathrm{1}} \begin{pmatrix}{−\mathrm{1}}&{\mathrm{2}}\\{\mathrm{4}}&{−\mathrm{3}}\end{pmatrix}=\begin{pmatrix}{−\mathrm{3}}&{\mathrm{6}}\\{\mathrm{12}}&{−\mathrm{9}}\end{pmatrix}=\begin{pmatrix}{\mathrm{4}}&{\mathrm{6}}\\{\mathrm{5}}&{\mathrm{5}}\end{pmatrix}…
Question Number 204187 by mnjuly1970 last updated on 08/Feb/24 $$ \\ $$$$\:\:\:\:\:\:{If}\:\:\:{p}\:,\:{q}\:,\:{r}\:>\mathrm{0}\:,\:\:{pqr}=\:\mathrm{1} \\ $$$$\:\:\:\:\: \\ $$$$\:\Rightarrow\:\:{min}\left(\frac{\:{p}^{\mathrm{3}} }{{q}+{r}}\:+\:\frac{{q}^{\:\mathrm{3}} }{{p}+{r}}\:+\frac{{r}^{\mathrm{3}} }{{p}+{q}}\:\right)=? \\ $$$$\:\:\:\ast\:{give}\:{a}\:{reason}\:\ast \\ $$ Answered by…
Question Number 204180 by naka3546 last updated on 08/Feb/24 $$\mathrm{Solve}\:\:\mathrm{this}. \\ $$$$ \\ $$$$\frac{{x}+{y}−{a}}{{x}+{y}−{b}}\:\centerdot\:\frac{{dy}}{{dx}}\:=\:\frac{{x}+{y}+{a}}{{x}+{y}+{b}} \\ $$ Answered by mr W last updated on 08/Feb/24 $${u}={x}+{y}…
Question Number 204211 by mnjuly1970 last updated on 08/Feb/24 Answered by witcher3 last updated on 08/Feb/24 $$\mathrm{detA}=\mathrm{7}=\overset{−} {\mathrm{0}}\:\:\mathrm{in}\:\mathbb{Z}/\mathrm{7}\mathbb{Z} \\ $$$$\mathrm{A}\notin\mathrm{GL}\left(\mathrm{2};\mathbb{Z}/\mathrm{7}\mathbb{Z}\right) \\ $$$$ \\ $$ Commented…
Question Number 204179 by mr W last updated on 08/Feb/24 Answered by AST last updated on 08/Feb/24 $${f}\left({x}\right)={f}\left({y}\right)\Rightarrow{f}\left({f}\left({x}\right)\right)={f}\left({f}\left({y}\right)\right)\Rightarrow{x}^{\mathrm{2}} −{x}={y}^{\mathrm{2}} −{y} \\ $$$$\Rightarrow\left({x}−{y}\right)\left({x}+{y}\right)={x}−{y}\Rightarrow{x}=\mathrm{1}−{y}\:{or}\:{x}={y} \\ $$$$\Rightarrow{f}\left({x}\right)={f}\left(\mathrm{1}−{x}\right)\Rightarrow{f}\left(\mathrm{0}\right)={f}\left(\mathrm{1}\right) \\…
Question Number 204205 by universe last updated on 08/Feb/24 Answered by ajfour last updated on 08/Feb/24 $${x}={p}^{\mathrm{2}} \:,\:{y}={q}^{\mathrm{2}} \\ $$$${p}+{q}={p}^{\mathrm{2}} +{q}^{\mathrm{2}} ={t} \\ $$$${t}^{\mathrm{2}} ={t}+\mathrm{2}{pq}…
Question Number 204174 by patrice last updated on 08/Feb/24 Answered by Faetmaaa last updated on 27/Feb/24 $$\left.\mathrm{3}\right)- \\ $$$$\forall{n}\in\boldsymbol{\mathrm{N}}^{\bigstar} \\ $$$${S}_{{n}} \:=\:\frac{\mathrm{1}}{{n}}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\mathrm{ln}\left(\frac{{k}}{{n}}\right) \\…
Question Number 204197 by ajfour last updated on 08/Feb/24 Answered by mr W last updated on 08/Feb/24 $$\mathrm{sin}\:\frac{\theta}{\mathrm{2}}=\frac{{a}}{{R}−{a}} \\ $$$${OC}={OB}+{BC} \\ $$$$\frac{{R}}{\mathrm{cos}\:\theta}=\sqrt{\left({R}+\mathrm{1}\right)^{\mathrm{2}} −\mathrm{1}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{tan}\:\left(\frac{\frac{\pi}{\mathrm{2}}−\theta}{\mathrm{2}}\right)} \\…
Question Number 204198 by Shuhrat030 last updated on 08/Feb/24 $${Hisoblang}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 204157 by esmaeil last updated on 07/Feb/24 $${hello}\:{frinds} \\ $$$${I}\:{have}\:{a}\:{question} \\ $$$${when}\:{the}\:{most}\:{accurate}\:{math}\:{sofward} \\ $$$${it}\:{solves}\:{the}\:{most}\:{complex}\:{math} \\ $$$${problems}\:.{what}\:{is}\:{the}\:{need}\:{for}\:{us} \\ $$$${to}\:{spend}\:{hours}\:{to}\:{solve}\:{that}? \\ $$$$\left({Ofcourse}\:{i}\:{myself}\:{love}\:{math}\right) \\ $$$$\left({sorry}\:{i}'{m}\:{bad}\:{in}\:{english}\right) \\…