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Author: Tinku Tara

Question-204233

Question Number 204233 by Perelman last updated on 09/Feb/24 Answered by Frix last updated on 09/Feb/24 $$\int\frac{{x}^{\frac{\mathrm{1}}{\mathrm{2}}} }{{x}^{\frac{\mathrm{3}}{\mathrm{4}}} +\mathrm{1}}{dx}\:\overset{{t}={x}^{\frac{\mathrm{1}}{\mathrm{4}}} } {=}\:\mathrm{4}\int\frac{{t}^{\mathrm{5}} }{{t}^{\mathrm{3}} +\mathrm{1}}{dt}= \\ $$$$=\mathrm{4}\int{t}^{\mathrm{2}}…

God-Damn-it-why-my-Integration-Test-is-Wrong-h-0-h-J-h-is-Conv-Laplace-transform-0-e-st-We-already-Know-0-e-st-J-t-dt-1-s-2-1-s-s-2-1-d-

Question Number 204226 by MathedUp last updated on 09/Feb/24 $$\mathrm{God}\:\mathrm{Damn}\:\mathrm{it}\:\mathrm{why}\:\mathrm{my}\:\mathrm{Integration}\:\mathrm{Test}\:\mathrm{is}\:\mathrm{Wrong}? \\ $$$$\underset{{h}=\mathrm{0}} {\overset{\infty} {\sum}}\:{h}\centerdot{J}_{\nu} \left({h}\right)\:\mathrm{is}\:\mathrm{Conv}?? \\ $$$$\mathrm{Laplace}\:\mathrm{transform}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{st}} \centerdot \\ $$$$\mathrm{We}\:\mathrm{already}\:\mathrm{Know}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{st}} {J}_{\nu}…

Question-204227

Question Number 204227 by abdomath last updated on 09/Feb/24 Answered by AST last updated on 09/Feb/24 $${Let}\:{y}={f}\left({x}\right)\Rightarrow{x}^{\mathrm{2}} {y}^{\mathrm{3}} =\left({x}+{y}\right)^{\mathrm{5}} \Rightarrow{x}^{\mathrm{2}} \left[{f}\left({x}\right)\right]^{\mathrm{3}} =\left({x}+{f}\left({x}\right)\right)^{\mathrm{5}} \\ $$$$\Rightarrow\frac{{d}}{{dx}}\left({x}^{\mathrm{2}} \left[{f}\left({x}\right)\right]^{\mathrm{3}}…

Question-204218

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}…

If-p-q-r-gt-0-pqr-1-min-p-3-q-r-q-3-p-r-r-3-p-q-give-a-reason-

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-204211

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…