Question Number 203502 by Frix last updated on 20/Jan/24 $${z}\mathrm{e}^{{z}} =\mathrm{e} \\ $$$$\mathrm{Obviously}\:{z}=\mathrm{1} \\ $$$$\mathrm{Now}\:\mathrm{find}\:\mathrm{at}\:\mathrm{least}\:\mathrm{one}\:\mathrm{solution}\:\mathrm{for}\:{z}\in\mathbb{C} \\ $$ Commented by Frix last updated on 22/Jan/24 $$\mathrm{See}\:\mathrm{question}\:\mathrm{203570}…
Question Number 203497 by ajfour last updated on 20/Jan/24 $${x}^{\mathrm{4}} +{cx}+{d}=\mathrm{0} \\ $$$${then}\:\:{find}\:{p}\:\:{from} \\ $$$${p}^{\mathrm{6}} −\mathrm{4}\left(\frac{{d}^{\:\mathrm{3}} }{{c}^{\mathrm{4}} }\right)^{\mathrm{1}/\mathrm{3}} {p}^{\mathrm{2}} −\mathrm{1}=\mathrm{0} \\ $$$${x}=\frac{{c}^{\mathrm{1}/\mathrm{3}} }{\mathrm{2}}\left({p}\pm\sqrt{−{p}^{\mathrm{2}} −\frac{\mathrm{8}}{{p}}}\:\right) \\…
Question Number 203498 by ajfour last updated on 20/Jan/24 $$\frac{{d}^{\mathrm{3}\:} {y}}{{dx}^{\mathrm{3}} }=\mathrm{4}\left({x}+\frac{\mathrm{1}}{\mathrm{4}}\right)^{\mathrm{2}} −\mathrm{4}{y} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 203490 by cortano12 last updated on 20/Jan/24 $$\:\:\:\:\mathrm{1}×\mathrm{3}×\mathrm{5}×\mathrm{7}×\mathrm{9}×…×\mathrm{2005}\:=\:…\:\left(\mathrm{mod}\:\mathrm{1000}\right) \\ $$ Answered by AST last updated on 20/Jan/24 $${x}=\mathrm{1}×\mathrm{3}×\mathrm{5}…×\mathrm{2005}\equiv\mathrm{0}\left({mod}\:\mathrm{125}\right) \\ $$$${x}\equiv\left(\mathrm{1}×\mathrm{3}×\mathrm{5}×\mathrm{7}\right)^{\mathrm{250}} ×\mathrm{1}×\mathrm{3}×\mathrm{5}\left({mod}\:\mathrm{8}\right)\equiv\mathrm{7}\left({mod}\:\mathrm{8}\right) \\ $$$${x}=\mathrm{125}{q}\equiv\mathrm{7}\left({mod}\:\mathrm{8}\right)\Rightarrow\mathrm{5}{q}\equiv\mathrm{15}\left({mod}\:\mathrm{8}\right)\Rightarrow{q}\equiv\mathrm{3}\left({mod}\:\mathrm{8}\right)…
Question Number 203454 by Denis_volosenko352 last updated on 19/Jan/24 $$\sqrt{\mathrm{5}}+\sqrt{\mathrm{5}}={x} \\ $$$${x}×\mathrm{5}\pi=?\:{find}\:{all}\:{answers}\:{until}\:\mathrm{24}.\mathrm{01}.\mathrm{2024} \\ $$ Answered by MathematicalUser2357 last updated on 20/Jan/24 $${x}=\sqrt{\mathrm{5}}+\sqrt{\mathrm{5}}=\mathrm{2}\sqrt{\mathrm{5}} \\ $$$${x}×\mathrm{5}\pi=\mathrm{2}\sqrt{\mathrm{5}}×\mathrm{5}\pi=\mathrm{10}\pi\sqrt{\mathrm{5}} \\…
Question Number 203448 by hardmath last updated on 19/Jan/24 $$\mathrm{y}\:=\:\mathrm{sin3x}−\mathrm{ln}\left(\mathrm{3x}+\mathrm{1}\right)+\mathrm{3}^{\mathrm{2}\boldsymbol{\mathrm{x}}} \\ $$$$\mathrm{find}:\:\:\:\mathrm{y}^{'} \:=\:? \\ $$ Commented by hardmath last updated on 19/Jan/24 $$ \\ $$find…
Question Number 203445 by mathlove last updated on 19/Jan/24 Commented by mr W last updated on 19/Jan/24 $$\Rightarrow{Q}\mathrm{203387} \\ $$ Terms of Service Privacy Policy…
Question Number 203468 by MrGHK last updated on 19/Jan/24 $$\:\boldsymbol{\mathrm{let}}\:\boldsymbol{\mathrm{A}}\:{B}\:{and}\:{C}\:\:\boldsymbol{\mathrm{be}}\:\boldsymbol{\mathrm{sets}}\:\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{using}}\:\boldsymbol{\mathrm{venn}}\:\boldsymbol{\mathrm{diagrams}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{by}}\:\boldsymbol{\mathrm{first}}\:\boldsymbol{\mathrm{principle}} \\ $$$$\left.\:\boldsymbol{\mathrm{a}}\right)\boldsymbol{\mathrm{A}}×\left(\boldsymbol{\mathrm{B}}\cup\boldsymbol{\mathrm{C}}\right)=\left(\boldsymbol{\mathrm{A}}×\boldsymbol{\mathrm{B}}\right)\cup\left(\boldsymbol{\mathrm{A}}×\boldsymbol{\mathrm{C}}\right) \\ $$$$\left.\boldsymbol{\mathrm{b}}\right)\mathrm{A}×\left(\boldsymbol{\mathrm{B}}\cap\boldsymbol{\mathrm{C}}\right)=\left(\boldsymbol{\mathrm{A}}×\boldsymbol{\mathrm{B}}\right)\cap\left(\boldsymbol{\mathrm{A}}×\boldsymbol{\mathrm{C}}\right) \\ $$$$\left.\boldsymbol{\mathrm{c}}\right)\left(\boldsymbol{\mathrm{A}}−\boldsymbol{\mathrm{B}}\right)\cap\left(\boldsymbol{{A}}\cap\boldsymbol{\mathrm{B}}\right)\cap\left(\boldsymbol{\mathrm{B}}−\boldsymbol{\mathrm{A}}\right)=\left\{\right\} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 203471 by DEGWE last updated on 19/Jan/24 Answered by MathematicalUser2357 last updated on 20/Jan/24 $$=\frac{\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}{x}^{\mathrm{cosec}\:{x}+\mathrm{cot}\:{x}} }{\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\left(\mathrm{cosec}\:{x}+\mathrm{cot}\:{x}\right)} \\ $$$$=\frac{\underset{{x}\rightarrow\mathrm{0}^{+} }…
Question Number 203465 by princemurtuja last updated on 19/Jan/24 $$\mathrm{Focus}\:\mathrm{and}\:\mathrm{vertex}\:\mathrm{of}\:\mathrm{a}\:\mathrm{parabola}\:\mathrm{are}\:\mathrm{at}\:\left(\mathrm{3},\:\mathrm{4}\right)\:\mathrm{and}\:\left(\mathrm{0},\mathrm{0}\right). \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{directrix}. \\ $$ Answered by mr W last updated on 20/Jan/24 $${F}\left(\mathrm{3},\:\mathrm{4}\right) \\ $$$${V}\left(\mathrm{0},\:\mathrm{0}\right)…