Question Number 207731 by efronzo1 last updated on 24/May/24 $$\:\:\:\downharpoonleft\underline{\:} \\ $$ Answered by A5T last updated on 24/May/24 Commented by A5T last updated on…
Question Number 207724 by hardmath last updated on 24/May/24 $$\mathrm{2}\:\mathrm{tg}^{\mathrm{3}} \:\boldsymbol{\mathrm{x}}\:−\:\mathrm{2}\:\mathrm{tg}^{\mathrm{2}} \:\boldsymbol{\mathrm{x}}\:+\:\mathrm{6}\:\mathrm{tg}\:\boldsymbol{\mathrm{x}}\:=\:\mathrm{3}\:\:\:,\:\:\:\left[\mathrm{0}\:;\:\mathrm{2}\boldsymbol{\pi}\right] \\ $$$$\mathrm{Sum}\:\mathrm{of}\:\mathrm{roots}\:=\:? \\ $$ Answered by Frix last updated on 24/May/24 $$\mathrm{tan}^{\mathrm{3}} \:{x}\:−\mathrm{tan}^{\mathrm{2}}…
Question Number 207723 by SANOGO last updated on 24/May/24 $$\mathrm{li}{m}\int_{\mathrm{0}} ^{\infty} \left(\mathrm{1}−{e}^{−{ncos}\left({x}\right)} \right){dx} \\ $$ Commented by Frix last updated on 24/May/24 $${f}\left({x}\right)=\mathrm{1}−\mathrm{e}^{−{n}\mathrm{cos}\:{x}} \\ $$$${n}\rightarrow\infty\:\Rightarrow\:{f}\left({x}\right)=\begin{cases}{\mathrm{1};\:−\frac{\pi}{\mathrm{2}}+{k}\pi\leqslant{x}\leqslant\frac{\pi}{\mathrm{2}}+{k}\pi}\\{−\infty;\:\frac{\pi}{\mathrm{2}}+{k}\pi<{x}<\frac{\mathrm{3}\pi}{\mathrm{2}}+{k}\pi}\end{cases}\forall{k}\in\mathbb{Z}…
Question Number 207717 by hardmath last updated on 24/May/24 $$\mathrm{lg}^{\mathrm{2}} \:\left(\mathrm{10x}\right)\:−\:\mathrm{lg}\:\mathrm{10x}\:+\:\mathrm{1}\:=\:\mathrm{6}\:−\:\mathrm{lg}\:\mathrm{x} \\ $$$$\mathrm{find}:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$ Answered by TonyCWX08 last updated on 24/May/24 $$\left(\mathrm{1}+{lg}\left({x}\right)\right)^{\mathrm{2}} −\left(\mathrm{1}+{lg}\left({x}\right)\right)+{lg}\left({x}\right)+\mathrm{1}−\mathrm{6}=\mathrm{0} \\…
Question Number 207718 by hardmath last updated on 24/May/24 $$\mid\mathrm{x}−\mathrm{3}\mid\:+\:\mid\mathrm{x}\:+\mathrm{2}\mid\:=\:\mathrm{9} \\ $$$$\mathrm{find}:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$ Answered by TonyCWX08 last updated on 24/May/24 $${There}\:{are}\:\mathrm{4}\:{possible}\:{cases}. \\ $$$${x}−\mathrm{3}+{x}+\mathrm{2}=\mathrm{9} \\…
Question Number 207712 by efronzo1 last updated on 24/May/24 Answered by Frix last updated on 24/May/24 $$\mathrm{For}\:{x}={q}\:\mathrm{and}\:{A}=\begin{pmatrix}{{p}}\\{\mathrm{0}}\end{pmatrix}\:\mathrm{the}\:\mathrm{area}\:\mathrm{is}\:\left({q}−{p}\right)\sqrt{{p}} \\ $$$$\frac{{d}\left[\left({q}−{p}\right)\sqrt{{p}}\right]}{{dp}}=\mathrm{0} \\ $$$$\frac{{q}−\mathrm{3}{p}}{\mathrm{2}\sqrt{{p}}}=\mathrm{0}\:\Rightarrow\:{p}=\frac{{q}}{\mathrm{3}} \\ $$$$\mathrm{Max}\:\mathrm{area}\:=\frac{\mathrm{2}\sqrt{\mathrm{3}}{q}^{\frac{\mathrm{3}}{\mathrm{2}}} }{\mathrm{9}} \\…
Question Number 207713 by efronzo1 last updated on 24/May/24 Answered by Berbere last updated on 24/May/24 $$\underset{{i}=\mathrm{1}} {\overset{\mathrm{2023}} {\sum}}{x}_{{i}} ^{\mathrm{2}} =\mathrm{125}\Rightarrow{only}\:\mathrm{125}\:{number}\:\neq\mathrm{0}\:{at}\:{least} \\ $$$$\underset{{i}=\mathrm{1}} {\overset{\mathrm{125}} {\sum}}{x}_{{i}}…
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