Question Number 207771 by hardmath last updated on 25/May/24 $$\mathrm{Simplify}:\:\:\:\:\:\frac{\sqrt[{\mathrm{4}}]{\boldsymbol{\mathrm{b}}}\:\:\sqrt{\boldsymbol{\mathrm{c}}}\:\:−\:\:\sqrt[{\mathrm{4}}]{\boldsymbol{\mathrm{c}}}\:\:\sqrt{\boldsymbol{\mathrm{b}}}}{\:\sqrt[{\mathrm{4}}]{\boldsymbol{\mathrm{b}}}\:\:\sqrt{\boldsymbol{\mathrm{c}}}\:\:−\:\:\sqrt[{\mathrm{4}}]{\boldsymbol{\mathrm{c}}}}\:\:=\:\:? \\ $$ Answered by Rasheed.Sindhi last updated on 26/May/24 $$\frac{{b}^{\mathrm{1}/\mathrm{4}} {c}^{\mathrm{1}/\mathrm{2}} −{c}^{\mathrm{1}/\mathrm{4}} {b}^{\mathrm{1}/\mathrm{2}} }{{b}^{\mathrm{1}/\mathrm{4}} {c}^{\mathrm{1}/\mathrm{2}}…
Question Number 207764 by mr W last updated on 25/May/24 Answered by som(math1967) last updated on 25/May/24 $$\:{R}^{\mathrm{2}} +\mathrm{4}^{\mathrm{2}} =\mathrm{2}\left(\mathrm{2}^{\mathrm{2}} +{R}^{\mathrm{2}} \right) \\ $$$$\Rightarrow{R}^{\mathrm{2}} =\mathrm{16}−\mathrm{8}…
Question Number 207751 by efronzo1 last updated on 25/May/24 $$\:\:\mathrm{It}\:\mathrm{is}\:\mathrm{known}\:\mathrm{that}\:\mathrm{a}\:\mathrm{balanced}\:\mathrm{6}−\mathrm{sided}\: \\ $$$$\:\mathrm{dice}\:\mathrm{originally}\:\mathrm{had}\:\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6}\:\mathrm{and}\:\mathrm{7}. \\ $$$$\:\mathrm{The}\:\mathrm{dice}\:\mathrm{wre}\:\mathrm{thrown}\:\mathrm{once}\:\mathrm{and}\: \\ $$$$\:\mathrm{the}\:\mathrm{result}\:\mathrm{was}\:\mathrm{observed}.\:\mathrm{If}\:\mathrm{an}\: \\ $$$$\mathrm{odd}\:\mathrm{numbers}\:\mathrm{appears},\:\mathrm{than}\:\mathrm{the}\: \\ $$$$\:\mathrm{number}\:\mathrm{is}\:\mathrm{replaced}\:\mathrm{with}\:\mathrm{the}\: \\ $$$$\:\mathrm{number}\:\mathrm{8}.\:\mathrm{However},\:\mathrm{if}\:\mathrm{an}\:\mathrm{even}\: \\ $$$$\:\mathrm{number}\:\mathrm{appears}\:,\:\mathrm{the}\:\mathrm{number} \\…
Question Number 207747 by MASANJAJJ last updated on 25/May/24 $${find}\:{the}\:{value}\:{of}\:{y}\:{given}\:{that}\:{y}^{{y}\:} =\mathrm{3}^{{y}+\mathrm{9}} \\ $$ Commented by A5T last updated on 25/May/24 $$\mathrm{3}^{\mathrm{9}+\mathrm{9}} =\mathrm{3}^{\mathrm{18}} =\left(\mathrm{3}^{\mathrm{2}} \right)^{\mathrm{3}^{\mathrm{2}} }…
Question Number 207738 by mr W last updated on 24/May/24 Answered by som(math1967) last updated on 24/May/24 $$\mathrm{180}−\mathrm{50}−\mathrm{60}=\mathrm{70} \\ $$$$\theta=\mathrm{180}−\mathrm{70}=\mathrm{110} \\ $$ Commented by mr…
Question Number 207730 by mr W last updated on 24/May/24 Commented by mr W last updated on 24/May/24 $${is}\:{this}\:{possible}? \\ $$ Commented by efronzo1 last…
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} \\…