Question Number 117101 by harckinwunmy last updated on 09/Oct/20 $$\mathrm{If}\:\mathrm{sin}^{\mathrm{2}} \theta\:\mathrm{and}\:\mathrm{cos}^{\mathrm{2}} \theta\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\: \\ $$$$\mathrm{of}\:\mathrm{quadratic}\:\mathrm{equation},\:\mathrm{find}\:\mathrm{the}\:\mathrm{equation}. \\ $$ Answered by bemath last updated on 09/Oct/20 $$\Rightarrow\left(\mathrm{x}−\mathrm{sin}\:^{\mathrm{2}} \theta\right)\left(\mathrm{x}−\mathrm{cos}\:^{\mathrm{2}}…
Question Number 117095 by bemath last updated on 09/Oct/20 Answered by Olaf last updated on 09/Oct/20 $$\frac{{u}_{{n}+\mathrm{1}} }{\mathrm{2}}+\mathrm{1}\:=\:{u}_{{n}} \\ $$$$\frac{{l}_{\mathrm{1}} }{\mathrm{2}}+\mathrm{1}\:=\:{l}_{\mathrm{1}} \:\Rightarrow\:{l}_{\mathrm{1}} \:=\:\mathrm{2} \\ $$$$…
Question Number 117082 by bobhans last updated on 09/Oct/20 $$\mathrm{If}\:\mathrm{6}−\mathrm{3x}\:\mathrm{is}\:\mathrm{the}\:\mathrm{geometric}\:\mathrm{mean}\:\mathrm{between} \\ $$$$\mathrm{the}\:\mathrm{integer}\:\mathrm{x}^{\mathrm{2}} +\mathrm{2}\:\mathrm{and}\:\bar {\mathrm{2}}\:\mathrm{what}\:\mathrm{are}\:\mathrm{the}\: \\ $$$$\mathrm{values}\:\mathrm{of}\:\mathrm{x}\:? \\ $$ Answered by bemath last updated on 09/Oct/20…
Question Number 182575 by CrispyXYZ last updated on 11/Dec/22 $$\sqrt[{{x}}]{{x}+\mathrm{1}}>\sqrt[{{e}}]{{e}} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{Solve}\:\mathrm{for}\:{x}\left({x}\in\mathbb{N}^{+} \right). \\ $$$$\left.\mathrm{2}\right)\:\mathrm{Solve}\:\mathrm{for}\:{x}\left({x}>\mathrm{0}\right). \\ $$ Answered by mr W last updated on 12/Dec/22…
Question Number 117026 by bemath last updated on 08/Oct/20 $$\:\frac{\sqrt{\mathrm{1}−\mathrm{x}}}{\:\sqrt{\mathrm{x}}}\:+\:\frac{\sqrt{\mathrm{x}}}{\:\sqrt{\mathrm{1}−\mathrm{x}}}\:=\:\frac{\mathrm{13}}{\mathrm{6}} \\ $$ Answered by 1549442205PVT last updated on 09/Oct/20 $$\mathrm{We}\:\mathrm{need}\:\mathrm{the}\:\mathrm{condition}\:\mathrm{for}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{is}\:\mathrm{defined}\:\mathrm{as}\:\mathrm{0}<\mathrm{x}<\mathrm{1}\left(\ast\right) \\ $$$$\:\frac{\sqrt{\mathrm{1}−\mathrm{x}}}{\:\sqrt{\mathrm{x}}}\:+\:\frac{\sqrt{\mathrm{x}}}{\:\sqrt{\mathrm{1}−\mathrm{x}}}\:=\:\frac{\mathrm{13}}{\mathrm{6}}\:\left(\mathrm{1}\right) \\…
Question Number 117027 by I want to learn more last updated on 09/Oct/20 $$\mathrm{solve}:\:\:\:\:\frac{\mathrm{x}\:\:−\:\:\mathrm{4}}{\mathrm{x}\:\:−\:\:\mathrm{3}}\:\:\:<\:\:\:\frac{\mathrm{2x}\:\:−\:\:\mathrm{1}}{\mathrm{2}} \\ $$ Answered by bemath last updated on 09/Oct/20 $$\Rightarrow\frac{\mathrm{x}−\mathrm{4}}{\mathrm{x}−\mathrm{3}}\:−\frac{\mathrm{2x}−\mathrm{1}}{\mathrm{2}}\:<\:\mathrm{0} \\…
Question Number 182530 by HeferH last updated on 10/Dec/22 $${If}:\:\:\:\frac{{a}}{{x}^{\mathrm{9}} }\:+\:\frac{{x}^{\mathrm{9}} }{{a}}\:=\:\mathrm{7} \\ $$$$\:{find}:\:\sqrt[{\mathrm{4}}]{\frac{{a}}{{x}^{\mathrm{9}} }}\:+\:\sqrt[{\mathrm{4}}]{\frac{{x}^{\mathrm{9}} }{{a}}} \\ $$ Answered by mr W last updated on…
Question Number 182512 by mathlove last updated on 10/Dec/22 Answered by manxsol last updated on 10/Dec/22 $$\sqrt{\mathrm{7}} \\ $$ Answered by manxsol last updated on…
Question Number 182508 by peter frank last updated on 10/Dec/22 Answered by mahdipoor last updated on 10/Dec/22 $${lim}\:{f}\left({x}\right)\:,\:{x}\rightarrow{c}\:={F} \\ $$$$\Leftrightarrow\forall\epsilon_{\mathrm{1}} >\mathrm{0}\:\:\exists\delta_{\mathrm{1}} >\mathrm{0}\:\:\mid{x}−{c}\mid<\delta_{\mathrm{1}} \Rightarrow\mid{F}−{f}\left({x}\right)\mid<\epsilon_{\mathrm{1}} \\ $$$${lim}\:{g}\left({x}\right)\:,\:{x}\rightarrow{c}\:={G}…
Question Number 51436 by Tawa1 last updated on 26/Dec/18 $$\mathrm{If}\:\:\:\:\mathrm{y}\:=\:\frac{\left(\mathrm{e}^{\mathrm{x}} \:+\:\mathrm{e}^{−\mathrm{x}} \right).\:\mathrm{tanh}\:\mathrm{x}}{\mathrm{e}^{\mathrm{x}} \:−\:\mathrm{sinh}\:\mathrm{x}} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\:\:\:\:\:\:\mathrm{y}'\:\:=\:\:\mathrm{2}\:\mathrm{sech}^{\mathrm{2}} \:\mathrm{x} \\ $$ Answered by peter frank last updated on…