Question Number 24436 by Tinkutara last updated on 17/Nov/17 $$\mathrm{For}\:\mathrm{a}\:\mathrm{reversible}\:\mathrm{reaction}\:\mathrm{A}\:\rightleftharpoons\:\mathrm{B}.\:\mathrm{Find} \\ $$$$\mathrm{K}_{\mathrm{eq}} \:\mathrm{at}\:\mathrm{2727}°\mathrm{C}\:\mathrm{temperature}. \\ $$$$\mathrm{Given}\::\:\Delta_{\mathrm{r}} \mathrm{H}°\:=\:−\mathrm{30}\:\mathrm{kJ}\:\mathrm{mol}^{−\mathrm{1}} \:\left(\mathrm{at}\:\mathrm{2727}°\mathrm{C}\right) \\ $$$$\Delta_{\mathrm{r}} \mathrm{S}°\:=\:\mathrm{10}\:\mathrm{JK}^{−\mathrm{1}} \:\left(\mathrm{at}\:\mathrm{2727}°\mathrm{C}\right) \\ $$$$\mathrm{R}\:=\:\mathrm{8}.\mathrm{314}\:\mathrm{JK}^{−\mathrm{1}} \:\mathrm{mol}^{−\mathrm{1}} \\…
Question Number 89970 by jagoll last updated on 20/Apr/20 $$\mathrm{xy}\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\mathrm{y}^{\mathrm{2}} \left(\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\right)\: \\ $$ Commented by john santu last updated on 20/Apr/20 Terms of…
Question Number 24434 by Tinkutara last updated on 17/Nov/17 $$\mathrm{Two}\:\mathrm{cylindrical}\:\mathrm{hollow}\:\mathrm{drums}\:\mathrm{of}\:\mathrm{radii} \\ $$$${R}\:\mathrm{and}\:\mathrm{2}{R},\:\mathrm{and}\:\mathrm{of}\:\mathrm{a}\:\mathrm{common}\:\mathrm{height}\:{h}, \\ $$$$\mathrm{are}\:\mathrm{rotating}\:\mathrm{with}\:\mathrm{angular}\:\mathrm{velocities}\:\omega \\ $$$$\left(\mathrm{anti}-\mathrm{clockwise}\right)\:\mathrm{and}\:\omega\:\left(\mathrm{clockwise}\right), \\ $$$$\mathrm{respectively}.\:\mathrm{Their}\:\mathrm{axes},\:\mathrm{fixed}\:\mathrm{are} \\ $$$$\mathrm{parallel}\:\mathrm{and}\:\mathrm{in}\:\mathrm{a}\:\mathrm{horizontal}\:\mathrm{plane} \\ $$$$\mathrm{separated}\:\mathrm{by}\:\left(\mathrm{3}{R}\:+\:\delta\right).\:\mathrm{They}\:\mathrm{are}\:\mathrm{now} \\ $$$$\mathrm{brought}\:\mathrm{in}\:\mathrm{contact}\:\left(\delta\:\rightarrow\:\mathrm{0}\right). \\…
Question Number 155506 by VIDDD last updated on 01/Oct/21 Answered by amin96 last updated on 01/Oct/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{cos}^{\mathrm{2}} \left(\mathrm{1}−{cos}^{\mathrm{2}} \left(\mathrm{1}−\ldots{cos}^{\mathrm{2}} \left(\mathrm{1}−{cos}^{\mathrm{2}} \left({x}\right)\right)\right)\right)}{{sin}\left(\pi×\frac{\left(\sqrt{{x}+\mathrm{4}}−\mathrm{2}\right)\left(\sqrt{{x}+\mathrm{4}}+\mathrm{2}\right)}{\:{x}×\left(\sqrt{{x}+\mathrm{4}}+\mathrm{2}\right)}\right)}= \\ $$$$=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{cos}^{\mathrm{2}}…
Question Number 155500 by VIDDD last updated on 01/Oct/21 Answered by MJS_new last updated on 01/Oct/21 $${f}\left({x}+{y}\right)−\left({f}\left({x}\right)+{f}\left({y}\right)\right)=\mathrm{0} \\ $$$$\mathrm{2}{axy}−{c}=\mathrm{0} \\ $$$$\mathrm{this}\:\mathrm{is}\:\mathrm{only}\:\mathrm{true}\:\forall{x},{y}\in\mathbb{R}\:\mathrm{with}\:{a}=\mathrm{0}\:\Rightarrow\:{c}=\mathrm{0} \\ $$$${a}+{b}+{c}=\mathrm{3}\:\Rightarrow\:{b}=\mathrm{3} \\ $$$${f}\left({x}\right)=\mathrm{3}{x}…
Question Number 155497 by VIDDD last updated on 01/Oct/21 Answered by amin96 last updated on 01/Oct/21 $$\sqrt{\mathrm{4}−\frac{\mathrm{1}}{\mathrm{3}\sqrt{\mathrm{2}}}\underbrace{\sqrt{\mathrm{4}−\frac{\mathrm{1}}{\mathrm{3}\sqrt{\mathrm{2}}}\ldots}}}=\boldsymbol{\mathrm{x}}\:\: \\ $$$$\sqrt{\mathrm{4}−\frac{\mathrm{1}}{\mathrm{3}\sqrt{\mathrm{2}}}\boldsymbol{\mathrm{x}}}=\boldsymbol{\mathrm{x}}\:\:\:\Rightarrow\:\:\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} =\mathrm{4}−\frac{\boldsymbol{\mathrm{x}}}{\mathrm{3}\sqrt{\mathrm{2}}}\:\:\Rightarrow\:\:\mathrm{3}\boldsymbol{\mathrm{x}}^{\mathrm{2}} \sqrt{\mathrm{2}}+\boldsymbol{\mathrm{x}}−\mathrm{12}\sqrt{\mathrm{2}}=\mathrm{0} \\ $$$$\boldsymbol{\Delta}=\mathrm{289}\:\:\:\:\:\boldsymbol{\mathrm{x}}=\frac{−\mathrm{1}+\mathrm{17}}{\mathrm{6}\sqrt{\mathrm{2}}}=\frac{\mathrm{8}}{\mathrm{3}\sqrt{\mathrm{2}}} \\ $$$$\boldsymbol{\mathrm{A}}=\mathrm{10}+\boldsymbol{\mathrm{log}}_{\frac{\mathrm{3}}{\mathrm{2}}}…
Question Number 155496 by mathocean1 last updated on 01/Oct/21 $${Given}\:{I}_{{n}} =\underset{{n}\pi} {\overset{\left({n}+\mathrm{1}\right)\pi} {\int}}{e}^{−{x}} {sinx}\:{dx}\:,\:{n}\in\mathbb{N}. \\ $$$$\mathrm{1}.\:{Find}\:{a}\:{relation}\:{between}\:{I}_{{n}+\mathrm{1}} {and}\:{I}_{{n}} . \\ $$ Answered by ArielVyny last updated…
Question Number 89958 by 20000193 last updated on 20/Apr/20 $${prove}\:{that}\:\left(\mathrm{1}+\mathrm{sin}\:{x}/\mathrm{1}+\mathrm{cos}\:\mathrm{3}\left(\mathrm{1sin}\:{x}/\mathrm{1}+\mathrm{cosec}\:{x}\right)={tanx}\right. \\ $$ Commented by john santu last updated on 20/Apr/20 $$\frac{\mathrm{1}+\mathrm{sin}\:{x}}{\mathrm{1}+\mathrm{cos}\:\mathrm{3}\left(\mathrm{1sin}\:{x}+\frac{\mathrm{1}}{\mathrm{1}+\mathrm{cosec}\:{x}\:}\right)}\:=\:\mathrm{tan}\:{x}? \\ $$ Terms of…
Question Number 155495 by mathdanisur last updated on 01/Oct/21 $$\mathrm{if}\:\:\mathrm{a};\mathrm{b};\mathrm{c};\mathrm{d}\in\mathbb{R}\:\:\mathrm{verify}\:\:\mathrm{a}+\mathrm{2b}+\mathrm{3c}+\mathrm{4d}=\mathrm{6} \\ $$$$\mathrm{then}\:\mathrm{find}\:\:\boldsymbol{\mathrm{min}}\left(\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} +\mathrm{c}^{\mathrm{2}} +\mathrm{d}^{\mathrm{2}} \right) \\ $$ Answered by mr W last updated on…
Question Number 89956 by swizanjere@gmail.com last updated on 20/Apr/20 $$\mathrm{simplify}\kappa\mathrm{giving}\kappa\mathrm{your}\kappa\mathrm{answer}\kappa\mathrm{in}\kappa\mathrm{index}\kappa\mathrm{form} \\ $$$$\sqrt{\frac{\mathrm{ac}^{\mathrm{2}} }{\mathrm{9a}^{\mathrm{2}} \mathrm{c}^{\mathrm{4}} }} \\ $$ Commented by john santu last updated on 20/Apr/20…