Question Number 129242 by Adel last updated on 14/Jan/21 $$\mathrm{cot}^{\mathrm{2}} \frac{\pi}{\mathrm{7}}+\mathrm{cot}^{\mathrm{2}} \frac{\mathrm{2}\pi}{\mathrm{7}}+\mathrm{cot}^{\mathrm{2}} \frac{\mathrm{7}\pi}{\mathrm{2}}=? \\ $$$$\mathrm{answer}\:\:\mathrm{by}\:\mathrm{solve} \\ $$ Commented by liberty last updated on 14/Jan/21 $$\mathrm{qn}\:\mathrm{128582}…
Question Number 63636 by naka3546 last updated on 06/Jul/19 $${Find}\:\:{all}\:\:{solutions}\:\:{of}\:\:\left({x},\:{y},\:{a},\:{b}\right)\:\:{for}\:\:{these}\:\:{equations}\:: \\ $$$$\:\:\:\:\:\:\:\:{x}\:+\:{y}^{\mathrm{2}} \:\:=\:\:{p}^{{a}} \\ $$$$\:\:\:\:\:\:\:\:{x}^{\mathrm{2}} \:+\:{y}\:\:=\:\:{p}^{{b}} \\ $$$${which}\:\:\:{x},\:{y},\:{a},\:{b}\:\:{are}\:\:{integers}\:\:{and}\:\:{p}\:\:{prime}\:\:{number}\:. \\ $$ Terms of Service Privacy Policy…
Question Number 129147 by Adel last updated on 13/Jan/21 $$\mathrm{cot}^{\mathrm{2}} \boldsymbol{\pi}/\mathrm{7}+\mathrm{cot}^{\mathrm{2}} \mathrm{2}\boldsymbol{\pi}/\mathrm{7}+\mathrm{cot}^{\mathrm{2}} \mathrm{3}\boldsymbol{\pi}/\mathrm{7}=? \\ $$ Commented by benjo_mathlover last updated on 13/Jan/21 $$\:\mathrm{ans}\::\:\mathrm{5} \\ $$…
Question Number 129130 by bounhome last updated on 13/Jan/21 $${solve}\:: \\ $$$$\:\:{y}''+\mathrm{4}{y}={cos}\mathrm{2}{x} \\ $$$$\: \\ $$ Answered by liberty last updated on 13/Jan/21 $$\:\mathrm{Homogenous}\:\mathrm{solution}\:\mathrm{y}_{\mathrm{h}} =\mathrm{C}_{\mathrm{1}}…
Question Number 129129 by Adel last updated on 13/Jan/21 Commented by MJS_new last updated on 13/Jan/21 $$\mathrm{I}\:\mathrm{think}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{is}\:\frac{\mathrm{1}}{\mathrm{e}}\:\mathrm{but}\:\mathrm{I}\:\mathrm{cannot}\:\mathrm{yet}\:\mathrm{show}\:\mathrm{it} \\ $$ Commented by Adel last updated on…
Question Number 129098 by Adel last updated on 12/Jan/21 Answered by liberty last updated on 12/Jan/21 $$\mathrm{let}\:\mathrm{x}−\mathrm{1}=\mathrm{t} \\ $$$$\:\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2}\sqrt{\mathrm{1}+\mathrm{t}}\:−\mathrm{sin}\:\mathrm{t}−\mathrm{2cos}\:\mathrm{t}}{\mathrm{arctan}\:\mathrm{t}−\mathrm{ln}\:\left(\mathrm{1}+\mathrm{t}\right)}\:= \\ $$$$\:\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{2}\left(\mathrm{1}+\frac{\mathrm{t}}{\mathrm{2}}−\frac{\mathrm{t}^{\mathrm{2}} }{\mathrm{2}}\right)−\left(\mathrm{t}−\frac{\mathrm{t}^{\mathrm{3}} }{\mathrm{6}}\right)−\mathrm{2}\left(\mathrm{1}−\frac{\mathrm{t}^{\mathrm{2}}…
Question Number 129094 by Adel last updated on 12/Jan/21 $$\mathrm{p}\left(\boldsymbol{\mathrm{x}}\right)+\boldsymbol{\mathrm{p}}\left(\boldsymbol{\mathrm{x}}+\mathrm{2}\right)=\mathrm{2}\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{2}\boldsymbol{\mathrm{x}}+\mathrm{4}\:\:\:\:\:\:\:\boldsymbol{\mathrm{p}}\left(\boldsymbol{\mathrm{x}}\right)=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 129090 by Adel last updated on 12/Jan/21 $$\mathrm{p}\left(\mathrm{x}\right)+\mathrm{p}\left(\mathrm{x}+\mathrm{2}\right)=\mathrm{2X}^{\mathrm{2}} +\mathrm{2X}+\mathrm{4}\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{p}}\left(\boldsymbol{\mathrm{x}}\right)=? \\ $$ Answered by MJS_new last updated on 12/Jan/21 $${p}\left({x}\right)={ax}^{\mathrm{2}} +{bx}+{c} \\ $$$${p}\left({x}+\mathrm{2}\right)={ax}^{\mathrm{2}} +\left(\mathrm{4}{a}+{b}\right){x}+\left(\mathrm{4}{a}+\mathrm{2}{b}+{c}\right)…
Question Number 129087 by Adel last updated on 12/Jan/21 Answered by MJS_new last updated on 12/Jan/21 $$\mathrm{2}^{\mathrm{10}} \mathrm{10}!\left(\mathrm{1}×\mathrm{3}×\mathrm{5}×\mathrm{7}×\mathrm{9}×\mathrm{11}×\mathrm{13}×\mathrm{15}×\mathrm{17}×\mathrm{19}\right)= \\ $$$$=\mathrm{10}!×\mathrm{11}×\left(\mathrm{3}×\mathrm{2}^{\mathrm{2}} \right)×\mathrm{13}×\left(\mathrm{7}×\mathrm{2}\right)×\mathrm{15}×\left(\mathrm{2}^{\mathrm{4}} \right)×\mathrm{17}×\left(\mathrm{9}×\mathrm{2}\right)×\mathrm{19}×\left(\mathrm{5}×\mathrm{2}^{\mathrm{2}} \right)= \\ $$$$=\mathrm{20}!…
Question Number 63536 by Rio Michael last updated on 05/Jul/19 $$\left.{a}\right)\:\:{if}\:{y}=\:{x}^{{m}} \left(\mathrm{1}−{x}\right)^{{n}} ,\:{where}\:{n}\in\:\mathbb{Z}^{+} ,\:{the}\:{set}\:{of}\:{positive}\:{integers}, \\ $$$${show}\:{that}\:{when}\:\frac{{dy}}{{dx}}=\mathrm{0},\:{x}=\frac{{m}}{{m}+{n}} \\ $$$$\left.{b}\right){if}\:{y}\:=\:\mathrm{2}\left({x}−\mathrm{5}\right)\sqrt{{x}+\mathrm{4}}\:,{show}\:{that}\:\frac{{dy}}{{dx}}\:=\:\frac{\mathrm{3}\left({x}+\mathrm{1}\right)}{\:\sqrt{{x}+\mathrm{4}}\:} \\ $$$$\left.{c}\right)\:{solve}\:{the}\:{equation}\:\:{sinx}−{sin}\mathrm{5}{x}+{cos}\mathrm{3}{x}\:=\:\mathrm{0}\:{for}\:\:\mathrm{0}°\leqslant{x}\leqslant\mathrm{180}° \\ $$ Commented by Prithwish…