Question Number 75849 by behi83417@gmail.com last updated on 18/Dec/19 $$\boldsymbol{\mathrm{In}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{A}}\overset{\bigtriangleup} {\boldsymbol{\mathrm{B}C}}: \\ $$$$\begin{cases}{\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{b}}+\boldsymbol{\mathrm{c}}=\mathrm{2}\left(\boldsymbol{\mathrm{h}}_{\boldsymbol{\mathrm{a}}} +\boldsymbol{\mathrm{h}}_{\boldsymbol{\mathrm{b}}} +\boldsymbol{\mathrm{h}}_{\boldsymbol{\mathrm{c}}} \right)}\\{\boldsymbol{\mathrm{a}}^{\mathrm{2}} +\boldsymbol{\mathrm{b}}^{\mathrm{2}} +\boldsymbol{\mathrm{c}}^{\mathrm{2}} =\mathrm{6}\boldsymbol{\mathrm{abc}}}\\{\boldsymbol{\mathrm{h}}_{\boldsymbol{\mathrm{a}}} ^{\mathrm{2}} +\boldsymbol{\mathrm{h}}_{\boldsymbol{\mathrm{b}}} ^{\mathrm{2}} +\boldsymbol{\mathrm{h}}_{\boldsymbol{\mathrm{c}}} ^{\mathrm{2}} =\mathrm{6}\boldsymbol{\mathrm{h}}_{\boldsymbol{\mathrm{a}}}…
Question Number 141381 by loveineq last updated on 19/May/21 $$\mathrm{Let}\:\:{a},{b}\:\geqslant\:\mathrm{0}\:.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left({a}+{b}+\mathrm{2}\right)^{\mathrm{3}} \:\geqslant\:\frac{\mathrm{27}}{\mathrm{2}}\left({a}^{\mathrm{2}} +{ab}+{b}^{\mathrm{2}} \right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 75846 by behi83417@gmail.com last updated on 18/Dec/19 $$\boldsymbol{\mathrm{sin}}^{\mathrm{5}} \boldsymbol{\mathrm{x}}+\sqrt{\mathrm{2}}\boldsymbol{\mathrm{sinx}}=\mathrm{1}\:\:\:\:\:\:\:\:,\:\:\boldsymbol{\mathrm{x}}\in\left[\mathrm{0},\mathrm{2}\boldsymbol{\pi}\right] \\ $$ Answered by MJS last updated on 18/Dec/19 $${t}=\mathrm{sin}\:{x} \\ $$$${t}^{\mathrm{5}} +\sqrt{\mathrm{2}}{t}−\mathrm{1}=\mathrm{0} \\…
Question Number 141380 by BHOOPENDRA last updated on 18/May/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 75847 by behi83417@gmail.com last updated on 18/Dec/19 $$\begin{cases}{\frac{\boldsymbol{\mathrm{tgx}}−\boldsymbol{\mathrm{tgy}}}{\mathrm{1}−\boldsymbol{\mathrm{tgx}}.\boldsymbol{\mathrm{tgy}}}=\boldsymbol{\mathrm{tg}}\frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}}\\{\:\:\frac{\boldsymbol{\mathrm{tgx}}+\boldsymbol{\mathrm{tgy}}}{\mathrm{1}+\boldsymbol{\mathrm{tgxtgy}}}=\boldsymbol{\mathrm{tg}}\frac{\boldsymbol{\mathrm{y}}}{\mathrm{2}}}\end{cases} \\ $$ Commented by MJS last updated on 19/Dec/19 $$\mathrm{the}\:\mathrm{path}\:\mathrm{is} \\ $$$$\mathrm{let}\:{x}=\mathrm{2arctan}\:{p};\:{y}=\mathrm{2arctan}\:{q} \\ $$$$\Rightarrow \\…
Question Number 141383 by Willson last updated on 18/May/21 $$\mathrm{sin}^{\mathrm{2}} \left(\frac{\mathrm{f}\left(\mathrm{x}\right)}{\mathrm{2}}\right)=\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} } \\ $$$$\mathrm{find}\:\mathrm{f}\left(\mathrm{x}\right) \\ $$ Answered by mr W last updated on 18/May/21 $$\mathrm{sin}^{\mathrm{2}}…
Question Number 10309 by Tawakalitu ayo mi last updated on 03/Feb/17 $$\mathrm{An}\:\mathrm{helium}\:\mathrm{atom}\:\mathrm{has}\:\mathrm{a}\:\mathrm{mass}\:\mathrm{of}\:\mathrm{6}.\mathrm{64}×\mathrm{10}^{−\mathrm{27}} \mathrm{kg} \\ $$$$\mathrm{and}\:\mathrm{a}\:\mathrm{charge}\:\mathrm{Q}\:\mathrm{is}\:+\mathrm{2}\:\mathrm{electron}.\:\mathrm{Compare}\:\mathrm{the} \\ $$$$\mathrm{magnitude}\:\mathrm{of}\:\mathrm{the}\:\mathrm{electric}\:\mathrm{repultion}\:\mathrm{to}\:\mathrm{that} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{gravitational}\:\mathrm{attraction}\:\mathrm{between}\:\mathrm{them}. \\ $$ Terms of Service Privacy…
Question Number 75845 by behi83417@gmail.com last updated on 18/Dec/19 $$\begin{cases}{\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{yz}}=\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\\{\boldsymbol{\mathrm{y}}+\boldsymbol{\mathrm{xz}}=\boldsymbol{\mathrm{y}}^{\mathrm{2}} }\\{\boldsymbol{\mathrm{z}}+\boldsymbol{\mathrm{xy}}=\boldsymbol{\mathrm{z}}^{\mathrm{2}} }\end{cases}\:\:\:\:\:\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{x}},\boldsymbol{\mathrm{y}},\boldsymbol{\mathrm{z}}. \\ $$ Commented by mr W last updated on 18/Dec/19 $${x}={y}={z}=\mathrm{0} \\…
Question Number 141378 by mnjuly1970 last updated on 18/May/21 $$\:\:\:{prove}\:{that}:: \\ $$$$\:\:\:\:\:\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\prod}}\frac{\left(\mathrm{5}{n}+\mathrm{2}\right)\left(\mathrm{5}{n}+\mathrm{3}\right)}{\left(\mathrm{5}{n}+\mathrm{1}\right)\left(\mathrm{5}{n}+\mathrm{4}\right)}\:=\varphi\: \\ $$$$\:\:\:\:\:\:\:\varphi:=\:\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}} \\ $$ Answered by Dwaipayan Shikari last updated on…
Question Number 141373 by SLVR last updated on 18/May/21 Commented by SLVR last updated on 18/May/21 $${kindly}\:{help}\:{me} \\ $$ Answered by mathmax by abdo last…