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Prove-that-among-all-triangles-which-have-same-circum-radius-the-equilateral-triangle-has-maximum-area-

Question Number 5822 by Rasheed Soomro last updated on 30/May/16 $$\mathcal{P}{rove}\:{that}\:{among}\:{all}\:\boldsymbol{{triangles}}, \\ $$$${which}\:{have}\:{same}\:\boldsymbol{{circum}}-\boldsymbol{{radius}}, \\ $$$${the}\:\boldsymbol{{equilateral}}\:\boldsymbol{{triangle}}\:{has} \\ $$$$\boldsymbol{{maximum}}\:\boldsymbol{{area}}. \\ $$ Terms of Service Privacy Policy Contact:…

L-lim-x-0-x-x-

Question Number 5821 by FilupSmith last updated on 30/May/16 $${L}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:{x}^{{x}} \\ $$ Answered by bahmanfeshki last updated on 27/Feb/17 $$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:{e}^{{x}\mathrm{ln}\:{x}} =\underset{{x}\rightarrow\mathrm{0}^{+} }…

Prove-that-among-all-cyclic-n-gons-which-have-same-radius-regular-n-gon-has-maximum-area-

Question Number 5816 by Rasheed Soomro last updated on 29/May/16 $$\mathcal{P}{rove}\:{that}\:{among}\:{all}\:{cyclic}\:\:{n}-{gons},\: \\ $$$${which}\:{have}\:{same}\:{radius},\:{regular}\:{n}-{gon} \\ $$$${has}\:{maximum}\:{area}. \\ $$ Commented by Yozzii last updated on 29/May/16 $${Is}\:{induction}\:{possible}\:{for}\:{n}\geqslant\mathrm{3}?…

Question-136885

Question Number 136885 by BHOOPENDRA last updated on 27/Mar/21 Answered by bramlexs22 last updated on 27/Mar/21 $$\lambda^{\mathrm{3}} −\left(\mathrm{trace}\:\mathrm{A}\right)\lambda^{\mathrm{2}} +\:\begin{pmatrix}{\mathrm{minor}\:\mathrm{of}\:\mathrm{the}\:\mathrm{terms}}\\{\mathrm{on}\:\mathrm{the}\:\mathrm{leading}\:\mathrm{diag}\:\mathrm{A}\:}\end{pmatrix}\lambda−\mathrm{det}\left(\mathrm{A}\right)=\mathrm{0} \\ $$$$\lambda^{\mathrm{3}} −\mathrm{3}\lambda^{\mathrm{2}} +\left(\begin{vmatrix}{\mathrm{1}\:\:\mathrm{2}}\\{\mathrm{2}\:\:\mathrm{1}}\end{vmatrix}+\begin{vmatrix}{\mathrm{1}\:\:\:\mathrm{0}}\\{\mathrm{1}\:\:\:\mathrm{1}}\end{vmatrix}+\begin{vmatrix}{\:\:\mathrm{1}\:\:\:\:\:\mathrm{2}}\\{−\mathrm{1}\:\:\:\mathrm{1}}\end{vmatrix}\right)\lambda−\mathrm{3}\:=\mathrm{0} \\ $$$$\lambda^{\mathrm{3}}…

Given-log-5-7-a-2-log-7-5-a-2-Find-the-value-a-e-1-ln-x-x-x-x-x-dx-

Question Number 136883 by bramlexs22 last updated on 27/Mar/21 $$\mathrm{Given}\:\mathrm{log}\:_{\mathrm{5}} \left(\mathrm{7}^{{a}} −\mathrm{2}\right)=\:\mathrm{log}\:_{\mathrm{7}} \left(\mathrm{5}^{{a}} +\mathrm{2}\right) \\ $$$$.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\int_{{a}} ^{\mathrm{e}} \:\frac{\mathrm{1}+\mathrm{ln}\:\left(\mathrm{x}\right)}{\mathrm{x}^{\mathrm{x}} +\mathrm{x}^{−\mathrm{x}} }\:\mathrm{dx}\:. \\ $$ Answered by Olaf…

Town-A-is-36-kilometers-from-town-B-Two-persons-start-to-travel-at-the-same-time-one-from-A-to-B-and-other-from-B-to-A-After-meeting-in-a-way-the-first-person-covers-the-remaining-distance-in-2

Question Number 5807 by Rasheed Soomro last updated on 28/May/16 $$\mathcal{T}{own}\:\boldsymbol{\mathrm{A}}\:\:{is}\:\:\mathrm{36}\:{kilometers}\:{from}\: \\ $$$${town}\:\boldsymbol{\mathrm{B}}.\:\:{Two}\:{persons}\:{start}\:{to}\:{travel} \\ $$$${at}\:{the}\:{same}\:{time},\:{one}\:{from}\:\boldsymbol{\mathrm{A}}\:{to}\:\boldsymbol{\mathrm{B}} \\ $$$${and}\:{other}\:{from}\:\boldsymbol{\mathrm{B}}\:{to}\:\boldsymbol{\mathrm{A}}.\:{After}\:{meeting} \\ $$$${in}\:{a}\:{way}\:{the}\:{first}\:{person}\:{covers}\:{the} \\ $$$${remaining}\:{distance}\:{in}\:\mathrm{2}\:{hours}\:{and} \\ $$$${the}\:{second}\:\:{in}\:\mathrm{8}\:{hours}.\:{Determine}\:{their} \\ $$$${speed}.\:\:\:\:\:\left(\mathrm{From}\:\mathrm{a}\:\mathrm{book}\right)…