Question Number 140749 by SOMEDAVONG last updated on 12/May/21 $$\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mathrm{5}^{\frac{\mathrm{1}}{\mathrm{k}}} \left(\mathrm{1}−\mathrm{5}^{−\frac{\mathrm{1}}{\mathrm{k}\left(\mathrm{k}+\mathrm{1}\right)}} \right)=? \\ $$ Answered by Dwaipayan Shikari last updated on 12/May/21 $$\mathrm{5}^{\frac{\mathrm{1}}{{k}}}…
Question Number 9678 by ridwan balatif last updated on 23/Dec/16 Commented by ridwan balatif last updated on 23/Dec/16 $$\mathrm{let}\:\mathrm{x}\:\:\mathrm{and}\:\mathrm{y}\:\mathrm{is}\:\mathrm{real}\:\mathrm{number}\:\mathrm{that}\:\mathrm{x}+\mathrm{y}=\mathrm{2}.\:\mathrm{If} \\ $$$$\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\sqrt{\mathrm{16}+\mathrm{3x}^{\mathrm{2}} }+\mathrm{2}\sqrt{\mathrm{73}+\mathrm{3y}^{\mathrm{2}} }=\mathrm{m} \\ $$$$\mathrm{find}\:\mathrm{value}\:\mathrm{of}\:\mathrm{m}^{\mathrm{2}}…
Question Number 140750 by SOMEDAVONG last updated on 12/May/21 $$\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\mathrm{cos}^{\mathrm{3}} \mathrm{k}=? \\ $$ Answered by Dwaipayan Shikari last updated on 12/May/21 $$\mathrm{4}{cos}^{\mathrm{3}} {k}−\mathrm{3}{cosk}={cos}\mathrm{3}{k}\Rightarrow{cos}^{\mathrm{3}}…
Question Number 9677 by ridwan balatif last updated on 23/Dec/16 Commented by geovane10math last updated on 23/Dec/16 $${An}\:{acute}\:{angle}\:{can}\:{not}\:{measure}\:\mathrm{129}° \\ $$$$\mathrm{51}°\:+\:\mathrm{78}°\:=\:\mathrm{129}° \\ $$ Commented by ridwan…
Question Number 9675 by ridwan balatif last updated on 23/Dec/16 Commented by ridwan balatif last updated on 23/Dec/16 $$\mathrm{please}\:\mathrm{someone}\:\mathrm{help}\:\mathrm{me}\:\mathrm{to}\:\mathrm{translate}\:\mathrm{this}\:\mathrm{question} \\ $$$$\mathrm{into}\:\mathrm{English}\:\mathrm{and}\:\mathrm{help}\:\mathrm{me}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{this}\:\mathrm{question} \\ $$ Commented by…
Question Number 140735 by ZiYangLee last updated on 12/May/21 $$\mathrm{Using}\:\mathrm{vector}\:\mathrm{method},\:\mathrm{prove}\:\mathrm{that}\:\mathrm{three} \\ $$$$\mathrm{median}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{are}\:\mathrm{concurrent}. \\ $$ Answered by MJS_new last updated on 12/May/21 $$\mathrm{let}\:{A}=\begin{pmatrix}{\mathrm{0}}\\{\mathrm{0}}\end{pmatrix}\:\wedge{B}=\begin{pmatrix}{{c}}\\{\mathrm{0}}\end{pmatrix}\:\wedge{C}=\begin{pmatrix}{{p}}\\{{h}}\end{pmatrix} \\ $$$${M}_{{a}} =\frac{{B}+{C}}{\mathrm{2}}=\begin{pmatrix}{\frac{{c}+{p}}{\mathrm{2}}}\\{\frac{{h}}{\mathrm{2}}}\end{pmatrix}\:\:\:\:\:{M}_{{b}}…
Question Number 75186 by Hassen_Timol last updated on 08/Dec/19 $$\mathrm{7}{n}\:\equiv\:\mathrm{1}\:\left(\mathrm{mod}\:\mathrm{5}\right) \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{general}\:\mathrm{form}\:\mathrm{of}\:{n}\:? \\ $$ Commented by mr W last updated on 08/Dec/19 $$\mathrm{7}{n}=\mathrm{5}{m}+\mathrm{1} \\ $$$$\Rightarrow{n}=\mathrm{5}{k}+\mathrm{3}…
Question Number 9648 by Chantria last updated on 22/Dec/16 Answered by sandy_suhendra last updated on 23/Dec/16 $$\mathrm{x}^{\mathrm{4}} +\mathrm{x}^{\mathrm{2}} −\mathrm{2x}+\mathrm{2}+\frac{\mathrm{3}}{\mathrm{x}^{\mathrm{2}} }\:>\:\mathrm{0} \\ $$$$\frac{\mathrm{x}^{\mathrm{6}} +\mathrm{x}^{\mathrm{4}} −\mathrm{2x}^{\mathrm{3}} +\mathrm{2x}^{\mathrm{2}}…
Question Number 140708 by mathocean1 last updated on 11/May/21 $$\mathrm{Given}\:\mathrm{an}\:\mathrm{Elipsis}\:\mathrm{in}\:\left(\mathrm{O};\overset{\rightarrow} {\mathrm{i}};\overset{\rightarrow} {\mathrm{j}}\right) \\ $$$$\left(\mathrm{E}\right):\:\frac{{x}^{\mathrm{2}} }{\mathrm{1}/\mathrm{4}}+\frac{{y}^{\mathrm{2}} }{\mathrm{1}}=\mathrm{1}.\: \\ $$$${W}\mathrm{e}\:\mathrm{admit}\:\mathrm{that}\:\mathrm{it}\:\mathrm{image}\:\mathrm{by}\:\mathrm{the}\:\mathrm{transformation}\: \\ $$$$\mathrm{f}\::\:\begin{cases}{{x}'=\sqrt{\mathrm{2}}\left({x}+{y}\right)}\\{{y}'=\sqrt{\mathrm{2}}\left(−{x}+{y}\right)\:}\end{cases} \\ $$$${is}\:{an}\:{elipsis}\:\left({E}'\right):\:\mathrm{5}{x}^{\mathrm{2}} +\mathrm{5}{y}^{\mathrm{2}} +\mathrm{6}{xy}−\mathrm{8}=\mathrm{0} \\…
Question Number 75173 by liki last updated on 08/Dec/19 Commented by liki last updated on 08/Dec/19 $$…{i}\:{need}\:{help}\:{plz} \\ $$ Answered by mind is power last…