Question Number 157283 by MathSh last updated on 21/Oct/21 Answered by TheHoneyCat last updated on 21/Oct/21 $$\mathrm{This}\:\mathrm{post}\:\mathrm{has}\:\mathrm{already}\:\mathrm{been}\:\mathrm{posted} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 26207 by pieroo last updated on 22/Dec/17 $$\mathrm{I}\:\mathrm{think}\:\mathrm{of}\:\mathrm{a}\:\mathrm{two}\:\mathrm{digit}\:\mathrm{number}.\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{is}\:\mathrm{9}. \\ $$$$\mathrm{When}\:\mathrm{the}\:\mathrm{number}\:\mathrm{is}\:\mathrm{reversed}\:\mathrm{and}\:\mathrm{subtracted}\:\mathrm{from}\:\mathrm{the} \\ $$$$\mathrm{original},\:\mathrm{the}\:\mathrm{result}\:\mathrm{is}\:\mathrm{45}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{original}\:\mathrm{number} \\ $$ Answered by peileng8802 last updated on 22/Dec/17 $$\mathrm{let}\:\mathrm{x}\:\mathrm{be}\:\mathrm{tens}\:\:\:\mathrm{y}\:\mathrm{be}\:\mathrm{ones} \\…
Question Number 91744 by ajfour last updated on 02/May/20 Commented by ajfour last updated on 02/May/20 $${If}\:\:{the}\:{red}\:{cubic}\:{curve}\:{has}\:{equation} \\ $$$$\:\boldsymbol{{y}}=\boldsymbol{{x}}^{\mathrm{3}} +\boldsymbol{{ax}}^{\mathrm{2}} +\boldsymbol{{bx}}+\boldsymbol{{c}}\:\:\:\:{while}\:{the} \\ $$$${blue}\:{one}\:{is}\:{the}\:{same}\:{red} \\ $$$${one},\:{shifted}\:{such}\:{that}\:{two}\:{roots}…
Question Number 157265 by MathSh last updated on 21/Oct/21 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\mathrm{sin}\left(\mathrm{x}\right)\:+\:\mathrm{cos}\left(\mathrm{x}\right)\:+\:\mathrm{sec}\left(\mathrm{x}\right)\centerdot\mathrm{csc}\left(\mathrm{x}\right)=\mathrm{2}+\sqrt{\mathrm{2}} \\ $$ Answered by TheSupreme last updated on 21/Oct/21 $${sin}\left({x}\right)+{cos}\left({x}\right)−\frac{\mathrm{1}}{{sin}\left({x}\right){cos}\left({x}\right)}={A} \\ $$$$\pm{s}\sqrt{\mathrm{1}−{s}^{\mathrm{2}} }−\left(\pm\frac{\mathrm{1}}{{s}\sqrt{\mathrm{1}−{s}^{\mathrm{2}}…
Question Number 91732 by I want to learn more last updated on 02/May/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{least}\:\mathrm{possible}\:\mathrm{value}\:\mathrm{of}\:\:\mathrm{x} \\ $$$$\:\:\:\:\mathrm{8x}\:\equiv\:\mathrm{24}\:\left(\mathrm{mod}\:\mathrm{16}\right)\:\:\:\:\:….\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\mathrm{3x}\:\equiv\:\mathrm{6}\:\left(\mathrm{mod}\:\mathrm{25}\right)\:\:\:\:\:\:….\:\left(\mathrm{ii}\right) \\ $$ Commented by mr W last…
Question Number 157258 by MathSh last updated on 21/Oct/21 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\frac{\mathrm{1}}{\mathrm{sin}^{\mathrm{2}\boldsymbol{\mathrm{k}}} \left(\mathrm{x}\right)}\:+\:\frac{\mathrm{1}}{\mathrm{cos}^{\mathrm{2}\boldsymbol{\mathrm{k}}} \left(\mathrm{x}\right)}\:=\:\mathrm{8}\:\:\:;\:\:\:\mathrm{k}\in\mathbb{Z} \\ $$ Commented by mr W last updated on 21/Oct/21 $$\left(\frac{\mathrm{1}}{\mathrm{sin}^{\mathrm{2}}…
Question Number 157231 by mnjuly1970 last updated on 21/Oct/21 $$ \\ $$$$\:\:\:\:\:\:\mathcal{SOLVE}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\lfloor\:{x}\:\rfloor\:+\:\lfloor\mathrm{2}{x}\:\rfloor\:+\lfloor\:\mathrm{3}{x}\:\rfloor=\:\mathrm{1} \\ $$$$−−−−−−−−−− \\ $$$$ \\ $$ Answered by Javokhir…
Question Number 91688 by s.ayeni14@yahoo.com last updated on 02/May/20 $${solve}\:{equations}\:{x}^{{x}\:} +\:{y}^{{y}} \:=\:\mathrm{31}\:{and}\:{x}\:+\:{y}\:=\:\mathrm{5} \\ $$ Commented by mr W last updated on 02/May/20 $${i}\:{think}\:{you}\:{know}\:{by}\:{yourself}\:{x}=\mathrm{2},\:{y}=\mathrm{3} \\ $$$${since}\:\mathrm{2}^{\mathrm{2}}…
Question Number 26153 by bbbbbb last updated on 21/Dec/17 $${ratio}\:{of}\:{income}\:{of}\:{two}\:{persons}\:{is} \\ $$$$\mathrm{9}\:{is}\:{to}\:\mathrm{7}.{ratio}\:{of}\:{their}\:{expenses} \\ $$$${is}\:\mathrm{4}\:{is}\:{to}\:\mathrm{3}\:.{every}\:{person}\:{saves}\: \\ $$$${rupees}\:\mathrm{200}.\:{find}\:{income}\:{of}\:{each}. \\ $$ Answered by ajfour last updated on 21/Dec/17…
Question Number 157222 by amin96 last updated on 21/Oct/21 Answered by Dimitri_01 last updated on 21/Oct/21 $$\mathrm{A}=\underset{{n}=\mathrm{1}} {\overset{\mathrm{25}} {\sum}}\frac{\mathrm{1}}{{n}\left({n}+\mathrm{100}\right)}=\frac{\mathrm{1}}{\mathrm{100}}\underset{{n}=\mathrm{1}} {\overset{\mathrm{25}} {\sum}}\frac{\left({n}+\mathrm{100}\right)−{n}}{{n}\left({n}+\mathrm{100}\right)} \\ $$$$\:\:\:\:=\frac{\mathrm{1}}{\mathrm{100}}\underset{{n}=\mathrm{1}} {\overset{\mathrm{25}} {\sum}}\left(\frac{\mathrm{1}}{{n}}−\frac{\mathrm{1}}{{n}+\mathrm{100}}\right)=\frac{\mathrm{1}}{\mathrm{100}}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{101}}+\frac{\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{102}}+\frac{\mathrm{1}}{\mathrm{3}}−\frac{\mathrm{1}}{\mathrm{103}}+\centerdot\centerdot\centerdot+\frac{\mathrm{1}}{\mathrm{25}}−\frac{\mathrm{1}}{\mathrm{125}}\right)…