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Author: Tinku Tara

x-cos-sin-y-sin-cos-z-sin-r-x-e-x-y-e-y-z-e-z-r-r-r-

Question Number 4922 by 123456 last updated on 22/Mar/16 $$\begin{cases}{{x}\left(\rho,\theta,\psi\right)=\rho\:\mathrm{cos}\:\theta+\psi\:\mathrm{sin}\:\theta}\\{{y}\left(\rho,\theta,\psi\right)=\rho\:\mathrm{sin}\:\theta+\psi\:\mathrm{cos}\:\theta}\\{{z}\left(\rho,\theta,\psi\right)=\psi\:\mathrm{sin}\:\theta}\end{cases} \\ $$$$\boldsymbol{{r}}\left(\rho,\theta,\psi\right)={x}\left(\rho,\theta,\psi\right)\:\boldsymbol{{e}}_{{x}} +{y}\left(\rho,\theta,\psi\right)\:\boldsymbol{{e}}_{{y}} +{z}\left(\rho,\theta,\psi\right)\:\boldsymbol{{e}}_{{z}} \\ $$$$\frac{\partial\boldsymbol{{r}}}{\partial\rho}=? \\ $$$$\frac{\partial\boldsymbol{{r}}}{\partial\theta}=? \\ $$$$\frac{\partial\boldsymbol{{r}}}{\partial\psi}=? \\ $$ Commented by prakash…

Hey-guys-A-new-graphing-app-is-out-called-Desmos-It-is-really-amazing-Just-thought-I-d-let-you-know-

Question Number 4918 by FilupSmith last updated on 21/Mar/16 $$\mathrm{Hey}\:\mathrm{guys}!\:{A}\:\mathrm{new}\:\mathrm{graphing}\:\mathrm{app}\:\mathrm{is}\:\mathrm{out} \\ $$$$\mathrm{called}\:{Desmos} \\ $$$$ \\ $$$$\mathrm{It}\:\mathrm{is}\:\mathrm{really}\:\mathrm{amazing}! \\ $$$$ \\ $$$$\mathrm{Just}\:\mathrm{thought}\:\mathrm{I}'{d}\:\mathrm{let}\:\mathrm{you}\:\mathrm{know}! \\ $$ Commented by Yozzii…

Question-70452

Question Number 70452 by ajfour last updated on 04/Oct/19 Commented by ajfour last updated on 04/Oct/19 $${ABCD}\:{is}\:{a}\:{square}.\:{Find}\:{minimum} \\ $$$${side}\:{length}\:\boldsymbol{{s}}\:{of}\:{equilateral}\:\bigtriangleup{DEF} \\ $$$${in}\:{terms}\:{of}\:{quarter}\:{circle}\:{radii} \\ $$$${a}\:{and}\:{b}.\:{Also}\:{find}\:{range}\:{of}\: \\ $$$$\:\frac{{a}}{{b}}\:{so}\:{that}\:{such}\:{an}\:{equilateral}…

find-the-lowest-number-between-200-and-500-which-leaves-a-remainder-of-3-in-each-case-which-will-divisible-by-8-10-12-and-30-

Question Number 135990 by zakirullah last updated on 17/Mar/21 $$\:\:\:\:\:\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{lowest}}\:\boldsymbol{{number}}\:\boldsymbol{{between}}\:\mathrm{200}\:\boldsymbol{{and}}\:\mathrm{500}\:\boldsymbol{{which}} \\ $$$$\:\:\:\:\:\boldsymbol{{leaves}}\:\boldsymbol{{a}}\:\boldsymbol{{remainder}}\:\boldsymbol{{of}}\:\mathrm{3}\:\boldsymbol{{in}}\:\boldsymbol{{each}}\:\boldsymbol{{case}} \\ $$$$\:\:\:\:\boldsymbol{{which}}\:\boldsymbol{{will}}\:\boldsymbol{{divisible}}\:\boldsymbol{{by}}\:\mathrm{8}\:,\:\mathrm{10},\:\mathrm{12}\:\boldsymbol{{and}}\:\mathrm{30}? \\ $$ Answered by Olaf last updated on 17/Mar/21 $$\mathrm{N}\:=\:\mathrm{8}{k}+\mathrm{3}\:=\:\mathrm{10}{l}+\mathrm{3}\:=\:\mathrm{12}{m}+\mathrm{3}\:=\:\mathrm{30}{n}+\mathrm{3} \\…

I-e-sinx-xcos-2-x-sinx-cos-2-x-dx-

Question Number 135986 by SOMEDAVONG last updated on 17/Mar/21 $$\mathrm{I}=\int\mathrm{e}^{\mathrm{sinx}} \left(\frac{\mathrm{xcos}^{\mathrm{2}} \mathrm{x}−\mathrm{sinx}}{\mathrm{cos}^{\mathrm{2}} \mathrm{x}}\right)\mathrm{dx} \\ $$ Answered by Olaf last updated on 17/Mar/21 $$\mathrm{I}\:=\:\int{xe}^{\mathrm{sin}{x}} {dx}−\int{e}^{\mathrm{sin}{x}} \left(\frac{\mathrm{sin}{x}}{\mathrm{cos}^{\mathrm{2}}…

Prove-that-lim-n-n-n-0-Where-1-5-2-x-is-the-floor-function-

Question Number 4911 by FilupSmith last updated on 21/Mar/16 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\emptyset^{{n}} −\lfloor\phi^{{n}} \rfloor\right)=\mathrm{0} \\ $$$$ \\ $$$$\mathrm{Where}:\:\:\:\:\:\:\:\phi\:=\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\lfloor{x}\rfloor\:\mathrm{is}\:\mathrm{the}\:\mathrm{floor}\:\mathrm{function} \\ $$ Commented by…