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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…

Question-135976

Question Number 135976 by I want to learn more last updated on 17/Mar/21 Answered by mr W last updated on 17/Mar/21 $$\frac{{x}}{\mathrm{sin}\:\mathrm{90}°}=\frac{\mathrm{2}}{\mathrm{sin}\:\angle{ADC}}\:\:\:\:…\left({i}\right) \\ $$$$\frac{\mathrm{sin}\:\mathrm{30}°}{\mathrm{3}}=\frac{\mathrm{sin}\:\angle{BDC}}{{y}}\:\:\:…\left({ii}\right) \\…

f-x-0-is-a-even-function-or-a-odd-function-

Question Number 4905 by 123456 last updated on 20/Mar/16 $${f}\left({x}\right)=\mathrm{0}\:\mathrm{is}\:\mathrm{a}\:\mathrm{even}\:\mathrm{function}\:\mathrm{or}\:\mathrm{a}\:\mathrm{odd}\:\mathrm{function}? \\ $$ Commented by Yozzii last updated on 20/Mar/16 $${This}\:{is}\:{indeterminate}\:{I}\:{think}\:{since}\:{f}\left({x}\right)=\mathrm{0} \\ $$$${satisfies}\:{both}\:{f}\left({x}\right)=−{f}\left({x}\right)=\mathrm{0} \\ $$$${and}\:{f}\left(−{x}\right)=\mathrm{0}={f}\left({x}\right). \\…

Determine-the-smallest-natural-value-of-n-so-the-function-y-5x-sin-5nx-will-be-even-

Question Number 4904 by love math last updated on 20/Mar/16 $${Determine}\:{the}\:{smallest}\:{natural} \\ $$$${value}\:{of}\:{n},\:{so}\:{the}\:{function}\: \\ $$$${y}=\:\mathrm{5}{x}\:{sin}\:\mathrm{5}{nx}\:{will}\:{be}\:{even}. \\ $$ Commented by Yozzii last updated on 20/Mar/16 $${y}\left(−{x}\right)=\mathrm{5}\left(−{x}\right){sin}\left(−\mathrm{5}{nx}\right)…