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The-possible-value-of-x-that-satisfy-x-2-x-2-2x-x-2-2x-1-2017-x-R-and-x-2-2x-

Question Number 56719 by naka3546 last updated on 22/Mar/19 $${The}\:\:{possible}\:\:{value}\:\:{of}\:\:{x}\:\:{that}\:\:{satisfy}\:\:: \\ $$$$\:\:\:\:\:\:\:\:{x}^{\mathrm{2}} \:+\:\lfloor{x}^{\mathrm{2}} \:−\:\mathrm{2}{x}\rfloor\:+\:\lceil{x}^{\mathrm{2}} \:+\:\mathrm{2}{x}\:+\:\mathrm{1}\rceil\:\:=\:\:\mathrm{2017}\:\:,\:\:{x}\:\in\:\:\mathbb{R}^{+} \\ $$$${and}\:\:\:\lfloor{x}^{\mathrm{2}} \rfloor\:−\:\lceil\mathrm{2}{x}\rceil\:\:=\:\:… \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated…

Did-you-say-no-1-Yes-2-No-

Question Number 122244 by Olaf last updated on 15/Nov/20 $$\mathrm{Did}\:\mathrm{you}\:\mathrm{say}\:\mathrm{no}\:? \\ $$$$\mathrm{1}\:−\mathrm{Yes}. \\ $$$$\mathrm{2}\:−\:\mathrm{No}. \\ $$ Commented by Dwaipayan Shikari last updated on 15/Nov/20 $${I}\:{am}\:{in}\:{a}\:\boldsymbol{{Superposition}},\:\boldsymbol{{of}}\:\boldsymbol{{nothing}}…

A-tv-set-was-marked-for-sale-at-760-00-cedis-in-order-to-make-a-profit-of-20-The-tv-was-actually-sold-at-a-discount-of-5-Calculate-to-2-s-f-the-actual-percentage-profit-

Question Number 56694 by otchereabdullai@gmail.com last updated on 21/Mar/19 $$\mathrm{A}\:\mathrm{tv}\:\mathrm{set}\:\mathrm{was}\:\mathrm{marked}\:\mathrm{for}\:\mathrm{sale}\:\mathrm{at}\:\mathrm{760}.\mathrm{00} \\ $$$$\mathrm{cedis}\:\mathrm{in}\:\mathrm{order}\:\mathrm{to}\:\mathrm{make}\:\mathrm{a}\:\mathrm{profit}\:\mathrm{of}\:\mathrm{20\%}. \\ $$$$\mathrm{The}\:\mathrm{tv}\:\mathrm{was}\:\mathrm{actually}\:\mathrm{sold}\:\mathrm{at}\:\mathrm{a}\:\mathrm{discount}\: \\ $$$$\mathrm{of}\:\mathrm{5\%}.\:\mathrm{Calculate}\:\mathrm{to}\:\mathrm{2}\:\mathrm{s}.\mathrm{f}\:\mathrm{the}\:\mathrm{actual}\: \\ $$$$\mathrm{percentage}\:\mathrm{profit} \\ $$ Answered by mr W last…

Question-122216

Question Number 122216 by help last updated on 14/Nov/20 Answered by liberty last updated on 14/Nov/20 $$\:\ell\mathrm{n}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{arc}\:\mathrm{sin}\:\mathrm{4x}\: \\ $$$$\:\frac{\mathrm{f}\:'\left(\mathrm{x}\right)}{\mathrm{f}\left(\mathrm{x}\right)}\:=\:\frac{\mathrm{4}}{\:\sqrt{\mathrm{1}+\mathrm{16x}^{\mathrm{2}} }}\:\Rightarrow\:\mathrm{f}\:'\left(\mathrm{x}\right)=\:\frac{\mathrm{4e}^{\mathrm{arc}\:\mathrm{sin}\:\mathrm{4x}} }{\:\sqrt{\mathrm{1}+\mathrm{16x}^{\mathrm{2}} }} \\ $$$$\:\mathrm{f}\:'\left(\frac{\mathrm{1}}{\mathrm{8}}\right)\:=\:\frac{\mathrm{4e}^{\frac{\pi}{\mathrm{6}}} }{\:\sqrt{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{4}}}}\:=\:\frac{\mathrm{8e}^{\frac{\pi}{\mathrm{6}}}…

Question-187754

Question Number 187754 by 073 last updated on 21/Feb/23 Answered by horsebrand11 last updated on 21/Feb/23 $$\:{let}\:{f}\left({x}\right)={ax}+{b} \\ $$$$\:{f}\left(\mathrm{3}{x}+\mathrm{1}\right)=\mathrm{3}{ax}+{a}+{b} \\ $$$$\:{f}\left({x}−\mathrm{2}\right)={ax}−\mathrm{2}{a}+{b} \\ $$$$\:{f}\left(\mathrm{3}{x}+\mathrm{1}\right)+{f}\left({x}−\mathrm{2}\right)=\mathrm{4}{ax}−{a}+\mathrm{2}{b}=\mathrm{10}{x} \\ $$$$\:\begin{cases}{\mathrm{4}{a}=\mathrm{10}\Rightarrow{a}=\frac{\mathrm{5}}{\mathrm{2}}}\\{−{a}+\mathrm{2}{b}=\mathrm{0}\Rightarrow{b}=\frac{\mathrm{5}}{\mathrm{4}}}\end{cases}…

Question-122203

Question Number 122203 by help last updated on 14/Nov/20 Commented by Dwaipayan Shikari last updated on 14/Nov/20 $${K}^{\mathrm{2}} {x}+\mathrm{8}{y}=\mathrm{30} \\ $$$${Kx}+\mathrm{8}{y}=\mathrm{10} \\ $$$${x}\left({K}^{\mathrm{2}} −{K}\right)=\mathrm{20}\Rightarrow{K}^{\mathrm{2}} =\frac{\mathrm{20}}{{x}}+{K}…