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Mike-and-Stev-had-620-bucks-each-to-spend-Mike-used-all-his-money-to-buy-3pens-and-4books-while-Stev-bought-4pens-and-3books-and-had-a-balance-of-50-bucks-Find-the-cost-of-a-pen-and-book-

Question Number 40057 by Rio Mike last updated on 15/Jul/18 $${Mike}\:{and}\:{Stev}\:{had}\:\mathrm{620}\:{bucks} \\ $$$${each}\:{to}\:{spend}\:.\:{Mike}\:{used}\:{all} \\ $$$${his}\:{money}\:{to}\:{buy}\:\mathrm{3}{pens}\:{and}\: \\ $$$$\mathrm{4}{books},{while}\:{Stev}\:{bought}\: \\ $$$$\mathrm{4}{pens}\:{and}\:\mathrm{3}{books}\:{and}\:{had}\:{a} \\ $$$${balance}\:{of}\:\mathrm{50}\:{bucks}.{Find} \\ $$$${the}\:{cost}\:{of}\:{a}\:{pen}\:{and}\:{book}. \\ $$$$…

A-boy-starts-from-a-point-A-and-moves-on-a-bearing-of-20-to-a-point-B-which-is-5km-from-A-He-then-changes-his-course-to-a-bearing-of-11-and-moves-to-a-point-C-which-is-12km-from-B-Find-the-distanc

Question Number 40055 by Rio Mike last updated on 15/Jul/18 $${A}\:{boy}\:{starts}\:{from}\:{a}\:{point}\:{A} \\ $$$${and}\:{moves}\:{on}\:{a}\:{bearing}\:{of} \\ $$$$\mathrm{20}°\:{to}\:{a}\:{point}\:{B}\:{which}\:{is} \\ $$$$\mathrm{5}{km}\:{from}\:{A}.{He}\:{then}\:{changes} \\ $$$${his}\:{course}\:{to}\:{a}\:{bearing}\:{of}\: \\ $$$$\mathrm{11}°\:{and}\:{moves}\:{to}\:{a}\:{point}\:{C}\:{which}\:{is} \\ $$$$\mathrm{12}{km}\:{from}\:{B}. \\ $$$${Find}\:{the}\:{distance}\:{and}\:{bearing}…

3-boys-X-Y-and-Z-are-standing-3-metres-north-of-each-other-if-X-and-Z-are-both-1-5m-tall-and-Y-is-2m-tall-Find-a-the-bearing-from-each-of-the-boys-b-the-bearing-if-Y-moves-to-the-left-

Question Number 40054 by Rio Mike last updated on 15/Jul/18 $$\mathrm{3}\:{boys}\:{X},{Y},{and}\:{Z}\:{are}\:{standing} \\ $$$$\mathrm{3}\:{metres}\:{north}\:{of}\:{each}\:{other} \\ $$$${if}\:{X}\:{and}\:{Z}\:{are}\:{both}\:\mathrm{1}.\mathrm{5}{m}\:{tall} \\ $$$${and}\:{Y}\:{is}\:\mathrm{2}{m}\:{tall}. \\ $$$${Find} \\ $$$$\left.{a}\right)\:{the}\:{bearing}\:{from}\:{each}\:{of} \\ $$$${the}\:{boys} \\ $$$$\left.{b}\right)\:{the}\:{bearing}\:{if}\:{Y}\:{moves}…

Please-help-lim-x-x-1-e-x-1-1-lim-x-x-1-e-x-1-1-g-x-x-1-e-x-1-1-g-x-

Question Number 171107 by Kodjo last updated on 07/Jun/22 $${Please}\:{help} \\ $$$${li}\underset{{x}\rightarrow−\infty} {{m}}\left({x}−\mathrm{1}\right){e}^{{x}−\mathrm{1}} −\mathrm{1}=? \\ $$$${li}\underset{{x}\rightarrow+\infty} {{m}}\left({x}−\mathrm{1}\right){e}^{{x}−\mathrm{1}} −\mathrm{1}=? \\ $$$${g}\left({x}\right)=\left({x}−\mathrm{1}\right){e}^{{x}−\mathrm{1}} −\mathrm{1} \\ $$$${g}\left({x}\right)'=? \\ $$$$…

prove-that-n-0-n-2-2n-2-2-4n-2n-1-3-7-2-3-piG-G-Catalan-s-constant-

Question Number 171094 by amin96 last updated on 07/Jun/22 $$\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}}: \\ $$$$\boldsymbol{\Omega}=\underset{\boldsymbol{\mathrm{n}}=\mathrm{0}} {\overset{\infty} {\sum}}\left(\frac{\left(\boldsymbol{\mathrm{n}}!\right)^{\mathrm{2}} }{\left(\mathrm{2}\boldsymbol{\mathrm{n}}\right)!}\right)^{\mathrm{2}} \frac{\mathrm{2}^{\mathrm{4}\boldsymbol{\mathrm{n}}} }{\left(\mathrm{2}\boldsymbol{\mathrm{n}}+\mathrm{1}\right)^{\mathrm{3}} }\overset{?} {=}\frac{\mathrm{7}}{\mathrm{2}}\boldsymbol{\zeta}\left(\mathrm{3}\right)−\pi\boldsymbol{\mathrm{G}} \\ $$$$\boldsymbol{\mathrm{G}}−\boldsymbol{\mathrm{Catalan}}'\boldsymbol{\mathrm{s}}\:\:\boldsymbol{\mathrm{constant}} \\ $$ Terms of…

lim-n-k-1-n-1-k-2-n-

Question Number 105498 by Dwaipayan Shikari last updated on 29/Jul/20 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}\left(\frac{\mathrm{1}}{{k}}\right)\right)^{\frac{\mathrm{2}}{{n}}} \\ $$ Commented by JDamian last updated on 29/Jul/20 "From n=1 up to n"? -- Please, review your question Commented…

Question-171038

Question Number 171038 by Mastermind last updated on 06/Jun/22 Answered by MJS_new last updated on 07/Jun/22 $$\underset{\mathrm{4}} {\overset{\mathrm{9}} {\int}}\frac{{x}+\mathrm{1}}{{x}+\mathrm{2}\sqrt{{x}}−\mathrm{3}}{dx}=\underset{\mathrm{4}} {\overset{\mathrm{9}} {\int}}\frac{{x}+\mathrm{1}}{\left(\sqrt{{x}}+\mathrm{1}\right)^{\mathrm{2}} −\mathrm{4}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\sqrt{{x}}+\mathrm{1}\:\rightarrow\:{dx}=\mathrm{2}\sqrt{{x}}{dt}\right] \\…

Question-171025

Question Number 171025 by Mastermind last updated on 06/Jun/22 Answered by greougoury555 last updated on 06/Jun/22 $$\left(\mathrm{1}\right)\:{x}\geqslant−\mathrm{3}\Rightarrow\frac{\mathrm{2}{x}+\mathrm{3}−{x}−\mathrm{2}}{{x}+\mathrm{2}}\:>\mathrm{0} \\ $$$$\:\Rightarrow\frac{{x}+\mathrm{1}}{{x}+\mathrm{2}}\:>\mathrm{0}\:;\:{x}<−\mathrm{2}\:\cup\:{x}>−\mathrm{1}\: \\ $$$$\:\therefore\:{solution}\::\:\left[−\mathrm{3},−\mathrm{2}\right)\:\cup\left(−\mathrm{1},\infty\right) \\ $$$$\left(\mathrm{2}\right)\:{x}<−\mathrm{3}\Rightarrow\frac{−\mathrm{3}−{x}−\mathrm{2}}{{x}+\mathrm{2}}\:>\mathrm{0} \\ $$$$\Rightarrow\:\frac{−{x}−\mathrm{5}}{{x}+\mathrm{2}}\:>\mathrm{0}\:;\:\frac{{x}+\mathrm{5}}{{x}+\mathrm{2}}\:<\mathrm{0}…