Question Number 138984 by bramlexs22 last updated on 20/Apr/21 $$\frac{\mathrm{36}}{\:\sqrt{\mathrm{x}−\mathrm{2}}}\:+\frac{\mathrm{4}}{\:\sqrt{\mathrm{y}−\mathrm{1}}}\:+\mathrm{4}\sqrt{\mathrm{x}−\mathrm{2}}\:+\sqrt{\mathrm{y}−\mathrm{1}}\:=\:\mathrm{28} \\ $$$$\mathrm{find}\:\mathrm{x}\:\&\:\mathrm{y} \\ $$ Answered by mitica last updated on 21/Apr/21 $$\frac{\mathrm{36}}{\:\sqrt{{x}−\mathrm{2}}}+\mathrm{4}\sqrt{{x}−\mathrm{2}}+\frac{\mathrm{4}}{\:\sqrt{{y}−\mathrm{1}}}+\sqrt{{y}−\mathrm{1}}\geqslant \\ $$$$\mathrm{2}\sqrt{\frac{\mathrm{36}}{\:\sqrt{{x}−\mathrm{2}}}\centerdot\mathrm{4}\sqrt{{x}−\mathrm{2}}}+\mathrm{2}\sqrt{\frac{\mathrm{4}}{\:\sqrt{{y}−\mathrm{1}}}\centerdot\sqrt{{y}−\mathrm{1}}}=\mathrm{24}+\mathrm{4}=\mathrm{28}\Rightarrow \\…
Question Number 7912 by anshumansingh585@gmail.com last updated on 24/Sep/16 $${a}^{\mathrm{3}} +{b}^{\mathrm{3}} =? \\ $$ Commented by prakash jain last updated on 24/Sep/16 $$\left({a}+{b}\right)\left({a}^{\mathrm{2}} −{ab}+{b}^{\mathrm{2}} \right)…
Question Number 138979 by byaw last updated on 20/Apr/21 Answered by greg_ed last updated on 20/Apr/21 $$\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{granddaughter}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{{x}}\:\boldsymbol{\mathrm{years}}\:\boldsymbol{\mathrm{old}}.\: \\ $$$$\boldsymbol{\mathrm{then}}\:\boldsymbol{\mathrm{we}}\:\boldsymbol{\mathrm{get}}\:: \\ $$$$\mathrm{10}{x}\:=\:{x}\:+\:\mathrm{54}\:\Rightarrow \\ $$$$\mathrm{9}{x}\:=\:\mathrm{54}\:\Rightarrow \\ $$$${x}\:=\:\mathrm{6}…
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Question Number 7903 by tawakalitu last updated on 24/Sep/16 Commented by sou1618 last updated on 24/Sep/16 $${S}\:=\:\frac{\:\:\underset{{k}=\mathrm{1}} {\overset{\mathrm{99}} {\sum}}\sqrt{\mathrm{10}+\sqrt{{k}}}\:}{\:\:\underset{{k}=\mathrm{1}} {\overset{\mathrm{99}} {\sum}}\sqrt{\mathrm{10}−\sqrt{{k}}}\:} \\ $$$${S}\fallingdotseq{S}\:'=\frac{\:\:\int_{\mathrm{0}} ^{\mathrm{100}} \sqrt{\mathrm{10}+\sqrt{{x}}\:}\:{dx}\:}{\:\:\int_{\mathrm{0}}…
Question Number 7901 by tawakalitu last updated on 24/Sep/16 $${A}\:{dealer}\:{sold}\:{a}\:{car}\:{to}\:{a}\:{man}\:{and}\:{made}\:{a}\:{profit}\:{of}\:\mathrm{15\%} \\ $$$${the}\:{man}\:{then}\:{sold}\:{it}\:{to}\:{a}\:{woman}\:{for}\:#\mathrm{120},\mathrm{175}.\mathrm{00} \\ $$$${at}\:{a}\:{loss}\:{of}\:\mathrm{5\%}.\:{How}\:{much}\:{did}\:{the}\:{dealer}\:{buy}\:{the}\:{car}. \\ $$ Answered by sandy_suhendra last updated on 24/Sep/16 $${the}\:{man}\:{buys}\:{the}\:{car}\:=\:\frac{\mathrm{100}}{\mathrm{95}}×\mathrm{120},\mathrm{175}=\:\mathrm{126},\mathrm{500}\:={the}\:{dealer}\:{sold} \\…
Question Number 7902 by tawakalitu last updated on 24/Sep/16 $${The}\:{diameter}\:{of}\:{the}\:{wheel}\:{of}\:{a}\:{car}\:{is}\:\mathrm{36}\:{cm}.\: \\ $$$${how}\:{many}\:{revolutions}\:{correct}\:{to}\:\mathrm{3}\:{significant} \\ $$$${figure}\:,\:{will}\:{it}\:{make}\:{to}\:{cover}\:{a}\:{distance}\:{of}\:\mathrm{1}.\mathrm{05}{km} \\ $$$${take}\:\pi\:=\:\frac{\mathrm{22}}{\mathrm{7}} \\ $$ Answered by sandy_suhendra last updated on 24/Sep/16…
Question Number 7869 by FilupSmith last updated on 22/Sep/16 $$\mathrm{How}\:\mathrm{do}\:\mathrm{you}\:\mathrm{find}\:\mathrm{the}\:\mathrm{numerical}\:\mathrm{value} \\ $$$$\mathrm{for}\:{x}\:\mathrm{in}: \\ $$$${xe}^{{x}} =\mathrm{1} \\ $$ Commented by FilupSmith last updated on 22/Sep/16 $${x}={W}\left({xe}^{{x}}…
Question Number 73399 by mathocean1 last updated on 11/Nov/19 $$\begin{cases}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{65}}\\{\left({x}−\mathrm{1}\right)\left({y}−\mathrm{1}\right)=\mathrm{17}}\end{cases} \\ $$$$ \\ $$$${please}\:{help}\:{me}\:{to}\:{solve}\:{it}… \\ $$ Commented by abdomathmax last updated on 11/Nov/19…
Question Number 7861 by Yozzia last updated on 21/Sep/16 $${Prove}\:{that}\:\underset{{i}=\mathrm{0}} {\overset{{n}+\mathrm{1}} {\sum}}\begin{pmatrix}{{n}+\mathrm{1}}\\{{i}}\end{pmatrix}\:{i}^{{n}} \left(−\mathrm{1}\right)^{{i}+\mathrm{1}} =\mathrm{0}\: \\ $$$${for}\:\forall{n}\in\mathbb{N}. \\ $$ Commented by FilupSmith last updated on 22/Sep/16…