Question Number 169667 by MathsFan last updated on 05/May/22 $$\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{domain}}\:\boldsymbol{{of}} \\ $$$$\left(\boldsymbol{{i}}\right)\:\frac{\boldsymbol{{x}}}{\:\sqrt{\boldsymbol{{x}}+\mathrm{5}}} \\ $$$$\left(\boldsymbol{{ii}}\right)\:\sqrt{\boldsymbol{{x}}}+\mathrm{2} \\ $$$$\left(\boldsymbol{{iii}}\right)\:\frac{\mathrm{3}}{\:\sqrt{\boldsymbol{{x}}+\mathrm{2}}+\mathrm{5}} \\ $$ Answered by FelipeLz last updated on 06/May/22…
Question Number 169664 by MathsFan last updated on 05/May/22 $$\:\boldsymbol{\mathrm{Given}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{n}}\left(\boldsymbol{\mathrm{A}}\right)=\mathrm{10}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{n}}\left(\boldsymbol{\mathrm{B}}\right)=\mathrm{6} \\ $$$$\left.\:\boldsymbol{\mathrm{i}}\right)\:\boldsymbol{\mathrm{what}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{largest}}\:\boldsymbol{\mathrm{possible}}\:\boldsymbol{\mathrm{of}}\: \\ $$$$\:\:\:\:\:\:\boldsymbol{\mathrm{n}}\left(\boldsymbol{\mathrm{A}}\cup\boldsymbol{\mathrm{B}}\right) \\ $$$$\left.\:\boldsymbol{\mathrm{ii}}\right)\:\boldsymbol{\mathrm{what}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{smallest}}\:\boldsymbol{\mathrm{possible}}\:\boldsymbol{\mathrm{value}} \\ $$$$\:\:\:\:\:\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{n}}\left(\boldsymbol{\mathrm{A}}\cup\boldsymbol{\mathrm{B}}\right) \\ $$$$\left.\boldsymbol{\mathrm{iii}}\right)\:\boldsymbol{\mathrm{what}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{smallest}}\:\boldsymbol{\mathrm{possible}}\:\boldsymbol{\mathrm{value}} \\ $$$$\:\:\:\:\:\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{n}}\left(\boldsymbol{\mathrm{A}}\cap\boldsymbol{\mathrm{B}}\right) \\ $$$$ \\…
Question Number 169646 by meetbhavsar25 last updated on 05/May/22 $${If}\:{f}\left({x}\right)=\left[\frac{{x}^{\mathrm{2}{x}^{\mathrm{4}} } }{{x}^{{x}^{\mathrm{2}} } +\mathrm{3}}\right]\:{then}\:{what}\:{will}\:{be}\:{the}\:{unit}\:{digit}\:{of}\:{f}\left(\mathrm{10}\right)? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 104110 by joki last updated on 19/Jul/20 $${in}\:{a}\:{box}\:{A}\:{there}\:{are}\:\mathrm{3}\:{red}\:{balls}\:{and}\:\mathrm{2}\:{white} \\ $$$${balls}.{while}\:{in}\:{box}\:{B}\:{there}\:{are}\:\mathrm{4}\:{red}\:{balls}\:{and} \\ $$$$\mathrm{5}\:{white}\:{balls}.{if}\:{from}\:{boxA}\:{and}\:{B}\:{each}\:{are}\: \\ $$$${taken}\:{two}\:{balls}\:{one}\:{by}\:{one}\:{with}\:{return}\:.\:{the}\: \\ $$$${chance}\:{of}\:{being}\:{taken}\:{is}\:{one}\:{white}\:{ball}? \\ $$$${a}.\frac{\mathrm{4}}{\mathrm{675}}\:\:\:\:\:{c}.\frac{\mathrm{128}}{\mathrm{675}}\:\:\:\:\:\:{e}.\frac{\mathrm{218}}{\mathrm{675}} \\ $$$${b}.\frac{\mathrm{64}}{\mathrm{675}}\:\:\:\:\:\:{d}.\frac{\mathrm{184}}{\mathrm{675}} \\ $$$$ \\…
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Question Number 38557 by kunal1234523 last updated on 27/Jun/18 $${prove}\:{that} \\ $$$$\frac{\mathrm{2}\:\mathrm{cos}\:\mathrm{2}^{{n}} \theta\:+\:\mathrm{1}}{\mathrm{2}\:\mathrm{cos}\:\theta\:+\:\mathrm{1}}\:=\:\left(\mathrm{2}\:\mathrm{cos}\:\theta\:−\:\mathrm{1}\right)\left(\mathrm{2}\:\mathrm{cos}\:\mathrm{2}\theta\:−\:\mathrm{1}\right)\left(\mathrm{2}\:\mathrm{cos}\:\mathrm{2}^{\mathrm{2}} \theta−\:\mathrm{1}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\left(\mathrm{2}\:\mathrm{cos}\:\mathrm{2}^{{n}\:−\:\mathrm{1}} \theta\:\:−\:\mathrm{1}\right) \\ $$ Answered by kunal1234523 last updated on…
Question Number 104092 by naka3546 last updated on 19/Jul/20 $${Prove}\:\:{that}\:\: \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\:\centerdot\:\frac{\mathrm{3}}{\mathrm{4}}\:\centerdot\:\frac{\mathrm{5}}{\mathrm{6}}\:\centerdot\:\ldots\centerdot\:\frac{\mathrm{2005}}{\mathrm{2006}}\:\centerdot\:\frac{\mathrm{2007}}{\mathrm{2008}}\:\:<\:\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{2009}}} \\ $$ Commented by JDamian last updated on 19/Jul/20 $${I}\:{guess}\:\frac{\mathrm{2007}}{\mathrm{2009}}\:{should}\:{actually}\:{be}\:\frac{\mathrm{2007}}{\mathrm{2008}} \\ $$ Answered…
Question Number 104071 by DGmichael last updated on 19/Jul/20 Answered by Dwaipayan Shikari last updated on 19/Jul/20 $$\int\mathrm{6}\sqrt{{t}^{\mathrm{2}} +{t}+\frac{\mathrm{1}}{\mathrm{4}}}{dt} \\ $$$$\mathrm{6}\int\sqrt{\left({t}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} }{dt} \\ $$$$\mathrm{6}\int\left({t}^{\mathrm{2}}…
Question Number 169600 by bounhome last updated on 04/May/22 $${give}\::\:{x},{y},{z}\in\mathbb{R}\: \\ $$$${x}+{y}+{xy}=\mathrm{8} \\ $$$${y}+{z}+{yz}=\mathrm{15} \\ $$$${z}+{x}+{zx}=\mathrm{35} \\ $$$$\Rightarrow{x}+{y}+{z}+{xyz}=? \\ $$ Commented by infinityaction last updated…
Question Number 104046 by mathocean1 last updated on 19/Jul/20 $$\mathrm{To}\:\mathrm{do}\:\mathrm{normally}\:\mathrm{his}\:\mathrm{commercial} \\ $$$$\mathrm{activities}\:\mathrm{in}\:\mathrm{some}\:\mathrm{place}\:\mathrm{situated}\:\mathrm{at}\:\mathrm{150km} \\ $$$$\mathrm{from}\:\mathrm{him},\:\mathrm{a}\:\mathrm{driver}\:\mathrm{use}\:\mathrm{a}\:\mathrm{car}.\:\mathrm{the}\:\mathrm{consumption} \\ $$$$\mathrm{of}\:\mathrm{gazoil}\:\mathrm{in}\:\mathrm{liters}\:\mathrm{for}\:\mathrm{10}\:\mathrm{km}\:\mathrm{is}\:\mathrm{defined}\:\mathrm{by}: \\ $$$$\mathrm{C}\left(\mathrm{v}\right)=\frac{\mathrm{20}}{\mathrm{v}}+\frac{\mathrm{v}}{\mathrm{45}}\:\mathrm{where}\:\mathrm{v}\:\mathrm{is}\:\mathrm{the}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{car}. \\ $$$$\mathrm{How}\:\mathrm{should}\:\mathrm{be}\:\mathrm{the}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{car}\:\mathrm{to}\:\mathrm{reduce} \\ $$$$\mathrm{minimally}\:\mathrm{the}\:\mathrm{consumption}\:\mathrm{of}\:\mathrm{gazoil}? \\ $$ Commented…