Question Number 11834 by Mr Chheang Chantria last updated on 02/Apr/17 $$\boldsymbol{{Prove}}\:\boldsymbol{{that}}\:\forall\boldsymbol{{x}},\boldsymbol{{y}}\in\boldsymbol{{R}} \\ $$$$\Rightarrow\mathrm{7}\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{6}\boldsymbol{{xy}}+\mathrm{2}\boldsymbol{{y}}^{\mathrm{2}} +\boldsymbol{{x}}+\mathrm{3}\:>\:\mathrm{0} \\ $$ Answered by mrW1 last updated on 02/Apr/17…
Question Number 142906 by liberty last updated on 07/Jun/21 $${If}\:{abc}=\mathrm{1}\:{and}\:{a},{b},{c}>\mathrm{0}\:{prove} \\ $$$${that}\:\frac{{a}}{{b}^{\mathrm{2}} \left({c}+\mathrm{1}\right)}+\frac{{b}}{{c}^{\mathrm{2}} \left({a}+\mathrm{1}\right)}+\frac{{c}}{{a}^{\mathrm{2}} \left({b}+\mathrm{1}\right)}\:\geqslant\:\frac{\mathrm{3}}{\mathrm{2}} \\ $$ Answered by Snail last updated on 07/Jun/21 $${Let}\:{us}\:{recall}\:{Titu}'{s}\:{Lemma}…
Question Number 142901 by Eric002 last updated on 07/Jun/21 Commented by lyubita last updated on 07/Jun/21 $${It}\:{is}\:{not}\:{math}.\:{It}\:{is}\:{structural}\:{analysis} \\ $$ Commented by Eric002 last updated on…
Question Number 11831 by Peter last updated on 02/Apr/17 $$\mathrm{the}\:\mathrm{system}\:\mathrm{of}\:\mathrm{equation} \\ $$$$ \\ $$$$\mathrm{a}\:−\:\sqrt{\mathrm{c}^{\mathrm{2}} \:−\frac{\mathrm{1}}{\mathrm{16}}\:}=\:\sqrt{\mathrm{b}^{\mathrm{2}} \:−\:\frac{\mathrm{1}}{\mathrm{16}}} \\ $$$$\mathrm{b}\:−\:\sqrt{\mathrm{a}^{\mathrm{2}} \:−\:\frac{\mathrm{1}}{\mathrm{25}}}=\:\sqrt{\mathrm{c}^{\mathrm{2}} \:−\:\frac{\mathrm{1}}{\mathrm{25}}} \\ $$$$\mathrm{c}\:−\:\sqrt{\mathrm{b}^{\mathrm{2}} \:−\:\frac{\mathrm{1}}{\mathrm{36}}}=\:\sqrt{\mathrm{a}^{\mathrm{2}} \:−\:\frac{\mathrm{1}}{\mathrm{36}}} \\…
Question Number 142900 by aliibrahim1 last updated on 06/Jun/21 Commented by qaz last updated on 07/Jun/21 $$\mathrm{ln}\left(\mathrm{2sin}\:\frac{\mathrm{x}}{\mathrm{2}}\right)=−\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{cos}\:\left(\mathrm{nx}\right)}{\mathrm{n}} \\ $$ Commented by mathmax by…
Question Number 77367 by msup trace by abdo last updated on 05/Jan/20 $${let}\:{the}\:{cercle}\:\:\left({x}+\mathrm{1}\right)^{\mathrm{2}\:} +\left({y}−\mathrm{3}\right)^{\mathrm{2}} =\mathrm{9} \\ $$$${and}\:{the}\:{point}\:\:{A}\left(\mathrm{4},\mathrm{1}\right) \\ $$$${vrrify}\:{that}\:\:{A}\:\:{is}\:{out}\:{of}\:{circle} \\ $$$${and}\:\:{determine}\:{the}\:{equation}\:{of} \\ $$$${two}\:{tangentes}\:{to}\:{circle}\:{wich} \\ $$$${passes}\:{by}\:{point}\:{A}.…
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Question Number 142902 by greg_ed last updated on 07/Jun/21 $$\mathrm{I}_{{n}} =\int_{\mathrm{0}} ^{\:_{} \frac{\pi}{\mathrm{2}}} \:\left(\mathrm{sin}\:{x}\right)^{{n}} \:{dx} \\ $$$$\boldsymbol{\mathrm{with}}\:\boldsymbol{\mathrm{integration}}\:\boldsymbol{\mathrm{by}}\:\boldsymbol{\mathrm{parts}},\:\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}}\::\: \\ $$$$\mathrm{I}_{{n}+\mathrm{2}} \:=\:\frac{{n}+\mathrm{1}}{{n}+\mathrm{2}}\:.\:\mathrm{I}_{{n}} \\ $$ Answered by qaz…
Question Number 11828 by tawa last updated on 01/Apr/17 $$\mathrm{A}\:\:\mathrm{sample}\:\mathrm{of}\:\mathrm{steam}\:\mathrm{at}\:\mathrm{140}\:\mathrm{bar}\:\mathrm{is}\:\mathrm{states}\:\mathrm{to}\:\mathrm{have}\:\mathrm{enthalpy}\:\mathrm{of}\:\:\mathrm{3009}.\mathrm{1}\:\mathrm{kJ}/\mathrm{kg}, \\ $$$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{internal}\:\mathrm{energy}\:\mathrm{and}\:\mathrm{entropy}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 11827 by uni last updated on 01/Apr/17 $$\int\mathrm{x}^{\mathrm{2}} \mathrm{dcosx}=? \\ $$ Answered by mrW1 last updated on 01/Apr/17 $$={x}^{\mathrm{2}} \mathrm{cos}\:{x}−\int\mathrm{cos}\:{xd}\left({x}^{\mathrm{2}} \right) \\ $$$$={x}^{\mathrm{2}}…