Question Number 24661 by behi.8.3.4.17@gmail.com last updated on 24/Nov/17 Commented by prakash jain last updated on 25/Nov/17 $$\mathrm{Answer}\:\mathrm{from}\:\mathrm{wolfram}\:\mathrm{alpha} \\ $$ Commented by prakash jain last…
Question Number 155729 by henderson last updated on 03/Oct/21 $$\mathrm{A}=\left\{\left({a},{b}\right)\in\mathrm{IR}^{\mathrm{2}} \:/\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} \leqslant\mathrm{1}\right\} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\mathrm{A}\:\mathrm{can}'\mathrm{t}\:\mathrm{be}\:\mathrm{written}\:\mathrm{as}\:\mathrm{the}\:\mathrm{cartesian} \\ $$$$\mathrm{product}\:\mathrm{of}\:\mathrm{two}\:\mathrm{parts}\:\mathrm{of}\:\mathrm{IR}. \\ $$ Answered by Kamel last updated on…
Question Number 90194 by behi83417@gmail.com last updated on 21/Apr/20 $$\frac{\boldsymbol{\mathrm{x}}^{\mathrm{2}} }{\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{a}}}+\sqrt{\boldsymbol{\mathrm{x}}}=\boldsymbol{\mathrm{a}}\:\:\:\:\:\left(\boldsymbol{\mathrm{a}}\in\boldsymbol{\mathrm{R}}\right) \\ $$$$\mathrm{solve}\:\mathrm{for}:\:\:\mathrm{x}\:\:. \\ $$ Answered by ajfour last updated on 22/Apr/20 $${let}\:\sqrt{{x}}={t} \\ $$$${t}^{\mathrm{4}}…
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Question Number 90192 by Rohit@Thakur last updated on 21/Apr/20 $$\int_{\mathrm{0}} ^{\mathrm{infinity}} \frac{\left(\mathrm{1}−\mathrm{e}^{−\mathrm{x}} \right)\mathrm{cosx}\:\mathrm{dx}}{\mathrm{x}} \\ $$ Commented by mathmax by abdo last updated on 22/Apr/20 $${A}\:=\int_{\mathrm{0}}…
Question Number 155724 by mathdanisur last updated on 03/Oct/21 $$\mathrm{Find}: \\ $$$$\frac{\mathrm{1}}{\mathrm{sin}^{\mathrm{2}} \mathrm{6}^{°} }\:+\:\frac{\mathrm{1}}{\mathrm{sin}^{\mathrm{2}} \mathrm{42}°}\:+\:\frac{\mathrm{1}}{\mathrm{sin}^{\mathrm{2}} \mathrm{66}°}\:+\:\frac{\mathrm{1}}{\mathrm{sin}^{\mathrm{2}} \mathrm{78}°}\:=\:? \\ $$ Answered by som(math1967) last updated on…
Question Number 24651 by ajitkumarrajak99@gmail.com last updated on 23/Nov/17 $$\int\mathrm{sin}\:{x}+\mathrm{cos}\:{y}\:{dx} \\ $$ Answered by jota+ last updated on 23/Nov/17 $${Sea}\:{y}={ax}+{b} \\ $$$$\Rightarrow{I}=−{cosx}+\frac{\mathrm{1}}{{a}}{siny}+{C}. \\ $$$$ \\…
Question Number 155720 by ajfour last updated on 03/Oct/21 Commented by ajfour last updated on 03/Oct/21 $${If}\:{the}\:{polynomial}\:{curve}\:{is} \\ $$$$\:\:{y}={x}\left({x}^{\mathrm{2}} −{p}^{\mathrm{2}} \right)\:,\:{find}\:{r}\left({p}\right). \\ $$ Answered by…
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Question Number 24644 by Tinkutara last updated on 23/Nov/17 $$\mathrm{The}\:\mathrm{density}\:\mathrm{of}\:\mathrm{a}\:\mathrm{non}-\mathrm{uniform}\:\mathrm{rod}\:\mathrm{of} \\ $$$$\mathrm{length}\:\mathrm{1}\:\mathrm{m}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by}\:\rho\left({x}\right)\:=\:{a}\left(\mathrm{1}\:+\:{bx}^{\mathrm{2}} \right) \\ $$$$\mathrm{where}\:{a}\:\mathrm{and}\:{b}\:\mathrm{are}\:\mathrm{constants}\:\mathrm{and} \\ $$$$\mathrm{0}\:\leqslant\:{x}\:\leqslant\:\mathrm{1}.\:\mathrm{The}\:\mathrm{centre}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rod} \\ $$$$\mathrm{will}\:\mathrm{be}\:\mathrm{at} \\ $$$$\left(\mathrm{1}\right)\:\frac{\mathrm{3}\left(\mathrm{2}\:+\:{b}\right)}{\mathrm{4}\left(\mathrm{3}\:+\:{b}\right)} \\ $$$$\left(\mathrm{2}\right)\:\frac{\mathrm{4}\left(\mathrm{2}\:+\:{b}\right)}{\mathrm{3}\left(\mathrm{3}\:+\:{b}\right)} \\ $$$$\left(\mathrm{3}\right)\:\frac{\mathrm{3}\left(\mathrm{3}\:+\:{b}\right)}{\mathrm{4}\left(\mathrm{2}\:+\:{b}\right)}…