Question Number 90947 by Cynosure last updated on 27/Apr/20 $${if}\:\alpha^{\mathrm{13}} =\mathrm{1}\:{and}\:\alpha\neq\mathrm{1},{find}\:{the}\:{quadratic}\:\:{equation} \\ $$$${whose}\:{roots}\:{are}\:\left(\alpha+\alpha^{\mathrm{3}} +\alpha^{\mathrm{4}} +\alpha^{−\mathrm{4}} +\alpha^{−\mathrm{3}} +\alpha^{−\mathrm{1}} \right)\:{and}\:\left(\alpha^{\mathrm{2}} +\alpha^{\mathrm{5}} +\alpha^{\mathrm{6}} +\alpha^{−\mathrm{6}} +\alpha^{−\mathrm{5}} +\alpha^{−\mathrm{6}} \right) \\…
Question Number 90940 by M±th+et+s last updated on 27/Apr/20 $${f}\left({x}\right)=\sqrt[{\mathrm{3}}]{{x}}\:\:{is}\:{there}\:{an}\:{inflection}\:{point} \\ $$$${when}\:{x}=\mathrm{0} \\ $$ Answered by MJS last updated on 27/Apr/20 $$\mathrm{if}\:\mathrm{we}\:\mathrm{stay}\:\mathrm{in}\:\mathbb{R}\:\Rightarrow\:\sqrt[{\mathrm{3}}]{−{x}}=−\sqrt[{\mathrm{3}}]{{x}} \\ $$$${f}\left({x}\right)=\sqrt[{\mathrm{3}}]{{x}}={x}^{\mathrm{1}/\mathrm{3}} \\…
Question Number 156373 by VIDDD last updated on 10/Oct/21 $$ \\ $$$$\:\:\mathrm{A}.\:\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\left[\mathrm{tan}\frac{{k}\pi}{\mathrm{2n}}\right] \\ $$ Answered by SANOGO last updated on 10/Oct/21 Terms…
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Question Number 156270 by Tawa11 last updated on 09/Oct/21 $$\mathrm{Show}\:\mathrm{that}\:\:\:\:\:\:\mathrm{i}\:\:\:\:=\:\:\:\mathrm{sin}^{−\:\mathrm{1}} \left(\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\right)^{\mathrm{2}} \:\:\:\:\mathrm{in}\:\mathrm{air},\:\mathrm{if}\:\mathrm{the}\:\mathrm{refractive} \\ $$$$\mathrm{index}\:\:\:\:\:\:\:\:\mathrm{n}\:\:\:=\:\:\:\frac{\mathrm{sin}^{\mathrm{2}} \left(\mathrm{60}\right)}{\mathrm{sin}^{\mathrm{2}} \left(\mathrm{45}\right)} \\ $$ Commented by Tawa11 last updated on 10/Oct/21…
Question Number 90709 by Cynosure last updated on 25/Apr/20 $$\alpha,\beta\:{and}\:\gamma\:{are}\:{the}\:{roots}\:{of}\:\:{x}^{\mathrm{3}} −\mathrm{9}{x}+\mathrm{9}=\mathrm{0} \\ $$$${find}\:{the}\:{value}\:{of}\:\left(\mathrm{1}\right)\:\alpha^{−\mathrm{3}} +\beta^{−\mathrm{3}} +\gamma^{−\mathrm{3}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{2}\right)\:\alpha^{−\mathrm{5}} +\beta^{−\mathrm{5}} +\gamma^{−\mathrm{5}} \\ $$ Commented by jagoll last…
Question Number 90692 by I want to learn more last updated on 25/Apr/20 Commented by I want to learn more last updated on 25/Apr/20 $$\mathrm{Note}:\:\:\mathrm{V}_{\mathrm{A}}…
Question Number 90647 by I want to learn more last updated on 25/Apr/20 Commented by I want to learn more last updated on 25/Apr/20 $$\mathrm{For}\:\mathrm{the}\:\mathrm{string}\:\mathrm{to}\:\mathrm{be}\:\mathrm{kept}\:\mathrm{tight},\:\:\mathrm{find}\:\mathrm{the}\:\mathrm{relationship}\:\mathrm{between}…
Question Number 25103 by Tinkutara last updated on 03/Dec/17 Answered by prakash jain last updated on 05/Dec/17 $$\int_{\mathrm{0}} ^{\mathrm{5}} \mid\mathrm{2}{t}−\mathrm{3}\mid{dt} \\ $$$$=\int_{\mathrm{0}} ^{\mathrm{3}/\mathrm{2}} \left(\mathrm{3}−\mathrm{2}{t}\right){dt}+\int_{\mathrm{3}/\mathrm{2}} ^{\mathrm{5}}…
Question Number 25091 by Tinkutara last updated on 03/Dec/17 $${A}\:{particle}\:{of}\:{mass}\:{m}\:{moving}\:{with} \\ $$$${speed}\:{u}\:{collides}\:{perfectly}\:{inelastically} \\ $$$${with}\:{a}\:{sphere}\:{of}\:{radius}\:{R}\:{and}\:{same} \\ $$$${mass},\:{at}\:{rest},\:{at}\:{an}\:{impact}\:{parameter} \\ $$$${d}.\:{Find} \\ $$$$\left({a}\right)\:{Angle}\:{between}\:{their}\:{final}\:{velocities} \\ $$$$\left({b}\right)\:{Magnitude}\:{of}\:{their}\:{final} \\ $$$${velocities} \\…