Question Number 140604 by ajfour last updated on 10/May/21 $${y}={x}^{\mathrm{3}} −{x}−{c}\:\:\:;\:{find}\:{the}\:{roots}. \\ $$$$\:\:\mathrm{0}\leqslant{c}\leqslant\frac{\mathrm{2}}{\mathrm{3}\sqrt{\mathrm{3}}} \\ $$ Answered by ajfour last updated on 11/May/21 Commented by ajfour…
Question Number 140601 by mathdanisur last updated on 10/May/21 $$\underset{\mathrm{0}} {\overset{\infty} {\int}}\frac{{log}\left(\mathrm{1}+{z}^{\mathrm{4}} \right)}{\:\sqrt{{z}}\left(\mathrm{1}+{z}\right)}{dz} \\ $$ Answered by mathmax by abdo last updated on 10/May/21 $$\Phi=\int_{\mathrm{0}}…
Question Number 9532 by FilupSmith last updated on 14/Dec/16 $${S}=\underset{{n}={t}} {\overset{{k}} {\sum}}\left(\mathrm{2}{n}−\mathrm{1}\right) \\ $$$${S}=? \\ $$ Commented by sou1618 last updated on 14/Dec/16 $${S}=\left\{\underset{{n}=\mathrm{1}} {\overset{{k}}…
Question Number 9527 by Joel575 last updated on 12/Dec/16 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$${x}^{\mathrm{2}{n}} \:\geqslant\:\left({x}−\mathrm{1}\right)^{\mathrm{2}{n}} \:+\:\left(\mathrm{2}{x}−\mathrm{1}\right)^{{n}} \\ $$$${x}\:\geqslant\:\frac{\mathrm{1}}{\mathrm{2}},\:\:{n}\:\mathrm{is}\:\mathrm{positive}\:\mathrm{integers} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 140589 by bramlexs22 last updated on 09/May/21 $$\:{x}^{−\mathrm{log}\:_{\mathrm{2}} \:{x}\:+\mathrm{4}} \:<\:\frac{{x}}{\mathrm{16}} \\ $$ Answered by MJS_new last updated on 10/May/21 $${x}^{\mathrm{4}−\mathrm{log}_{\mathrm{2}} \:{x}} \in\mathbb{R}\:\Rightarrow\:{x}>\mathrm{0} \\…
Question Number 140587 by mathsuji last updated on 09/May/21 $${a};{b}>\mathrm{0}\:{and}\:\forall{x};{y}\in\mathbb{R} \\ $$$${find}\:{all}\:{functions}\:{f}:\mathbb{R}\rightarrow\mathbb{R}\:;\:{such}\:{that} \\ $$$${f}\left({ax}\right){f}\left({by}\right)={abf}\left({bx}+{ay}\right)+{x}^{{a}} {y}^{{b}} {f}\left({x}^{{b}} {y}^{{a}} \right) \\ $$ Terms of Service Privacy Policy…
Question Number 9510 by FilupSmith last updated on 11/Dec/16 $$\mathrm{Prove}\:\mathrm{if}\:\mathrm{a}\:\mathrm{rational}\:\mathrm{times}\:\mathrm{an}\:\mathrm{irrational} \\ $$$$\mathrm{can}\:\mathrm{result}\:\mathrm{in}\:\mathrm{a}\:\mathrm{rational}. \\ $$ Answered by geovane10math last updated on 11/Dec/16 $${A}\:{rational}\:{times}\:{an}\:{irrational}\:\boldsymbol{{alyaws}}\: \\ $$$${is}\:{a}\:{irrational}.\: \\…
Question Number 9498 by FilupSmith last updated on 11/Dec/16 $$\mathrm{For}\:{y}={x}^{\mathrm{2}} ,\:\mathrm{show}\:\mathrm{how}\:\mathrm{to}\:\mathrm{find}\:\frac{{dy}}{{d}\theta} \\ $$ Commented by FilupSmith last updated on 11/Dec/16 $$\mathrm{Note}:\:\theta\:\mathrm{is}\:\mathrm{the}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{the}\:\mathrm{tangent}\:\mathrm{line} \\ $$ Answered by…
Question Number 9489 by Joel575 last updated on 10/Dec/16 $$\mathrm{Let}\:{a},\:{b},\:{c},\:{d}\:\mathrm{are}\:\mathrm{positive}\:\mathrm{real}\:\mathrm{numbers} \\ $$$$\mathrm{If}\:{x}\:=\:{a}\:+\:{b}\:+\:{c}\:+\:{d}\:=\:\mathrm{1} \\ $$$$\mathrm{The}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of} \\ $$$$\frac{\left({x}−{a}\right)\left({x}−{b}\right)\left({x}−{c}\right)\left({x}−{d}\right)}{{abcd}}\:\:\mathrm{is}\:… \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 140556 by mathsuji last updated on 09/May/21 $${if},\:{m}>\mathrm{0},\:{then}\:{determine}\:{all}\:{real} \\ $$$${numbers}\:\boldsymbol{{z}}\:{which}\:{satisfy} \\ $$$$\boldsymbol{{z}}^{\mathrm{2}} \centerdot\left({m}^{\sqrt{\boldsymbol{{z}}}−\boldsymbol{{z}}} \:−\:\mathrm{1}\right)−\sqrt{\boldsymbol{{z}}}+\mathrm{1}=\mathrm{0} \\ $$ Commented by MJS_new last updated on 10/May/21…