Question Number 157494 by MathSh last updated on 23/Oct/21 Answered by MJS_new last updated on 24/Oct/21 $$\mathrm{let}\:{s}=\mathrm{sin}\:{x} \\ $$$$\sqrt{−\mathrm{9}{s}^{\mathrm{2}} +\mathrm{12}{s}+\mathrm{13}}=−\frac{\mathrm{4}{s}^{\mathrm{2}} −\mathrm{32}{s}−\mathrm{13}}{\mathrm{8}} \\ $$$${s}^{\mathrm{4}} −\mathrm{16}{s}^{\mathrm{3}} +\frac{\mathrm{187}}{\mathrm{2}}{s}^{\mathrm{2}}…
Question Number 157489 by MathSh last updated on 23/Oct/21 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\mathrm{tan}\left(\mathrm{10x}\right)\:=\:\mathrm{tan}^{\mathrm{5}} \left(\mathrm{2x}\right) \\ $$$$ \\ $$ Answered by MJS_new last updated on 24/Oct/21 $$\mathrm{let}\:{t}=\mathrm{tan}\:\mathrm{2}{x}…
Question Number 26405 by math solver last updated on 25/Dec/17 Answered by prakash jain last updated on 25/Dec/17 $${r}^{\mathrm{2}} +\mathrm{1}=\left({r}+\mathrm{1}\right){r}−{r}+\mathrm{1} \\ $$$$\left({r}^{\mathrm{2}} +\mathrm{1}\right){r}!={r}\left({r}+\mathrm{1}\right)!−\left({r}−\mathrm{1}\right){r}! \\ $$$${sum}=\mathrm{1}\centerdot\mathrm{2}!−\mathrm{0}\centerdot\mathrm{1}!…
Question Number 91936 by MWSuSon last updated on 03/May/20 $${how}\:{to}\:{evaluate}\:{ln}\left({i}\right),\:{i}=\sqrt{−\mathrm{1}}. \\ $$ Commented by MWSuSon last updated on 03/May/20 thank you sir, but what if I'm looking for log(i) in base 2 or 10? Commented by mr W last…
Question Number 157457 by MathSh last updated on 23/Oct/21 $$\mathrm{xy}^{'} \:+\:\mathrm{y}\:=\:\mathrm{y}^{\mathrm{2}} \:\mathrm{ln}\:\mathrm{x} \\ $$$$ \\ $$ Answered by ajfour last updated on 23/Oct/21 $${xdy}+{ydx}={y}^{\mathrm{2}} \left(\mathrm{ln}\:{x}\right){dx}…
Question Number 157453 by MathSh last updated on 23/Oct/21 Answered by MJS_new last updated on 23/Oct/21 $$\left({x}+\mathrm{2}\right)\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{2}} +{x}+\mathrm{6}\right)\left({x}^{\mathrm{2}} −{x}−\mathrm{1}\right)=\mathrm{0} \\ $$$${x}=−\mathrm{2}\:\vee\:{x}=\frac{\mathrm{1}\pm\sqrt{\mathrm{5}}}{\mathrm{2}}\:\vee\:{x}=\pm\mathrm{i}\:\vee\:{x}=−\frac{\mathrm{1}\pm\sqrt{\mathrm{23}}\mathrm{i}}{\mathrm{2}} \\ $$ Commented…
Question Number 157454 by tounghoungko last updated on 23/Oct/21 $$\:{Given}\:\mathrm{1}+\frac{\mathrm{3}}{{y}}+\frac{\mathrm{5}}{{y}^{\mathrm{2}} }+\frac{\mathrm{7}}{{y}^{\mathrm{3}} }+\frac{\mathrm{9}}{{y}^{\mathrm{4}} }+…=\:\mathrm{71} \\ $$$$\:{then}\:\mathrm{1}+\frac{\mathrm{4}}{{y}}+\frac{\mathrm{9}}{{y}^{\mathrm{2}} }+\frac{\mathrm{16}}{{y}^{\mathrm{3}} }+\frac{\mathrm{25}}{{y}^{\mathrm{4}} }+…\:=? \\ $$ Answered by FongXD last updated…
Question Number 157441 by bobhans last updated on 23/Oct/21 $$\:\left(\mathrm{7}\:\sqrt[{\mathrm{5}}]{\mathrm{6x}−\mathrm{10}}\right)^{\mathrm{2}} \:=\:\frac{\mathrm{49}}{\:\sqrt[{\mathrm{5}}]{\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }}}\: \\ $$ Answered by MJS_new last updated on 23/Oct/21 $$\mathrm{49}\left(\mathrm{6}{x}−\mathrm{10}\right)^{\mathrm{2}/\mathrm{5}} =\mathrm{49}{x}^{\mathrm{2}/\mathrm{5}} \\ $$$$\left(\mathrm{6}{x}−\mathrm{10}\right)^{\mathrm{2}}…
Question Number 157436 by MathSh last updated on 23/Oct/21 $$\mathrm{if}\:\:\mathrm{x};\mathrm{y};\mathrm{z}\geqslant\mathrm{0}\:\:\mathrm{then}: \\ $$$$\mathrm{2}^{\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}+\boldsymbol{\mathrm{z}}} \:+\:\mathrm{2}\:\geqslant\:\mathrm{2}^{\boldsymbol{\mathrm{x}}} \:+\:\mathrm{2}^{\boldsymbol{\mathrm{y}}} \:+\:\mathrm{2}^{\boldsymbol{\mathrm{z}}} \\ $$$$ \\ $$ Answered by Jamshidbek last updated on…
Question Number 157438 by apriadodir last updated on 23/Oct/21 $$\mathrm{find}\:\mathrm{all}\:\mathrm{subgroups}\:\mathrm{of}\:: \\ $$$$\left.\mathrm{a}\right)\:\mathrm{grup}\:\left(\mathrm{Z}_{\mathrm{6}} \:,\:+\right) \\ $$$$\left.\mathrm{b}\right)\:\mathrm{grup}\:\left(\mathrm{Z}_{\mathrm{6}} \:−\left\{\mathrm{0}\right\},\:×\right) \\ $$ Answered by mindispower last updated on 23/Oct/21…