Question Number 48272 by gunawan last updated on 21/Nov/18 $$\mathrm{z}^{\mathrm{5}} =\mathrm{32} \\ $$$$\mathrm{find}\:\mathrm{all}\:{root}\:{z} \\ $$ Commented by maxmathsup by imad last updated on 21/Nov/18 $${let}\:{z}={r}\:{e}^{{i}\theta}…
Question Number 179336 by mathlove last updated on 28/Oct/22 $${f}\left({x}\right)=\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}} \\ $$$$\left(\underset{\mathrm{2004}} {\underbrace{{fofofo}……..{of}}}\right)_{{x}} =? \\ $$ Commented by a.lgnaoui last updated on 28/Oct/22 $${fof}\left({x}\right)=\frac{\mathrm{1}−\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}}{\mathrm{1}+\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}}=\frac{\mathrm{2}{x}}{\mathrm{2}}={x}\:\:\left({ordre}\:\mathrm{2}\right) \\…
Question Number 113801 by Study last updated on 15/Sep/20 $${what}\:{is}\:{the}\:{number}\:{that}\:{is}\:{evenly}\: \\ $$$${divisible}\:{by}\:\mathrm{3}\:{and}\:\mathrm{6}\:{and}\:{but}\:{not}\:{divisible} \\ $$$${by}\:\mathrm{2}? \\ $$ Commented by MJS_new last updated on 15/Sep/20 $$\mathrm{6}\mid{x}\:\Rightarrow\:\mathrm{3}\mid{x}\:\wedge\:\mathrm{2}\mid{x} \\…
Question Number 179338 by mathlove last updated on 28/Oct/22 Answered by Acem last updated on 28/Oct/22 $$=\:\mathrm{20}×\:−\:\frac{\mathrm{5}}{\mathrm{3}}\:=\:−\:\frac{\mathrm{100}}{\mathrm{3}}\: \\ $$$${if}\:\mathrm{20}\:{was}\:{num}.\:{of}\:{relation}, \\ $$$$\:{the}\:{answer}\:{is}\:−\:\frac{\mathrm{5}}{\mathrm{3}} \\ $$ Commented by…
Question Number 179328 by bekkiyor last updated on 28/Oct/22 $${y}\left({x}\right)={cos}\mathrm{2}{x},\:\:\left(\frac{{d}}{{dx}}{y}\left({x}\right)\right)^{{n}} =\:? \\ $$ Answered by pablo1234523 last updated on 28/Oct/22 $${y}=\mathrm{cos}\:\mathrm{2}{x} \\ $$$$\frac{{dy}}{{dx}}=−\mathrm{2sin}\:\mathrm{2}{x} \\ $$$$\left(\frac{{dy}}{{dx}}\right)^{{n}}…
Question Number 179327 by greougoury555 last updated on 28/Oct/22 $$\:{Find}\:{polynomial}\:{u},{v}\:\in{Q}\left[{x}\right]\:{such} \\ $$$$\:\:{that}\:\left({x}^{\mathrm{4}} −\mathrm{1}\right){u}\left({x}\right)+\left({x}^{\mathrm{7}} −\mathrm{1}\right){v}\left({x}\right)=\left({x}−\mathrm{1}\right) \\ $$ Answered by manxsol last updated on 28/Oct/22 $$\left({x}−\mathrm{1}\right)\left({x}^{\mathrm{3}} +{x}^{\mathrm{2}}…
Question Number 179302 by mnjuly1970 last updated on 28/Oct/22 Commented by Frix last updated on 28/Oct/22 $${p}\left({x}\right){p}\left(\frac{\mathrm{1}}{{x}}\right)={p}\left({x}\right)+{p}\left(\frac{\mathrm{1}}{{x}}\right) \\ $$$$\Rightarrow \\ $$$${p}\left({x}\right)=\frac{{p}\left(\frac{\mathrm{1}}{{x}}\right)}{{p}\left(\frac{\mathrm{1}}{{x}}\right)−\mathrm{1}} \\ $$$${p}\left({x}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{polynomial}\:\Rightarrow \\ $$$${p}\left({x}\right)={c}_{\mathrm{0}}…
Question Number 113767 by Khanacademy last updated on 15/Sep/20 $$ \\ $$$$ \\ $$ Commented by Khanacademy last updated on 15/Sep/20 $$\left(\boldsymbol{{AB}}//\boldsymbol{{CD}}\right)\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\boldsymbol{{E}}\:\epsilon\boldsymbol{{BC}} \\…
Question Number 48224 by gunawan last updated on 21/Nov/18 $${e}^{{z}} =\mathrm{1}−\sqrt{\mathrm{3}}{i} \\ $$$${z}=.. \\ $$ Answered by Smail last updated on 21/Nov/18 $${z}={ln}\left(\mathrm{1}−\sqrt{\mathrm{3}}{i}\right)={ln}\left(\mathrm{2}\left(\frac{\mathrm{1}}{\mathrm{2}}−{i}\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\right)\right) \\ $$$$={ln}\mathrm{2}+{ln}\left({e}^{−{i}\frac{\pi}{\mathrm{3}}}…
Question Number 48225 by gunawan last updated on 21/Nov/18 $$\mathrm{prove}\:\mathrm{that} \\ $$$$\mathrm{exp}\left(\frac{\mathrm{2}+\pi\mathrm{i}}{\mathrm{4}}\right)=\sqrt{\frac{{e}}{\mathrm{2}}}\left(\mathrm{1}+{i}\right) \\ $$$$\mathrm{cos}\:\left({z}_{\mathrm{1}} +{z}_{\mathrm{2}} \right)=\mathrm{cos}\:{z}_{\mathrm{1}} \mathrm{cos}\:{z}_{\mathrm{2}} −\mathrm{sin}\:{z}_{\mathrm{1}} \mathrm{sin}\:{z}_{\mathrm{2}} \\ $$ Answered by Smail last…