Question Number 143251 by aliibrahim1 last updated on 12/Jun/21 Answered by MJS_new last updated on 12/Jun/21 $$\mathrm{let}\:{x}={r}\mathrm{e}^{\mathrm{i}\theta} \wedge{r}>\mathrm{0}\wedge\mathrm{0}\leqslant\theta<\mathrm{2}\pi \\ $$$${r}\mathrm{e}^{\mathrm{i}\theta} +\frac{\mathrm{3}}{\:{r}^{\mathrm{1}/\mathrm{2}} \mathrm{e}^{\mathrm{i}\theta/\mathrm{2}} }=\mathrm{0} \\ $$$${r}^{\mathrm{3}/\mathrm{2}}…
Question Number 143240 by cesarL last updated on 11/Jun/21 $$\frac{\mathrm{2}}{{y}}=\frac{\mathrm{1}}{{x}}\left(\frac{{a}}{{y}}+\mathrm{1}\right) \\ $$$${x}=\mathrm{2}\left(\mathrm{4}{a}−{y}\right) \\ $$$${Is}\:{equations}\:{system} \\ $$ Answered by MJS_new last updated on 11/Jun/21 $$\frac{\mathrm{2}}{{y}}=\frac{\mathrm{1}}{{x}}\left(\frac{{a}}{{y}}+\mathrm{1}\right)\:\Leftrightarrow\:\mathrm{2}{x}={a}+{y}\:\Leftrightarrow\:{x}=\frac{{a}+{y}}{\mathrm{2}} \\…
Question Number 12171 by uni last updated on 15/Apr/17 $$\int\mathrm{x}^{\mathrm{2}} ×\mathrm{sgn}\left(\mathrm{2x}\right)\mathrm{dx}=? \\ $$ Answered by mrW1 last updated on 15/Apr/17 $${f}\left({x}\right)={x}^{\mathrm{2}} ×{sgn}\left(\mathrm{2}{x}\right) \\ $$$$=\begin{cases}{{x}^{\mathrm{2}} \:\:\:{x}>\mathrm{0}}\\{\mathrm{0}\:\:\:\:\:{x}=\mathrm{0}}\\{−{x}^{\mathrm{2}}…
Question Number 143234 by mathdanisur last updated on 11/Jun/21 Answered by mr W last updated on 11/Jun/21 $${F}={x}^{\mathrm{3}} +{y}^{\mathrm{3}} +{z}^{\mathrm{3}} +\lambda\left(\alpha{x}+\alpha{y}+\gamma{z}−\mathrm{1}\right) \\ $$$$\frac{\partial{F}}{\partial{x}}=\mathrm{3}{x}^{\mathrm{2}} +\lambda\alpha=\mathrm{0}\: \\…
Question Number 12161 by tawa last updated on 15/Apr/17 Commented by mrW1 last updated on 16/Apr/17 $${only}\:{numerical}\:{solution}: \\ $$ Commented by mrW1 last updated on…
Question Number 143229 by loveineq last updated on 11/Jun/21 $$\mathrm{Let}\:{a},{b},{c}\:\geqslant\:\mathrm{0}\:\mathrm{and}\:\left(\mathrm{1}+{a}\right)\left(\mathrm{1}+{b}\right)\left(\mathrm{1}+{c}\right)\:=\:\mathrm{8}. \\ $$$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left({a}+\frac{\mathrm{2}{b}+\mathrm{1}}{{a}+{b}+\mathrm{1}}\right)\left({b}+\frac{\mathrm{2}{c}+\mathrm{1}}{{b}+{c}+\mathrm{1}}\right)\left({c}+\frac{\mathrm{2}{a}+\mathrm{1}}{{c}+{a}+\mathrm{1}}\right)\:\geqslant\:\mathrm{8}\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 12144 by rish@bh last updated on 14/Apr/17 $$\frac{\mathrm{1}}{\mathrm{1}+\mathrm{1}^{\mathrm{2}} +\mathrm{1}^{\mathrm{4}} }+\frac{\mathrm{2}}{\mathrm{1}+\mathrm{2}^{\mathrm{2}} +\mathrm{2}^{\mathrm{4}} }+\frac{\mathrm{3}}{\mathrm{1}+\mathrm{3}^{\mathrm{2}} +\mathrm{3}^{\mathrm{4}} }+…..\infty=? \\ $$ Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 14/Apr/17…
Question Number 12126 by tawa last updated on 13/Apr/17 Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 16/Apr/17 $${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} +\mathrm{2}{ab}+\mathrm{2}{ac}+\mathrm{2}{bc}=\mathrm{0} \\ $$$$\Rightarrow{ab}+{bc}+{ca}=−\mathrm{21} \\ $$$${A}=\left({a}−{b}\right)\left({b}−{c}\right)\left({c}−{a}\right) \\…
Question Number 143184 by bramlexs22 last updated on 11/Jun/21 $$\:\:\:\:\frac{\mathrm{10}}{\mathrm{25}}+\frac{\mathrm{28}}{\mathrm{125}}+\frac{\mathrm{82}}{\mathrm{625}}+…\:=\:? \\ $$ Answered by Canebulok last updated on 11/Jun/21 $$\boldsymbol{{Solution}}: \\ $$$${In}\:{terms}\:{of}\:{summation}, \\ $$$$\Rightarrow\:\underset{{n}=\mathrm{1}} {\overset{\infty}…
Question Number 12109 by FilupS last updated on 13/Apr/17 $$\mathrm{show}\:\mathrm{that}: \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} }{{n}}=\mathrm{ln}\left(\mathrm{2}\right) \\ $$$$\mathrm{please}\:\mathrm{show}\:\mathrm{your}\:\mathrm{working} \\ $$ Terms of Service Privacy Policy Contact:…