Question Number 13002 by Joel577 last updated on 10/May/17 $$\mathrm{3}^{\left({x}\:−\:\mathrm{3}\right)\left({x}\:−\:{y}\:−\:\mathrm{2}\right)} \:=\:\mathrm{1} \\ $$$$\mathrm{5}^{\left({x}^{\mathrm{2}} \:−\:\mathrm{2}{xy}\:+\:{y}^{\mathrm{2}} \:+\:{x}\:−\:{y}\:−\:\mathrm{3}/\mathrm{2}\right)} \:=\:\sqrt{\mathrm{5}} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x}\:\mathrm{and}\:{y} \\ $$ Answered by 433 last updated…
Question Number 144049 by physicstutes last updated on 20/Jun/21 $$\:\mathrm{Given}\:\mathrm{the}\:\mathrm{equation}\:\:\mathrm{1000}\:=\:\mathrm{2000}\left(\frac{\mathrm{1}−\left(\mathrm{1}+{t}\right)^{−{n}} }{{t}}\right) \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{t}. \\ $$ Answered by Olaf_Thorendsen last updated on 21/Jun/21 $$\mathrm{1000}\:=\:\mathrm{2000}\left(\frac{\mathrm{1}−\left(\mathrm{1}+{t}\right)^{−{n}} }{{t}}\right) \\…
Question Number 78503 by jagoll last updated on 18/Jan/20 $${if}\:{x},{y}\:>\mathrm{1}\: \\ $$$${prove}\:\frac{{x}^{\mathrm{2}} }{{y}−\mathrm{1}}+\frac{{y}^{\mathrm{2}} }{{x}−\mathrm{1}}\geqslant\mathrm{8} \\ $$ Answered by ~blr237~ last updated on 18/Jan/20 $$\:\mathrm{We}\:\mathrm{know}\:\mathrm{that}\:\mathrm{for}\:\mathrm{all}\:\mathrm{a},\mathrm{b}\in\mathbb{R}\: \\…
Question Number 144031 by mathdanisur last updated on 20/Jun/21 Answered by mindispower last updated on 20/Jun/21 $$\frac{\mathrm{1}}{{sin}\left(\mathrm{2}^{{k}} \right)}+\frac{\mathrm{1}}{{tg}\left(\mathrm{2}^{{k}} \right)}=\frac{\mathrm{1}+{cos}\left(\mathrm{2}{k}\right)}{{sin}\left(\mathrm{2}{k}\right)}=\frac{\mathrm{1}}{{tg}\left(\mathrm{2}^{{k}−\mathrm{1}} \right)} \\ $$$$\frac{\mathrm{1}}{{sin}\left(\mathrm{2}^{{k}} \right)}=\frac{\mathrm{1}}{{tg}\left(\mathrm{2}^{{k}−\mathrm{1}} \right)}−\frac{\mathrm{1}}{{tg}\left(\mathrm{2}^{{k}} \right)}…
Question Number 144021 by mathdanisur last updated on 20/Jun/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 78465 by TawaTawa last updated on 17/Jan/20 Answered by mind is power last updated on 17/Jan/20 $$\zeta\left(\mathrm{z}\right)=\underset{\mathrm{n}\geqslant\mathrm{1}} {\sum}\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{z}} } \\ $$$$\mathrm{Re}\left(\zeta\left(\mathrm{z}\right)\right)=\mathrm{Re}\left\{\underset{\mathrm{n}\geqslant\mathrm{1}} {\sum}\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{Re}\left(\mathrm{z}\right)+\mathrm{iIm}\left(\mathrm{z}\right)} }\right\}…
Question Number 12927 by satish1992.mishra@gmail.com last updated on 07/May/17 $$\Sigma\mathrm{cos}\:\left(\frac{\mathrm{1}}{{n}}\right) \\ $$ Commented by prakash jain last updated on 07/May/17 $${n}\:{from}\:\mathrm{0}\:{to}\:\infty? \\ $$$$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\mathrm{cos}\:\left(\frac{\mathrm{1}}{{n}}\right)?…
Question Number 78460 by Tony Lin last updated on 17/Jan/20 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{{n}^{\mathrm{3}} }{\mathrm{3}^{{n}} }=? \\ $$ Commented by mathmax by abdo last updated on…
Question Number 78449 by mathocean1 last updated on 17/Jan/20 $$\mathrm{find}\:\mathrm{the}\:\mathrm{domain}\:\mathrm{of}\:\mathrm{definition}\:\mathrm{of}\: \\ $$$$\mathrm{f}\left({x}\right)=\frac{−{x}}{\mid{x}\mid−{x}} \\ $$ Commented by Rio Michael last updated on 18/Jan/20 $${f}\left({x}\right)\:=\:\frac{{x}}{{x}−\mid{x}\mid} \\ $$$${so}\:{x}\:<\:\mathrm{0}\:{so}\:{that}\:{x}−\mid{x}\mid\:{should}\:{be}\:…
Question Number 143980 by mathdanisur last updated on 20/Jun/21 Answered by mitica last updated on 20/Jun/21 $${p}={a}+{b}+{c};{q}={ab}+{bc}+{ac};{r}={abc}\Rightarrow{q}^{\mathrm{2}} \geqslant\mathrm{3}{pr} \\ $$$$\mathrm{3}\Sigma\frac{{a}}{{b}}−\Sigma\frac{\mathrm{3}{a}+{b}+{c}}{{b}+{c}}=\mathrm{3}\Sigma\left(\frac{{a}}{{b}}−\frac{{a}}{{b}+{c}}\right)−\mathrm{3}= \\ $$$$\mathrm{3}\Sigma\frac{{ac}}{{b}\left({b}+{c}\right)}−\mathrm{3}=\frac{\mathrm{3}}{{abc}}\Sigma\frac{\left({ac}\right)^{\mathrm{2}} }{{b}+{c}}−\mathrm{3}\geqslant \\ $$$$\frac{\mathrm{3}}{{r}}\centerdot\frac{{q}^{\mathrm{2}}…