Question Number 143230 by qaz last updated on 11/Jun/21 $$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{x}^{\mathrm{3n}+\mathrm{1}} }{\mathrm{3n}+\mathrm{1}}=? \\ $$ Answered by mathmax by abdo last updated on 11/Jun/21 $$\mathrm{f}\left(\mathrm{x}\right)=\sum_{\mathrm{n}=\mathrm{o}}…
Question Number 12156 by tawa last updated on 15/Apr/17 $$\mathrm{If}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{the}\:\mathrm{students}\:\mathrm{that}\:\mathrm{pass}\:\mathrm{a}\:\mathrm{test}\:\mathrm{to}\:\mathrm{those}\:\mathrm{that}\:\mathrm{fail}\:\mathrm{is}\:\mathrm{in}\:\mathrm{ratio}\:\mathrm{4}:\mathrm{1}, \\ $$$$\mathrm{If}\:\:\mathrm{9}\:\mathrm{students}\:\mathrm{were}\:\mathrm{chosen}\:\mathrm{at}\:\mathrm{random},\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{exactly} \\ $$$$\mathrm{7}\:\mathrm{passed}\:\mathrm{the}\:\mathrm{test}. \\ $$ Answered by mrW1 last updated on 23/Apr/17 $${probability}\:{pass}\:{test}\:{p}=\frac{\mathrm{4}}{\mathrm{4}+\mathrm{1}}=\mathrm{0}.\mathrm{8} \\…
Question Number 143225 by Canebulok last updated on 11/Jun/21 $$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\:\:\frac{\mathrm{1}}{\left(\mathrm{2021}^{{n}} \right)\left({n}!\right)}\:=\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\:\:\:\frac{\mathrm{1}}{\left(\mathrm{2021}^{{n}} \right)\left(\int_{\mathrm{0}} ^{\:\infty} {t}^{{n}} .{e}^{−{t}} \:\:{dt}\right)} \\ $$ Answered by Dwaipayan…
Question Number 12155 by tawa last updated on 15/Apr/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{35th}\:\mathrm{derivative}\:\mathrm{of}\:\:\left(\mathrm{2x}^{\mathrm{3}} \:+\:\mathrm{5x}^{\mathrm{4}} \right)^{\mathrm{60}} \\ $$ Answered by mrW1 last updated on 15/Apr/17 $${y}=\left(\mathrm{2}{x}^{\mathrm{3}} +\mathrm{5}{x}^{\mathrm{4}} \right)^{\mathrm{60}} =\underset{{k}=\mathrm{0}}…
Question Number 77687 by jagoll last updated on 09/Jan/20 $${given}\:{function} \\ $$$${f}\left({x}\right)\:={f}\left({x}+\mathrm{2}\right)\:{for}\:\forall{x}\in\mathbb{R} \\ $$$${if}\:\underset{\mathrm{0}} {\overset{\mathrm{2}} {\int}}{f}\left({x}\right){dx}={B}\:,\:{what}\:{value}\:{of} \\ $$$$\underset{\mathrm{3}} {\overset{\mathrm{7}} {\int}}\:{f}\left({x}+\mathrm{8}\right){dx}\:=\:? \\ $$ Commented by mr…
Question Number 143222 by ZiYangLee last updated on 11/Jun/21 $$\mathrm{If}\:{z}=\mathrm{cos}\:\theta+{i}\:\mathrm{sin}\:\theta,\:\mathrm{by}\:\mathrm{expand} \\ $$$$\left({z}+\frac{\mathrm{1}}{{z}}\right)^{\mathrm{4}} \left({z}−\frac{\mathrm{1}}{{z}}\right)^{\mathrm{4}} \mathrm{or}\:\mathrm{other}\:\mathrm{method}, \\ $$$$\mathrm{prove}\:\mathrm{128}\:\mathrm{sin}^{\mathrm{4}} \theta\mathrm{cos}^{\mathrm{4}} \theta=\mathrm{cos}\:\mathrm{8}\theta−\mathrm{4cos}\:\mathrm{4}\theta+\mathrm{3}. \\ $$ Answered by Olaf_Thorendsen last updated…
Question Number 12148 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 14/Apr/17 Commented by b.e.h.i.8.3.4.1.7@gmail.com last updated on 14/Apr/17 $${OA}={OC}={OD}={OB}={R},{OE}=\frac{\sqrt{\mathrm{2}}}{\mathrm{2}} \\ $$$${BE}\bot{ED},{FG}\bot{CD},{FH}\bot{AB},\measuredangle{OEB}=\measuredangle{OED}. \\ $$$${find}:\:\:{HE}\:\:{and}\:{EG}\:{in}\:{term}\:{of}\::\:{R} \\ $$ Commented by…
Question Number 143219 by rs4089 last updated on 11/Jun/21 Commented by rs4089 last updated on 11/Jun/21 $${help}\:{me}\:{pleace} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 77681 by mr W last updated on 09/Jan/20 Commented by mr W last updated on 09/Jan/20 $${The}\:{radii}\:\boldsymbol{{a}},\:\boldsymbol{{b}},\:\boldsymbol{{c}}\:{are}\:{given}. \\ $$$$\mathrm{1}.\:{Find}\:{radius}\:\boldsymbol{{R}}\:{of}\:{the}\:{circumcircle} \\ $$$$\mathrm{2}.\:{Find}\:{radius}\:\boldsymbol{{d}}\:{of}\:{the}\:{fourth}\:{circle} \\ $$…
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…