Question Number 126913 by TANMAY PANACEA last updated on 25/Dec/20 $${to}\:{Tinku}\:{tara} \\ $$$${equation}\:{editor}\:{is}\:{not}\:{available}\:{in}\:{playstore} \\ $$$${now}…{pls}\:{check}..{i}\:{suggested}\:{a}\:{few}\:{students} \\ $$$${to}\:{dowmload}\:{it} \\ $$ Commented by Tinku Tara last updated…
Question Number 192450 by Mastermind last updated on 18/May/23 $$\mathrm{The}\:\mathrm{first}\:\mathrm{term}\:\mathrm{of}\:\mathrm{an}\:\mathrm{arithmetic}\:\mathrm{series} \\ $$$$\mathrm{is}\:\mathrm{7}\:\mathrm{and}\:\mathrm{the}\:\mathrm{last}\:\mathrm{is}\:\mathrm{70}.\:\mathrm{and}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{is} \\ $$$$\mathrm{385}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{terms}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{series}\:\mathrm{and}\:\mathrm{its}\:\mathrm{common}\:\mathrm{difference}. \\ $$ Answered by AST last updated on 18/May/23…
The-sum-of-three-numbers-in-arith-metic-progression-is-18-and-sum-of-square-is-206-find-the-numbers-
Question Number 192444 by Mastermind last updated on 18/May/23 $$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{three}\:\mathrm{numbers}\:\mathrm{in}\:\mathrm{arith}- \\ $$$$\mathrm{metic}\:\mathrm{progression}\:\mathrm{is}\:\mathrm{18}\:\mathrm{and}\:\mathrm{sum}\:\mathrm{of} \\ $$$$\mathrm{square}\:\mathrm{is}\:\mathrm{206}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{numbers} \\ $$ Commented by Tinku Tara last updated on 19/May/23 $$\mathrm{Automatic}\:\mathrm{tagging}\:\mathrm{may}\:\mathrm{sometime}…
Question Number 192443 by Mastermind last updated on 18/May/23 $$\mathrm{Find}\:\mathrm{the}\:\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first}\:\mathrm{16th}\:\mathrm{term} \\ $$$$\:\mathrm{of}\:\mathrm{the}\:\mathrm{series}\:\mathrm{3}\frac{\mathrm{1}}{\mathrm{2}}\:+\:\mathrm{4}\frac{\mathrm{3}}{\mathrm{4}}\:+\:\mathrm{6}\:+\:\mathrm{7}\frac{\mathrm{1}}{\mathrm{4}}\:… \\ $$ Answered by AST last updated on 18/May/23 $${S}_{\mathrm{16}} =\mathrm{8}\left(\mathrm{7}+\frac{\mathrm{75}}{\mathrm{4}}\right)=\mathrm{56}+\mathrm{150}=\mathrm{206} \\ $$…
Question Number 126907 by Dwaipayan Shikari last updated on 25/Dec/20 $$\boldsymbol{{Merry}}\:\boldsymbol{{christmas}}\:!! \\ $$$$ \\ $$🎅🤶☃️🌄🎄🦌 $$ \\ $$$$ \\ $$🔔🔔🔔🔔🔔🔔🔔🔔🔔 🎄🎄🎄🎄🎄🎄🎄🎄 $$\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \frac{\boldsymbol{{tanh}}^{−\mathrm{1}} \boldsymbol{{x}}}{\:\sqrt[{\mathrm{5}}]{\boldsymbol{{x}}}}\boldsymbol{{dx}}…
Question Number 61327 by olalekan2 last updated on 01/Jun/19 Answered by mr W last updated on 01/Jun/19 $$\mathrm{1}. \\ $$$$\mathrm{5}^{\mathrm{5}} =\mathrm{3125} \\ $$$$ \\ $$$$\mathrm{2}.…
Question Number 192397 by Mastermind last updated on 16/May/23 $$\mathrm{Let}\:\mathrm{f}:\mathrm{D}\left(\mathrm{f}\right)\subseteq\mathbb{R}^{\mathrm{n}} \rightarrow\mathbb{R}^{\mathrm{m}} \\ $$$$\mathrm{let}\:'\mathrm{a}'\:\mathrm{be}\:\mathrm{an}\:\mathrm{interior}\:\mathrm{point}\:\mathrm{of}\:\mathrm{Dom}\left(\mathrm{f}\right) \\ $$$$\mathrm{and}\:\mathrm{let}\:'\mathrm{u}'\:\mathrm{be}\:\mathrm{any}\:\mathrm{vector}\:\mathrm{in}\:\mathbb{R}^{\mathrm{n}} ,\:\mathrm{when} \\ $$$$\mathrm{is}\:\mathrm{a}\:\mathrm{vector}\:\mathrm{v}\in\mathbb{R}^{\mathrm{m}} \:\mathrm{called}\:\mathrm{the}\:\mathrm{directional} \\ $$$$\mathrm{derivative}\:\mathrm{of}\:\mathrm{f}\:\mathrm{at}\:'\mathrm{a}'\:\mathrm{along}\:\mathrm{the}\:\mathrm{line} \\ $$$$\mathrm{determine}\:\mathrm{by}\:\mathrm{u}\:? \\ $$$$…
Question Number 192396 by moh777 last updated on 16/May/23 Answered by mehdee42 last updated on 16/May/23 $$\mathrm{4}{x}−{x}^{\mathrm{2}} =\mathrm{3}\Rightarrow{x}=\mathrm{1},\mathrm{3} \\ $$$${v}_{\mathrm{1}} =\pi\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{4}{x}−{x}^{\mathrm{2}} \right)^{\mathrm{2}} {dx}=\pi\int_{\mathrm{0}}…
Question Number 192398 by Mastermind last updated on 16/May/23 $$\mathrm{Let}\:\mathrm{f}:\mathbb{R}^{\mathrm{3}} \rightarrow\mathbb{R}\:\mathrm{be}\:\mathrm{define}\:\mathrm{by}\: \\ $$$$\mathrm{f}\left(\mathrm{x},\:\mathrm{y},\:\mathrm{z}\right)\:=\:\mathrm{2x}^{\mathrm{2}} −\mathrm{y}+\mathrm{6xy}−\mathrm{z}^{\mathrm{3}} +\mathrm{3z}. \\ $$$$\mathrm{calculate}\:\mathrm{the}\:\mathrm{directional}\:\mathrm{deriva}− \\ $$$$\mathrm{tive}\:\mathrm{of}\:\mathrm{the}\:\mathrm{vector}\:\mathrm{u}=\left(\mathrm{2},\:\mathrm{1},\:−\mathrm{3}\right) \\ $$$$ \\ $$$$\mathrm{help}! \\ $$…
Question Number 61318 by Tawa1 last updated on 31/May/19 Answered by tanmay last updated on 01/Jun/19 $$\overset{\rightarrow} {{V}}_{{train}\:{w}.{r}.{t}\:{ground}} =\left(\frac{\mathrm{64000}}{\mathrm{3600}}\right){m}/{s}\:\overset{\rightarrow} {{i}}=\left(\frac{\mathrm{160}}{\mathrm{9}}\right){m}/{s}\:\overset{\rightarrow} {{i}} \\ $$$$\overset{\rightarrow} {{V}}_{{rain}\:{w}.{r}.{t}\:{ground}} =\mathrm{5}{m}/{s}\:\left(−\overset{\rightarrow}…