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A-particle-Q-is-moving-with-constant-velocity-5i-3j-m-s-At-time-t-5sec-Q-is-at-the-same-point-with-position-vector-i-5j-m-Find-the-distance-of-Q-from-the-origin-at-time-t-2sec-

Question Number 191052 by otchereabdullai last updated on 17/Apr/23 $${A}\:{particle}\:{Q}\:{is}\:{moving}\:{with}\:{constant} \\ $$$${velocity}\:\left(−\mathrm{5}{i}+\mathrm{3}{j}\right){m}/{s}.\:{At}\:{time}\: \\ $$$${t}=\mathrm{5}{sec}\:,\:{Q}\:{is}\:{at}\:{the}\:{same}\:{point}\:{with} \\ $$$${position}\:{vector}\:\left(−{i}−\mathrm{5}{j}\right){m}.\:{Find}\:{the} \\ $$$${distance}\:{of}\:{Q}\:{from}\:{the}\:{origin}\:{at}\: \\ $$$${time}\:{t}=\mathrm{2}{sec} \\ $$ Answered by mr…

if-f-x-f-x-for-x-R-3-3-f-x-dx-0-2-3-f-x-dx-5-then-0-2-f-x-dx-

Question Number 125511 by sandy_delta last updated on 11/Dec/20 $$\mathrm{if}\:: \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{f}\left(−\mathrm{x}\right)\:\mathrm{for}\:\mathrm{x}\in\mathbb{R} \\ $$$$\underset{−\mathrm{3}} {\overset{\mathrm{3}} {\int}}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}\:=\:\mathrm{0} \\ $$$$\underset{−\mathrm{2}} {\overset{\mathrm{3}} {\int}}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}\:=\:\mathrm{5} \\ $$$$\mathrm{then}\:\underset{\mathrm{0}} {\overset{\mathrm{2}} {\int}}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}\:=\:? \\…

Question-125482

Question Number 125482 by joki last updated on 11/Dec/20 Answered by MJS_new last updated on 11/Dec/20 $$\int\frac{\mathrm{4}{x}^{\mathrm{3}} +{x}^{\mathrm{2}} +\mathrm{1}}{\left({x}^{\mathrm{2}} −\mathrm{2}\right)^{\mathrm{3}} }{dx}= \\ $$$$\:\:\:\:\:\left[\mathrm{Ostrogradski}'\mathrm{s}\:\mathrm{Method}\right] \\ $$$$=\frac{{x}^{\mathrm{3}}…

f-2x-5-f-3x-5-7x-16-f-x-

Question Number 59942 by naka3546 last updated on 16/May/19 $${f}\left(\mathrm{2}{x}−\mathrm{5}\right)\:+\:{f}\left(\mathrm{3}{x}+\mathrm{5}\right)\:\:=\:\:\mathrm{7}{x}−\mathrm{16} \\ $$$${f}\left({x}\right)\:\:=\:\:? \\ $$ Answered by mr W last updated on 16/May/19 $${let}\:{f}\left({x}\right)={ax}+{b} \\ $$$${f}\left(\mathrm{2}{x}−\mathrm{5}\right)+{f}\left(\mathrm{3}{x}+\mathrm{5}\right)={a}\left(\mathrm{2}{x}−\mathrm{5}\right)+{b}+{a}\left(\mathrm{3}{x}+\mathrm{5}\right)+{b}…

Find-all-the-values-of-n-such-that-5-n-1-is-divisble-by-7-

Question Number 125471 by ZiYangLee last updated on 11/Dec/20 $$\mathrm{Find}\:\mathrm{all}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:{n}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{5}^{{n}} +\mathrm{1}\:\mathrm{is}\:\mathrm{divisble}\:\mathrm{by}\:\mathrm{7}. \\ $$ Answered by MJS_new last updated on 11/Dec/20 $$\mathrm{try}\:\mathrm{for}\:\mathrm{the}\:\mathrm{first}\:\mathrm{few}\:{n}\:\Rightarrow\:{n}=\mathrm{3}+\mathrm{6}{n} \\ $$…

Question-125450

Question Number 125450 by joki last updated on 11/Dec/20 Answered by Dwaipayan Shikari last updated on 11/Dec/20 $$\int\frac{\mathrm{2}{x}^{\mathrm{3}} \left({x}−\mathrm{1}\right)}{{x}^{\mathrm{2}} −{x}}+\frac{\mathrm{3}\left({x}^{\mathrm{2}} −\mathrm{1}\right)}{{x}^{\mathrm{2}} −{x}}+\frac{\mathrm{1}}{{x}\left({x}−\mathrm{1}\right)}{dx} \\ $$$$=\frac{\mathrm{2}}{\mathrm{3}}{x}^{\mathrm{3}} +\mathrm{3}{x}+\mathrm{3}{log}\left({x}\right)+{log}\left(\frac{{x}−\mathrm{1}}{{x}}\right)+{C}…