Question Number 152946 by john_santu last updated on 03/Sep/21 $$\:\:\:\frac{\mathrm{4038}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{6}}+\frac{\mathrm{1}}{\mathrm{10}}+\frac{\mathrm{1}}{\mathrm{15}}+…+\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}+…+\mathrm{2019}}}\:=? \\ $$ Commented by mathdanisur last updated on 03/Sep/21 $$\blacktriangle\:\frac{\mathrm{2}\centerdot\mathrm{2019}}{\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{2}\:+\:\mathrm{3}}\:+\:…\:+\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{2}\:+\:\mathrm{3}\:+\:…\:+\:\mathrm{2019}}} \\ $$$$\boldsymbol{\mathrm{A}}\:=\:\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{2}\:+\:\mathrm{3}}\:+\:…\:+\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{2}\:+\:…\:+\:\mathrm{2019}} \\ $$$$\boldsymbol{\mathrm{A}}\:=\:\mathrm{1}\:+\:\frac{\mathrm{2}}{\mathrm{2}\centerdot\mathrm{3}}\:+\:\frac{\mathrm{2}}{\mathrm{3}\centerdot\mathrm{4}}\:+\:…\:+\:\frac{\mathrm{2}}{\mathrm{2019}\centerdot\mathrm{2020}} \\…
Question Number 87409 by redmiiuser last updated on 04/Apr/20 $$\int\left({sinx}\right)^{\frac{\mathrm{1}}{\mathrm{5}}} {dx} \\ $$ Commented by Prithwish Sen 1 last updated on 04/Apr/20 $$\int\frac{\mathrm{sin}^{\frac{\mathrm{1}}{\mathrm{5}}} \mathrm{x}\:\mathrm{cosx}}{\mathrm{cosx}}\:\mathrm{dx}\:\:\:\mathrm{put}\:\mathrm{sinx}\:=\:\mathrm{u}^{\mathrm{5}} \:\:\mathrm{cosxdx}\:=\:\mathrm{5u}^{\mathrm{4}}…
Question Number 152940 by nadovic last updated on 03/Sep/21 $$\:\mathrm{In}\:\mathrm{bottle}\:\mathrm{manufacturing}\:\mathrm{company},\:\mathrm{it} \\ $$$$\mathrm{was}\:\mathrm{observed}\:\mathrm{that}\:\mathrm{5\%}\:\mathrm{of}\:\mathrm{the}\:\mathrm{bottles} \\ $$$$\mathrm{manufactured}\:\mathrm{were}\:\mathrm{defective}.\:\mathrm{In}\:\mathrm{a}\: \\ $$$$\mathrm{random}\:\mathrm{sample}\:\mathrm{of}\:\mathrm{150}\:\mathrm{bottles},\:\mathrm{find}\: \\ $$$$\mathrm{probability}\:\mathrm{that}\: \\ $$$$\:\left({a}\right)\:\mathrm{exactly}\:\mathrm{3}, \\ $$$$\:\left({b}\right)\:\mathrm{between}\:\mathrm{3}\:\mathrm{and}\:\mathrm{6}, \\ $$$$\:\left({c}\right)\:\mathrm{at}\:\mathrm{most}\:\mathrm{4}, \\…
Question Number 21870 by Tinkutara last updated on 05/Oct/17 $$\mathrm{A}\:\mathrm{wire}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{9}.\mathrm{8}\:×\:\mathrm{10}^{−\mathrm{3}} \:\mathrm{kg}\:\mathrm{per}\:\mathrm{meter} \\ $$$$\mathrm{passes}\:\mathrm{over}\:\mathrm{a}\:\mathrm{frictionless}\:\mathrm{pulley}\:\mathrm{fixed} \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{top}\:\mathrm{of}\:\mathrm{an}\:\mathrm{inclined}\:\mathrm{frictionless} \\ $$$$\mathrm{plane}\:\mathrm{which}\:\mathrm{makes}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{30}°\:\mathrm{with} \\ $$$$\mathrm{the}\:\mathrm{horizontal}.\:\mathrm{Masses}\:{M}_{\mathrm{1}} \:\mathrm{and}\:{M}_{\mathrm{2}} \:\mathrm{are} \\ $$$$\mathrm{tied}\:\mathrm{at}\:\mathrm{the}\:\mathrm{two}\:\mathrm{ends}\:\mathrm{of}\:\mathrm{the}\:\mathrm{wire}.\:\mathrm{The} \\ $$$$\mathrm{mass}\:{M}_{\mathrm{1}}…
Question Number 152942 by mathlove last updated on 03/Sep/21 Commented by mathdanisur last updated on 03/Sep/21 $$\mathrm{8}\:=\:\mathrm{8}^{\boldsymbol{\mathrm{x}}} \:\Rightarrow\:\mathrm{x}\:=\:\mathrm{1} \\ $$ Answered by puissant last updated…
Question Number 152937 by DELETED last updated on 03/Sep/21 Answered by DELETED last updated on 03/Sep/21 $$\left.\mathrm{4}\right).\:\mathrm{mean}\rightarrow\overset{−} {\mathrm{x}}\:=\frac{\Sigma\mathrm{x}_{\mathrm{i}} ×\mathrm{f}_{\mathrm{i}} }{\Sigma\mathrm{f}_{\mathrm{i}} } \\ $$$$\:\:\:\:\:\overset{−} {\mathrm{x}}=\frac{\mathrm{4}×\mathrm{33}+\mathrm{7}×\mathrm{38}+\mathrm{9}×\mathrm{43}+\mathrm{6}×\mathrm{48}+\mathrm{4}×\mathrm{53}}{\mathrm{30}} \\…
Question Number 21867 by Tinkutara last updated on 05/Oct/17 $$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{points}\:\mathrm{in}\:\mathrm{the}\:\mathrm{cartesian} \\ $$$$\mathrm{plane}\:\mathrm{with}\:\mathrm{integral}\:\mathrm{coordinates} \\ $$$$\mathrm{satisfying}\:\mathrm{the}\:\mathrm{inequalities}\:\mid{x}\mid\:\leqslant\:\mathrm{4},\:\mid{y}\mid\:\leqslant \\ $$$$\mathrm{4}\:\mathrm{and}\:\mid{x}\:−\:{y}\mid\:\leqslant\:\mathrm{4}\:\mathrm{is} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 152939 by mnjuly1970 last updated on 03/Sep/21 $$ \\ $$$$\:\:\:\:\:\mathrm{Q}\::\:\:\mathrm{If}\:\:\:\:{a}\:\:,\:\:{b}\:\:\:\:\mathrm{are}\:\mathrm{positive}\:\mathrm{numbers}\:\:\mathrm{and} \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\begin{cases}{\:\:{a}\:=\:\mathrm{1}\:+\:\sqrt[{\mathrm{3}}]{\:\mathrm{6}{a}\:−\mathrm{2}}\:\:}\\{\:\:\:{b}\:=\:\mathrm{1}\:+\:\sqrt[{\mathrm{3}}]{\:\mathrm{6}{b}\:−\mathrm{2}}}\end{cases} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:,\:\:\:\:{a}.{b}\:=? \\ $$$$\:\:\:\:…\:\mathrm{Compiled}\:\mathrm{by}\:\mathrm{m}.\mathrm{n}\::\:\left(\mathscr{E}\:{lementary}\:{olympiad}\:\right).\:\:\:\:\:\:\blacksquare \\ $$$$ \\ $$ Answered…
Question Number 87398 by jagoll last updated on 04/Apr/20 $$\mathrm{dear}\:\mathrm{mr}\:\mathrm{w} \\ $$$$\mathrm{a}_{\mathrm{n}+\mathrm{2}} \:=\:\mathrm{a}_{\mathrm{n}+\mathrm{1}} \:−\:\mathrm{a}_{\mathrm{n}} \\ $$$$\mathrm{find}\:\mathrm{a}_{\mathrm{n}} \\ $$ Commented by mr W last updated on…
Question Number 152935 by DELETED last updated on 03/Sep/21 Answered by DELETED last updated on 03/Sep/21 $$\left.\mathrm{3}.\mathrm{a}\right).\:\mathrm{Q}_{\mathrm{2}} =\mathrm{L}_{\mathrm{i}} +\left(\frac{\mathrm{N}/\mathrm{2}−<\Sigma\mathrm{f}}{\Sigma\mathrm{f}_{\mathrm{i}} }\right)×\mathrm{C} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\left(\mathrm{45}−\mathrm{0}.\mathrm{5}\right)+\left(\frac{\mathrm{40}/\mathrm{2}−\mathrm{16}}{\mathrm{12}}\right)×\mathrm{5} \\ $$$$\:\:\:\:\:=\mathrm{44},\mathrm{5}+\frac{\mathrm{4}×\mathrm{5}}{\mathrm{12}}=\mathrm{44},\mathrm{5}+\mathrm{1},\mathrm{67} \\…