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Author: Tinku Tara

Let-u-n-be-a-set-satisfying-u-1-1-amp-u-n-1-u-n-ln-n-u-n-n-1-1-Prove-that-u-2023-gt-2023-ln-2023-2-Find-lim-n-u-n-ln-n-n-

Question Number 209631 by York12 last updated on 17/Jul/24 $$\mathrm{Let}\:{u}_{{n}} \:\mathrm{be}\:\mathrm{a}\:\mathrm{set}\:\mathrm{satisfying}\:{u}_{\mathrm{1}} =\mathrm{1}\:\&\:{u}_{{n}+\mathrm{1}} ={u}_{{n}} +\frac{\mathrm{ln}\:{n}}{{u}_{{n}} }\:\:,\:\forall\:{n}\:\geqslant\mathrm{1} \\ $$$$\mathrm{1}.\:\mathrm{Prove}\:\mathrm{that}\:{u}_{\mathrm{2023}} >\sqrt{\mathrm{2023}.\mathrm{ln}\:\mathrm{2023}}. \\ $$$$\mathrm{2}.\:\mathrm{Find}:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{{u}_{{n}} .\mathrm{ln}\:{n}}{{n}}. \\ $$ Terms…

Question-209639

Question Number 209639 by SonGoku last updated on 17/Jul/24 Commented by SonGoku last updated on 17/Jul/24 $$\mathrm{In}\:\mathrm{the}\:\mathrm{figure},\:\mathrm{DC}//\mathrm{FG}\:\mathrm{is}\:\mathrm{the}\:\mathrm{width}\:\mathrm{of}\:\mathrm{a}\:\mathrm{river}. \\ $$$$\mathrm{How}\:\mathrm{wideis}\:\mathrm{this}\:\mathrm{river}? \\ $$$$\left(\mathrm{How}\:\mathrm{do}\:\mathrm{I}\:\mathrm{solve}\:\mathrm{it}?\right) \\ $$ Answered by…

Question-209633

Question Number 209633 by Abdullahrussell last updated on 17/Jul/24 Answered by som(math1967) last updated on 17/Jul/24 $$\left({x}+\mathrm{1}\right)\left(\mathrm{3}{x}+\mathrm{2}\right)\left(\mathrm{6}{x}+\mathrm{5}\right)^{\mathrm{2}} =\mathrm{6} \\ $$$$\Rightarrow\left(\mathrm{3}{x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{2}\right)\left(\mathrm{36}{x}^{\mathrm{2}} +\mathrm{60}{x}+\mathrm{25}\right)=\mathrm{6} \\ $$$$\Rightarrow\left({a}+\mathrm{2}\right)\left(\mathrm{12}{a}+\mathrm{25}\right)=\mathrm{6} \\…

Question-209597

Question Number 209597 by peter frank last updated on 16/Jul/24 Answered by mr W last updated on 16/Jul/24 $${ma}={mg}\:\mathrm{sin}\:\theta−\mu{mg}\:\mathrm{cos}\:\theta \\ $$$$\frac{{a}}{{g}}=\mathrm{sin}\:\theta−\mu\:\mathrm{cos}\:\theta \\ $$$$\mu=\frac{\mathrm{1}}{\mathrm{cos}\:\theta}\left(\mathrm{sin}\:\theta−\frac{{a}}{{g}}\right) \\ $$$$\:\:\:=\frac{\mathrm{1}}{\mathrm{cos}\:\mathrm{60}°}\left(\mathrm{sin}\:\mathrm{60}°−\frac{\mathrm{1}}{\mathrm{2}}\right)…

If-A-varies-as-r-2-and-V-varies-as-r-3-find-percentage-increase-in-A-and-V-if-r-is-increased-by-20-

Question Number 209630 by otchereabdullai@gmail.com last updated on 16/Jul/24 $$\:\:{If}\:{A}\:\:{varies}\:{as}\:{r}^{\mathrm{2}} \:{and}\:{V}\:\:{varies}\:{as}\:{r}^{\mathrm{3}} \\ $$$$\:{find}\:{percentage}\:{increase}\:{in}\:{A}\:{and}\:{V} \\ $$$$\:{if}\:\:{r}\:{is}\:{increased}\:{by}\:\mathrm{20\%} \\ $$ Answered by som(math1967) last updated on 17/Jul/24 $$\:{A}\propto{r}^{\mathrm{2}}…