Question Number 209670 by mokys last updated on 18/Jul/24 $${find}\:{the}\:{sum}\:{of}\:{sin}^{\mathrm{2}} \left(\mathrm{1}\right)+…+{sin}^{\mathrm{2}} \left(\mathrm{90}\right) \\ $$ Answered by Ar Brandon last updated on 18/Jul/24 $${S}=\underset{\theta=\mathrm{0}} {\overset{\mathrm{90}} {\sum}}\mathrm{sin}^{\mathrm{2}}…
Question Number 209671 by Ansu last updated on 18/Jul/24 $$\mathrm{5}{x}+\mathrm{3}{x}=\mathrm{10} \\ $$ Answered by SWPlaysMC last updated on 19/Jul/24 $${x}=\frac{\mathrm{5}}{\mathrm{4}} \\ $$ Answered by Frix…
Question Number 209696 by Ismoiljon_008 last updated on 18/Jul/24 Commented by Ismoiljon_008 last updated on 18/Jul/24 $${help}\:{me}\:{please} \\ $$$$ \\ $$ Terms of Service Privacy…
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 Number 209656 by Ismoiljon_008 last updated on 17/Jul/24 $$ \\ $$$$\:\:\:\mathrm{2}{cos}^{\mathrm{2}} {x}−\mathrm{3}{cosx}+{sinx}+\mathrm{1}=\mathrm{0} \\ $$$$\:\:\:{help} \\ $$$$ \\ $$ Answered by Berbere last updated on…
Question Number 209659 by mokys last updated on 17/Jul/24 Answered by efronzo1 last updated on 18/Jul/24 $$\:\:\:\mathrm{S}\:=\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\mathrm{2}^{\mathrm{x}} \:\mathrm{dx}\:+\:\underset{\mathrm{1}} {\overset{\sqrt{\mathrm{3}}} {\int}}\:\left(\mathrm{3}−\mathrm{x}^{\mathrm{2}} \right)\mathrm{dx} \\ $$…
Question Number 209637 by mr W last updated on 17/Jul/24 Commented by mr W last updated on 17/Jul/24 $${find}\:{minimum}\:{of}\:{AB}+{BC}+{CD}=? \\ $$ Commented by Frix last…
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 Number 209633 by Abdullahrussell last updated on 17/Jul/24 Answered by som(math1967) last updated on 17/Jul/24 $$\left({x}+\mathrm{1}\right)\left(\mathrm{3}{x}+\mathrm{2}\right)\left(\mathrm{6}{x}+\mathrm{5}\right)^{\mathrm{2}} =\mathrm{6} \\ $$$$\Rightarrow\left(\mathrm{3}{x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{2}\right)\left(\mathrm{36}{x}^{\mathrm{2}} +\mathrm{60}{x}+\mathrm{25}\right)=\mathrm{6} \\ $$$$\Rightarrow\left({a}+\mathrm{2}\right)\left(\mathrm{12}{a}+\mathrm{25}\right)=\mathrm{6} \\…
Question Number 209650 by Davidtim last updated on 17/Jul/24 $${if}\:{the}\:{acceleration}\:{is}\:{constant},\:{what}\: \\ $$$${will}\:{be}\:{the}\:{average}\:{and}\:{instantaneous} \\ $$$${accelerations}? \\ $$ Commented by mr W last updated on 18/Jul/24 $${if}\:{acc}.\:={constant}={a},\:{then}…