Question Number 17714 by tawa tawa last updated on 09/Jul/17 $$\mathrm{Two}\:\mathrm{boys}\:\mathrm{pull}\:\mathrm{a}\:\mathrm{cart}\:\mathrm{with}\:\mathrm{two}\:\mathrm{a}\:\mathrm{rope}\:\mathrm{along}\:\mathrm{the}\:\mathrm{horizontal}.\:\mathrm{if}\:\mathrm{the}\:\mathrm{two}\:\mathrm{boy} \\ $$$$\mathrm{exact}\:\mathrm{a}\:\mathrm{force}\:\mathrm{of}\:\mathrm{50N}\:\mathrm{each}.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{resultant}\:\mathrm{force}\:\mathrm{on}\:\mathrm{the}\:\mathrm{cart}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 17713 by tawa tawa last updated on 09/Jul/17 $$\mathrm{Evaluate}:\:\:\:\:\left(−\sqrt{\mathrm{3}}\right)^{\left(−\sqrt{\mathrm{2}}\right)} \\ $$ Commented by b.e.h.i.8.3.417@gmail.com last updated on 09/Jul/17 $${a}=\left(−\sqrt{\mathrm{3}}\right)^{\left(−\sqrt{\mathrm{2}}\right)} \\ $$$${lna}=−\sqrt{\mathrm{2}}{ln}\left(−\sqrt{\mathrm{3}}\right)=−\sqrt{\mathrm{2}}{ln}\left({i}^{\mathrm{2}} \sqrt{\mathrm{3}}\right)= \\…
Question Number 83246 by mathmax by abdo last updated on 29/Feb/20 $${fnd}\:\int\:{xe}^{−{x}^{\mathrm{2}} } {arctan}\left(\mathrm{1}−\frac{\mathrm{1}}{{x}}\right){dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 148780 by Jonathanwaweh last updated on 31/Jul/21 Answered by Kamel last updated on 31/Jul/21 $$ \\ $$$$\Omega=\underset{{n}=\mathrm{2}} {\overset{+\infty} {\prod}}{e}\left(\mathrm{1}−\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\right)^{{n}^{\mathrm{2}} } ={e}^{\underset{{n}=\mathrm{2}} {\overset{+\infty}…
Question Number 148783 by 0731619 last updated on 31/Jul/21 Commented by hknkrc46 last updated on 31/Jul/21 $$\left(\mathrm{1}\right)\:\underset{\boldsymbol{{h}}\:\rightarrow\:\mathrm{0}} {\mathrm{lim}}\frac{\boldsymbol{{f}}\left(\boldsymbol{{x}}\:+\:\boldsymbol{{h}}\right)\:−\:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)}{\boldsymbol{{h}}}\: \\ $$$$=\:\underset{\boldsymbol{{h}}\:\rightarrow\:\mathrm{0}} {\mathrm{lim}}\frac{−\mathrm{cos}\:\left(\boldsymbol{{x}}\:+\:\boldsymbol{{h}}\right)\:+\:\mathrm{cos}\:\boldsymbol{{x}}}{\boldsymbol{{h}}} \\ $$$$=\:\underset{\boldsymbol{{h}}\:\rightarrow\:\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{cos}\:\boldsymbol{{x}}\:−\:\mathrm{cos}\:\boldsymbol{{x}}\:\centerdot\:\mathrm{cos}\:\boldsymbol{{h}}\:+\:\mathrm{sin}\:\boldsymbol{{x}}\:\centerdot\:\mathrm{sin}\:\boldsymbol{{h}}}{\boldsymbol{{h}}} \\…
Question Number 83245 by mathmax by abdo last updated on 29/Feb/20 $${let}\:{f}\left({x}\right)\:={e}^{−\mathrm{2}{x}} {ln}\left(\mathrm{1}+\mathrm{2}{x}\right) \\ $$$$\left.\mathrm{1}\right)\:{find}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right){developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$ Commented by mathmax by…
Question Number 83242 by peter frank last updated on 29/Feb/20 Commented by john santu last updated on 29/Feb/20 $$\left(\mathrm{4b}\right)\:\underset{\mathrm{r}\:=\:\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mathrm{r}\left(\mathrm{r}+\mathrm{1}\right)\:=\:\underset{\mathrm{r}\:=\:\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mathrm{r}^{\mathrm{2}} \:+\:\underset{\mathrm{r}\:=\:\mathrm{1}} {\overset{\mathrm{n}}…
Question Number 148776 by liberty last updated on 31/Jul/21 Answered by mathmax by abdo last updated on 31/Jul/21 $$\mathrm{P}=\prod_{\mathrm{k}=\mathrm{2}} ^{\mathrm{2020}} \:\frac{\mathrm{k}^{\mathrm{2}} }{\mathrm{k}^{\mathrm{2}} −\mathrm{1}}=\prod_{\mathrm{k}=\mathrm{2}} ^{\mathrm{2020}} \:\frac{\mathrm{k}}{\mathrm{k}−\mathrm{1}}×\frac{\mathrm{k}}{\mathrm{k}+\mathrm{1}}…
Question Number 83240 by peter frank last updated on 28/Feb/20 Commented by peter frank last updated on 29/Feb/20 $${help}\:{b} \\ $$ Terms of Service Privacy…
Question Number 17704 by Tinkutara last updated on 09/Jul/17 $$\mathrm{A}\:\mathrm{monkey}\:\mathrm{climbs}\:\mathrm{up}\:\mathrm{a}\:\mathrm{slippery}\:\mathrm{pole}\:\mathrm{for} \\ $$$$\mathrm{3}\:\mathrm{seconds}\:\mathrm{and}\:\mathrm{subsequently}\:\mathrm{slips}\:\mathrm{for}\:\mathrm{3} \\ $$$$\mathrm{seconds}.\:\mathrm{Its}\:\mathrm{velocity}\:\mathrm{at}\:\mathrm{time}\:{t}\:\mathrm{is}\:\mathrm{given} \\ $$$$\mathrm{by}\:{v}\:\left({t}\right)\:=\:\mathrm{2}{t}\left(\mathrm{3}\:−\:{t}\right)\:;\:\mathrm{0}\:<\:{t}\:<\:\mathrm{3}\:\mathrm{and} \\ $$$${v}\:\left({t}\right)\:=\:−\:\left({t}\:−\:\mathrm{3}\right)\left(\mathrm{6}\:−\:{t}\right)\:\mathrm{for}\:\mathrm{3}\:<\:{t}\:<\:\mathrm{6}\:\mathrm{s} \\ $$$$\mathrm{in}\:\mathrm{m}/\mathrm{s}.\:\mathrm{It}\:\mathrm{repeats}\:\mathrm{this}\:\mathrm{cycle}\:\mathrm{till}\:\mathrm{it} \\ $$$$\mathrm{reaches}\:\mathrm{the}\:\mathrm{height}\:\mathrm{of}\:\mathrm{20}\:\mathrm{m}.\:\mathrm{At}\:\mathrm{what} \\ $$$$\mathrm{time}\:\mathrm{is}\:\mathrm{its}\:\mathrm{average}\:\mathrm{velocity}\:\mathrm{maximum}? \\…