Question Number 197373 by sciencestudentW last updated on 15/Sep/23 Answered by Tokugami last updated on 17/Sep/23 $$\mathrm{6}\:\frac{\cancel{\mathrm{km}}}{\cancel{\mathrm{h}}}×\frac{\mathrm{1000}\:\mathrm{m}}{\mathrm{1}\:\cancel{\mathrm{km}}}×\frac{\mathrm{1}\:\cancel{\mathrm{h}}}{\mathrm{60}\:\mathrm{m}}=\mathrm{100}\:\frac{\mathrm{m}}{\mathrm{min}} \\ $$$$\mathrm{8}\:\frac{\cancel{\mathrm{km}}}{\cancel{\mathrm{h}}}×\frac{\mathrm{1000}\:\mathrm{m}}{\mathrm{1}\:\cancel{\mathrm{km}}}×\frac{\mathrm{1}\:\cancel{\mathrm{h}}}{\mathrm{60}\:\mathrm{m}}=\frac{\mathrm{400}}{\mathrm{3}}\:\frac{\mathrm{m}}{\mathrm{min}} \\ $$$$\frac{\mathrm{400}}{\mathrm{3}}{t}=\mathrm{250}+\mathrm{100}{t} \\ $$$$\frac{\mathrm{400}}{\mathrm{3}}{t}−\mathrm{100}{t}=\mathrm{250}+\mathrm{100}{t}−\mathrm{100}{t} \\ $$$$\frac{\mathrm{100}}{\mathrm{3}}{t}×\frac{\mathrm{3}}{\mathrm{100}}=\mathrm{250}×\frac{\mathrm{3}}{\mathrm{100}}…
Question Number 197374 by sciencestudentW last updated on 15/Sep/23 Answered by som(math1967) last updated on 15/Sep/23 $$\left.\boldsymbol{{C}}\right)\:\mathrm{792}{km} \\ $$ Answered by Tokugami last updated on…
Question Number 197384 by Erico last updated on 15/Sep/23 $$\mathrm{If}\:{f}\left({x}\right)=\underset{\:\frac{\mathrm{1}}{\mathrm{x}}} {\int}^{\:\:\mathrm{x}} \frac{{lnt}}{{t}^{\mathrm{2}} −\mathrm{1}}{arctan}\left({t}\right){dt} \\ $$$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\bullet\:\forall{x}>\mathrm{0}\:\:\:\:\:\:\:\:{f}\left({x}\right)=\:\frac{\pi}{\mathrm{8}}\:\underset{\:\mathrm{0}} {\int}^{\:\pi} \mathrm{arctan}\left[\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{x}−\frac{\mathrm{1}}{\mathrm{x}}\right)\mathrm{sint}\right]\mathrm{dt} \\ $$$$\bullet\underset{\mathrm{x}\rightarrow+\infty} {\mathrm{lim}}\:{f}\left({x}\right)=\frac{\pi^{\mathrm{3}} }{\mathrm{16}} \\ $$…
Question Number 197371 by Mastermind last updated on 15/Sep/23 Answered by Rasheed.Sindhi last updated on 15/Sep/23 $${d}:{dog},\:{c}:{cat},\:{r}:{rat} \\ $$$${d}+{r}=\mathrm{20}…\left({i}\right) \\ $$$${c}+{r}=\mathrm{10}…\left({ii}\right) \\ $$$${d}+{c}=\mathrm{24}…\left({iii}\right) \\ $$$$\left({i}\right)+\left({ii}\right)+\left({iii}\right):…
Question Number 197380 by mokys last updated on 15/Sep/23 Commented by witcher3 last updated on 19/Sep/23 $$\mathrm{verry}\:\mathrm{Nice}\:\mathrm{one} \\ $$$$\mathrm{nice}\:\mathrm{Result} \\ $$ Commented by mokys last…
Question Number 197365 by mokys last updated on 15/Sep/23 Answered by witcher3 last updated on 15/Sep/23 $$\mathrm{x}=\frac{\mathrm{1}−\mathrm{t}}{\mathrm{1}+\mathrm{t}} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\left(\frac{\mathrm{1}−\mathrm{t}}{\mathrm{1}+\mathrm{t}}\right)^{\mathrm{1}−\mathrm{p}} \left(\frac{\mathrm{2t}}{\mathrm{1}+\mathrm{t}}\right)^{\mathrm{p}} }{\left(\frac{\mathrm{2}}{\mathrm{1}+\mathrm{t}}\right)^{\mathrm{3}} }.\frac{\mathrm{2}}{\left(\mathrm{1}+\mathrm{t}\right)^{\mathrm{2}} }\mathrm{dt}…
Question Number 197383 by universe last updated on 15/Sep/23 $$\:{evaluate}\:\:\int_{\mathrm{1}/\mathrm{4}} ^{\mathrm{1}} \int_{\sqrt{{x}−{x}^{\mathrm{2}} }} ^{\sqrt{{x}}} \frac{{x}^{\mathrm{2}} −{y}^{\mathrm{2}} }{{x}^{\mathrm{2}} }{dydx}\:=\:?? \\ $$ Commented by Frix last updated…
Question Number 197367 by sonukgindia last updated on 15/Sep/23 Answered by Frix last updated on 15/Sep/23 $$\mathrm{3}\:\mathrm{equations}\:\&\:\mathrm{4}\:\mathrm{unknowns}\:\Rightarrow \\ $$$$\mathrm{no}\:\mathrm{unique}\:\mathrm{answer} \\ $$ Terms of Service Privacy…
Question Number 197376 by megrex last updated on 15/Sep/23 $${Does}\:{anyone}\:{know}\:{how}\:{to}\:{prove}\:{this}? \\ $$$$\:\:\:\:\:\:\:\:\:\:\int\int\int_{{V}} \:\frac{{dxdydz}}{\mathrm{1}+{x}^{\mathrm{4}} +{y}^{\mathrm{4}} +{z}^{\mathrm{4}} }\:=\frac{\Gamma^{\mathrm{4}} \left(\frac{\mathrm{1}}{\mathrm{4}}\right)}{\mathrm{4}^{\mathrm{4}} } \\ $$$${where}\:{V}\:{is}\:{the}\:{unit}\:{cube}\:\left[\mathrm{0},\mathrm{1}\right]^{\mathrm{3}} \\ $$$${Thankyou}. \\ $$$$ \\…
Question Number 197359 by sniper237 last updated on 14/Sep/23 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{\mathrm{1}−{cosxcos}\mathrm{2}{x}…{cos}\left({nx}\right)}{{x}^{\mathrm{2}} }\:=\:\frac{{n}\left({n}+\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{1}\right)}{\mathrm{12}}\: \\ $$ Commented by universe last updated on 16/Sep/23 Answered by witcher3 last…