Question Number 208259 by hardmath last updated on 09/Jun/24 Answered by cherokeesay last updated on 09/Jun/24 Answered by mr W last updated on 09/Jun/24 Commented…
Question Number 208238 by alcohol last updated on 08/Jun/24 $$\mathrm{S}{how}\:{that} \\ $$$$\frac{\pi}{\mathrm{4}}\:<\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\sqrt{\mathrm{1}−{x}^{\mathrm{4}} }{dx}\:{using}\:{x}\:=\:{sint} \\ $$$${show}\:{that}\:\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}−{x}^{\mathrm{4}} }{dx}<\frac{\mathrm{2}\sqrt{\mathrm{2}}}{\mathrm{3}} \\ $$$${using}\:\left(\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({x}\right){g}\left({x}\right){dx}\right)^{\mathrm{2}} <\int_{\mathrm{0}}…
Question Number 208235 by efronzo1 last updated on 08/Jun/24 Answered by som(math1967) last updated on 08/Jun/24 $$\:{here}\:{f}\left({x}\right)={f}^{−\mathrm{1}} \left({x}\right) \\ $$$$\:\underset{\mathrm{2}} {\overset{\mathrm{4}} {\int}}\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}{dx} \\ $$$$=\underset{\mathrm{2}} {\overset{\mathrm{4}}…
Question Number 208245 by Shrodinger last updated on 08/Jun/24 $${K}=\int_{\mathrm{0}} ^{\frac{\mathrm{4}}{\pi}} {ln}\left({cosx}\right){dx} \\ $$ Answered by mathzup last updated on 09/Jun/24 $${K}=\int_{\mathrm{0}} ^{\frac{\mathrm{4}}{\pi}} {ln}\left(\frac{{e}^{{ix}} +{e}^{−{ix}}…
Question Number 208241 by Frix last updated on 08/Jun/24 $$\mathrm{Solve}\:\mathrm{for}\:{p},\:{q},\:{r} \\ $$$${p}+{q}+{r}=\alpha \\ $$$${p}^{\mathrm{2}} +{q}^{\mathrm{2}} +{r}^{\mathrm{2}} =\beta \\ $$$${pq}={r} \\ $$ Answered by mr W…
Question Number 208242 by alcohol last updated on 08/Jun/24 Commented by alcohol last updated on 08/Jun/24 $${please}\:{help}\:{me}\:{translate}\:{and}\:{solve} \\ $$ Answered by mr W last updated…
Question Number 208217 by mr W last updated on 07/Jun/24 $$\mathrm{1}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} +\mathrm{3}^{\mathrm{2}} +\mathrm{5}^{\mathrm{2}} +\mathrm{8}^{\mathrm{2}} +\mathrm{13}^{\mathrm{2}} +\mathrm{21}^{\mathrm{2}} =? \\ $$ Answered by A5T last updated…
Question Number 208218 by hardmath last updated on 07/Jun/24 $$\mathrm{a}_{\boldsymbol{\mathrm{n}}} \:\:\mathrm{numbers}\:\mathrm{series} \\ $$$$\mathrm{If}\:\:\mathrm{S}_{\mathrm{16}} \:−\:\mathrm{S}_{\mathrm{13}} \:\:=\:\:\mathrm{S}_{\mathrm{106}} \:−\:\mathrm{S}_{\mathrm{103}} \\ $$$$\mathrm{Find}:\:\:\:\:\frac{\mathrm{3a}_{\mathrm{3}} \:+\:\mathrm{4a}_{\mathrm{4}} \:+\:\mathrm{5a}_{\mathrm{5}} }{\mathrm{2a}_{\mathrm{12}} }\:\:=\:\:? \\ $$ Commented…
Question Number 208187 by hardmath last updated on 07/Jun/24 $$\mathrm{Find}:\:\:\:\mathrm{1},\mathrm{03}^{\mathrm{200}} \:=\:? \\ $$ Answered by Ghisom last updated on 07/Jun/24 $$=\mathrm{10}^{\mathrm{200log}\:\mathrm{1}.\mathrm{03}} \approx\mathrm{10}^{\mathrm{200}×.\mathrm{012837}} \approx\mathrm{10}^{\mathrm{2}.\mathrm{5675}} \approx\mathrm{369}.\mathrm{36} \\…
Question Number 208215 by MATHEMATICSAM last updated on 07/Jun/24 $$\mathrm{If}\:\frac{\mathrm{1}}{\mathrm{R}}\:=\:\frac{\mathrm{1}}{\mathrm{R}_{\mathrm{1}} }\:+\:\frac{\mathrm{1}}{\mathrm{R}_{\mathrm{2}} }\:\left[\mathrm{R}_{\mathrm{1}} ,\:\mathrm{R}_{\mathrm{2}} \:>\:\mathrm{0}\right]\:\mathrm{and}\: \\ $$$$\mathrm{R}_{\mathrm{1}} \:+\:\mathrm{R}_{\mathrm{2}} \:=\:\mathrm{C}\:\left(\mathrm{Constant}\right)\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\mathrm{R}\:\mathrm{will}\:\mathrm{be}\:\mathrm{maximum}\:\mathrm{when}\:\mathrm{R}_{\mathrm{1}} \:=\:\mathrm{R}_{\mathrm{2}} . \\ $$ Answered…