Question Number 210324 by Ghisom last updated on 06/Aug/24 $$\mathrm{rationalize}\:\mathrm{the}\:\mathrm{denominator}: \\ $$$$\frac{\mathrm{1}}{{a}+{b}^{\mathrm{1}/\mathrm{3}} +{c}^{\mathrm{1}/\mathrm{3}} } \\ $$ Commented by Spillover last updated on 06/Aug/24 $${ans}\: \\…
Question Number 210326 by Shrodinger last updated on 06/Aug/24 $$\int_{\mathrm{0}} ^{\pi} \:\frac{{tsin}\left({t}\right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt} \\ $$ Commented by Spillover last updated on 06/Aug/24 $${i}\:{got}\:\mathrm{1}.\mathrm{6583}\:\:{is}\:{it}\:{right}? \\ $$…
Question Number 210297 by Spillover last updated on 05/Aug/24 $${Prove}\:{the}\:{theorem}. \\ $$$${A}\:{non}\:{empty}\:{subset}\:{W}\:\:{of}\:{a}\:{vector}\:{space}\:{V}\left({F}\right) \\ $$$${is}\:{the}\:{subset}\:{of}\:{V}\:\:{if}\:\:{and}\:{only}\:{if} \\ $$$$\alpha{W}_{\mathrm{1}} +\beta{W}_{\mathrm{2}} \:\in{W}\:\:\forall\alpha,\beta\:\in\:{F}\:\:{and}\:{W}_{\mathrm{1}} ,{W}_{\mathrm{2}} \:\in{W} \\ $$ Terms of Service…
Question Number 210298 by Spillover last updated on 05/Aug/24 $${For}\:{the}\:{given}\:{system}\:{of}\:{simultaneous}\: \\ $$$${linear}\:{equation} \\ $$$$\mathrm{2}{x}_{\mathrm{1}} −\mathrm{2}{x}_{\mathrm{2}} +\mathrm{3}{x}_{\mathrm{3}} +\mathrm{4}{x}_{\mathrm{4}} −{x}_{\mathrm{5}} =\mathrm{0} \\ $$$$−{x}_{\mathrm{3}} −\mathrm{2}{x}_{\mathrm{4}} +\mathrm{3}{x}_{\mathrm{5}} =\mathrm{0} \\…
Question Number 210292 by 281981 last updated on 05/Aug/24 Commented by mr W last updated on 05/Aug/24 $${all}\:{answers}\:{are}\:{wrong}! \\ $$ Answered by mr W last…
Question Number 210295 by ibrahimmatematic last updated on 05/Aug/24 Commented by Frix last updated on 05/Aug/24 $$\mathrm{Question}\:\mathrm{210289} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 210289 by Abdullahrussell last updated on 05/Aug/24 Answered by Frix last updated on 05/Aug/24 $$\mathrm{There}'\mathrm{s}\:\mathrm{one}\:\mathrm{number}\:{x}\:\mathrm{with}\:\mathrm{nice}\:\mathrm{properties}: \\ $$$${x}^{\mathrm{2}} ={x}+\mathrm{1},\:{x}^{\mathrm{3}} =\mathrm{2}{x}+\mathrm{1}, \\ $$$$\frac{\mathrm{1}}{{x}}={x}−\mathrm{1},\:\frac{\mathrm{1}}{{x}^{\mathrm{2}} }=\mathrm{2}−{x},\:\frac{\mathrm{1}}{{x}^{\mathrm{3}} }=\mathrm{2}{x}−\mathrm{1}…
Question Number 210290 by Adeyemi889 last updated on 05/Aug/24 Answered by mr W last updated on 05/Aug/24 $$\left({i}\right) \\ $$$${C}_{\mathrm{3}} ^{\mathrm{7}} {C}_{\mathrm{3}} ^{\mathrm{6}} =\mathrm{700}\:{ways} \\…
Question Number 210291 by Ismoiljon_008 last updated on 05/Aug/24 Answered by mr W last updated on 06/Aug/24 $${x}=\sqrt{{x}^{\mathrm{2}} }=\sqrt{\mathrm{2}^{\mathrm{2}} +{x}^{\mathrm{2}} −\mathrm{2}^{\mathrm{2}} }=\sqrt{\mathrm{2}^{\mathrm{2}} +\left({x}−\mathrm{2}\right)\left({x}+\mathrm{2}\right)} \\ $$$$=\sqrt{\mathrm{2}^{\mathrm{2}}…
Question Number 210308 by Spillover last updated on 05/Aug/24 $${Evaluate}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\int\frac{\mathrm{2}{y}^{\mathrm{4}} }{{y}^{\mathrm{3}} −{y}^{\mathrm{2}} +{y}−\mathrm{1}}{dy} \\ $$ Commented by Frix last updated on 06/Aug/24 $$\mathrm{Simply}\:\mathrm{expand}\:\mathrm{it}:…