Question Number 11754 by Joel576 last updated on 31/Mar/17 $$\mathrm{How}\:\mathrm{many}\:\mathrm{numbers}\:\mathrm{between}\:\mathrm{1}\:−\:\mathrm{2017} \\ $$$$\mathrm{that}\:\mathrm{aren}'\mathrm{t}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{5},\:\mathrm{6},\:\mathrm{7},\:\mathrm{8}\:? \\ $$ Answered by mrW1 last updated on 31/Mar/17 $${let}\:{a}={count}\:{of}\:{numbers}\:{which}\:{are}\:{multiple}\:{of}\:\mathrm{5} \\ $$$${let}\:{b}={count}\:{of}\:{numbers}\:{which}\:{are}\:{multiple}\:{of}\:\mathrm{6} \\…
Question Number 11753 by Joel576 last updated on 31/Mar/17 $${a},\:{b},\:{c}\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{from}\:\mathrm{equation}\:{x}^{\mathrm{3}} \:−\:\mathrm{5}{x}^{\mathrm{2}} \:−\:\mathrm{9}{x}\:+\:\mathrm{10}\:=\:\mathrm{0} \\ $$$$\mathrm{If}\:{P}\left({x}\right)\:=\:{Ax}^{\mathrm{3}} \:+\:{Bx}^{\mathrm{2}} \:+\:{Cx}\:−\:\mathrm{2015}\:\mathrm{and} \\ $$$${P}\left({a}\right)\:=\:{b}\:+\:{c}\: \\ $$$${P}\left({b}\right)\:=\:{a}\:+\:{c} \\ $$$${P}\left({c}\right)\:=\:{a}\:+\:{b} \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{A}\:+\:{B}\:+\:{C}\:? \\…
Question Number 142822 by aupo14 last updated on 05/Jun/21 Answered by MJS_new last updated on 06/Jun/21 $${x}^{\mathrm{2}} ={i}+{x}\:\Rightarrow\:{x}=\frac{\mathrm{1}+\sqrt{\mathrm{1}+\mathrm{4i}}}{\mathrm{2}}=\frac{\mathrm{2}+\sqrt{\mathrm{2}\left(\mathrm{1}+\sqrt{\mathrm{17}}\right)}}{\mathrm{4}}+\frac{\sqrt{\mathrm{2}\left(−\mathrm{1}+\sqrt{\mathrm{17}}\right)}}{\mathrm{4}}\mathrm{i} \\ $$$$\mathrm{the}\:\mathrm{other}\:\mathrm{solution}\:\mathrm{doesn}'\mathrm{t}\:\mathrm{fit}\:\left(\mathrm{just}\:\mathrm{give}\:\mathrm{it}\:\mathrm{a}\:\mathrm{try}\right) \\ $$ Terms of Service…
Question Number 11748 by tawa last updated on 30/Mar/17 $$\mathrm{Solve}\:\mathrm{simultaneously} \\ $$$$\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{4y}^{\mathrm{2}} \:+\:\mathrm{xy}\:=\:\mathrm{6}\:\:\:\:\:…………..\:\mathrm{equation}\:\left(\mathrm{i}\right) \\ $$$$\mathrm{3x}^{\mathrm{2}} \:+\:\mathrm{8y}^{\mathrm{2}} \:=\:\mathrm{14}\:\:\:\:\:\:\:\:\:\:\:…………..\:\mathrm{equation}\:\left(\mathrm{ii}\right) \\ $$ Answered by mrW1 last updated…
Question Number 11741 by uni last updated on 30/Mar/17 $$\int\mathrm{xtan}^{\mathrm{2}} \:\mathrm{x}\:\mathrm{dx}=? \\ $$ Answered by mrW1 last updated on 30/Mar/17 $$\int{x}\mathrm{tan}^{\mathrm{2}} \:{x}\:{dx}=\int\mathrm{tan}^{\mathrm{2}} \:{x}\:{d}\left(\frac{{x}^{\mathrm{2}} }{\mathrm{2}}\right) \\…
Question Number 142814 by mathdanisur last updated on 05/Jun/21 Commented by mr W last updated on 05/Jun/21 $${what}\:{do}\:{you}\:{mean}\:{with}\:{F}={R}\centerdot{EF}? \\ $$ Commented by mathdanisur last updated…
Question Number 11714 by Nayon last updated on 30/Mar/17 $${Solve}\:{the}\:{Crazy}\:{equation}… \\ $$$${x}\left({lnx}\right)^{\mathrm{2}} +{xlnx}−\mathrm{1}=\mathrm{0} \\ $$ Commented by mrW1 last updated on 30/Mar/17 $$\mathrm{ln}\:{x}=\frac{\sqrt{\mathrm{1}+\frac{\mathrm{4}}{{x}}}−\mathrm{1}}{\mathrm{2}}\:\: \\ $$$${I}\:{don}'{t}\:{think}\:{there}\:{is}\:{an}\:{analytical}…
Question Number 11707 by Nayon last updated on 30/Mar/17 $$ \\ $$$$ \\ $$$${ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d}=\mathrm{0} \\ $$$${pls}.\:{solve}\:{it}\:{in}\:{a}\:{alzebric}\:{way}\:, \\ $$$${that}\:{a}\:{O}\:{level}\left({ssc}\right)\:{student}\:{can} \\ $$$${understand}… \\ $$$$ \\…
Question Number 77219 by john santu last updated on 04/Jan/20 $${if}\:\mathrm{log}_{\mathrm{9}} \left({a}\right)=\mathrm{log}_{\mathrm{4}} \left({a}+{b}\right)=\mathrm{log}_{\mathrm{6}} \left({b}\right)\: \\ $$$${what}\:{is}\:\frac{{a}}{{b}}\:? \\ $$ Answered by jagoll last updated on 04/Jan/20…
Question Number 77204 by mr W last updated on 04/Jan/20 $${is}\:{there}\:{a}\:{general}\:{solution}\:{for} \\ $$$${the}\:{equation} \\ $$$$\underset{{n}\:{times}\:{x}} {\boldsymbol{{x}}\left[\boldsymbol{{x}}\left[\boldsymbol{{x}}\left[\boldsymbol{{x}}…\right]\right]\right]}=\boldsymbol{{m}} \\ $$$${with}\:{x}>\mathrm{0},\:{m}>\mathrm{0}. \\ $$ Commented by MJS last updated…