Question Number 200051 by cortano12 last updated on 13/Nov/23 $$ \\ $$$$\mathrm{There}\:\mathrm{are}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{to}\:\mathrm{arrange}\:\mathrm{3}\:\mathrm{red} \\ $$$$\:\mathrm{balls}\:\mathrm{and}\:\mathrm{9}\:\mathrm{black}\:\mathrm{balls}\:\mathrm{in}\:\mathrm{a}\:\mathrm{circle}\: \\ $$$$\mathrm{so}\:\mathrm{that}\:\mathrm{there}\:\mathrm{are}\:\mathrm{a}\:\mathrm{minimum}\:\mathrm{of}\:\mathrm{2} \\ $$$$\mathrm{black}\:\mathrm{balls}\:\mathrm{between}\:\mathrm{2}\:\mathrm{adjacent}\:\mathrm{red} \\ $$$$\mathrm{balls}. \\ $$$$\left(\mathrm{a}\right)\:\mathrm{180}×\mathrm{8}!\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{240}×\mathrm{7}!\:\:\:\:\left(\mathrm{c}\right)\:\mathrm{364}×\mathrm{6}! \\ $$$$\:\left(\mathrm{d}\right)\:\mathrm{282}×\mathrm{4}!\:\:\:\:\left(\mathrm{e}\right)\:\mathrm{144}×\mathrm{5}!\: \\…
Question Number 200075 by sonukgindia last updated on 13/Nov/23 Answered by ajfour last updated on 13/Nov/23 $${R}\mathrm{cos}\:\theta=\frac{{a}+{b}}{\mathrm{2}} \\ $$$${R}={b}\mathrm{cos}\:\theta \\ $$$$\Rightarrow\:\:\mathrm{2}{b}\mathrm{cos}\:^{\mathrm{2}} \theta={a}+{b} \\ $$$$\frac{{a}}{{b}}=\mathrm{2cos}\:^{\mathrm{2}} \theta−\mathrm{1}…
Question Number 200102 by Blackpanther last updated on 13/Nov/23 Answered by som(math1967) last updated on 14/Nov/23 $$\:{E}\:{is}\:{mid}\:{pt}\:{of}\:{AC}\:{and}\:{AB}\parallel{DE} \\ $$$$\therefore\:{D}\:{is}\:{mid}\:{pt}\:{of}\:{BC} \\ $$$$\mathrm{2}{ar}\bigtriangleup{ABD}={ar}\bigtriangleup{ABC} \\ $$$$\:{AB}\parallel{DE}\:\therefore\:{ar}\bigtriangleup{ADE}={ar}\bigtriangleup{ABD} \\ $$$${ar}\:\bigtriangleup{ADE}=\bigtriangleup{AEF}+\bigtriangleup{EFD}…
Question Number 200066 by hardmath last updated on 13/Nov/23 $$\mathrm{If}\:\:\:\frac{\mathrm{1}\:+\:\mathrm{x}}{\:\sqrt{\mathrm{3}}}\:=\:\mathrm{3}\:\:\:\mathrm{find}\:\:\:\mathrm{x}\:+\:\frac{\mathrm{1}}{\mathrm{x}}\:−\:\mathrm{1}\:=\:? \\ $$ Answered by Frix last updated on 13/Nov/23 $${x}=−\mathrm{1}+\mathrm{3}\sqrt{\mathrm{3}}\:\Rightarrow\:\frac{\mathrm{1}}{{x}}=\frac{\mathrm{1}+\mathrm{3}\sqrt{\mathrm{3}}}{\mathrm{26}}\:\Rightarrow\:{x}+\frac{\mathrm{1}}{{x}}−\mathrm{1}=\frac{−\mathrm{51}+\mathrm{81}\sqrt{\mathrm{3}}}{\mathrm{26}} \\ $$ Commented by hardmath…
Question Number 199996 by jlewis last updated on 12/Nov/23 $$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{first}\:\mathrm{order}\:\mathrm{energy}\:\mathrm{correction}\:\mathrm{for} \\ $$$$\mathrm{1}−\mathrm{dimensional}\:\mathrm{non}−\mathrm{degenerate}\:\mathrm{anharmonic} \\ $$$$\mathrm{oscillator}\:\mathrm{whose}\:\mathrm{harmiltonian}\:\mathrm{is}\:\mathscr{H}\underline{\mathscr{L}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 200048 by Calculusboy last updated on 12/Nov/23 Commented by 0670322918 last updated on 13/Nov/23 $$\int\frac{{tan}^{−\mathrm{1}} \left({x}\right)}{\int{tan}^{−\mathrm{1}} \left({x}\right){dx}}{dx}= \\ $$$${f}\left({x}\right)=\int{tan}^{−\mathrm{1}} \left({x}\right){dx}={xtan}^{−\mathrm{1}} \left({x}\right)−\frac{\mathrm{1}}{\mathrm{2}}{ln}\left({x}^{\mathrm{2}} +\mathrm{1}\right)+{c} \\…
Question Number 200040 by mnjuly1970 last updated on 12/Nov/23 $$ \\ $$$$\:\:\:\:\:{Q}:\:\:{If}\:\:,\:\:{tan}\left(\frac{\pi}{\mathrm{4}}\:−\alpha\:\right)=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\:\Rightarrow{Find}\:{the}\:{value}\:{of}\:,\:{tan}\left(\mathrm{4}\alpha\right)=? \\ $$$$ \\ $$ Answered by witcher3 last updated on 12/Nov/23…
Question Number 200041 by depressiveshrek last updated on 12/Nov/23 $${By}\:{strong}\:{induction}\:{prove}\:{that}\:{any} \\ $$$${natural}\:{number}\:{equal}\:{to}\:{or}\:{bigger}\:{than} \\ $$$$\mathrm{8}\:{can}\:{be}\:{written}\:{as}\:\mathrm{3}{a}+\mathrm{5}{b}\:{where}\:{a}\:{and}\:{b} \\ $$$${are}\:{non}−{negative}\:{integers}. \\ $$ Answered by des_ last updated on 12/Nov/23…
Question Number 200035 by ajfour last updated on 12/Nov/23 Commented by ajfour last updated on 12/Nov/23 $${Find}\:{equation}\:{of}\:{parabola}\:{having}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:{same}\:{curvature}\:{as}\:\mathrm{sin}\:{x}, \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{at}\:{shown}\:{point} \\ $$ Commented by…
Question Number 200025 by cortano12 last updated on 12/Nov/23 Answered by Frix last updated on 12/Nov/23 $$\left(\mathrm{1}\right)\:\:\:\:\:\sqrt{{t}+\mathrm{8}}+\sqrt{{t}}=\mathrm{4}\:\Rightarrow\:{t}=\mathrm{1}\:\Rightarrow\:{y}=\frac{\mathrm{1}}{{x}} \\ $$$$\mathrm{Transforming}\:\left(\mathrm{2}\right)\:\mathrm{to} \\ $$$${x}^{\mathrm{3}} \left({x}+\mathrm{13}\right)\sqrt{{x}+\mathrm{1}}=\mathrm{6}{x}^{\mathrm{4}} +\mathrm{14}{x}^{\mathrm{3}} +\mathrm{8} \\…