Question Number 180838 by Mastermind last updated on 17/Nov/22 $$\mathrm{Find}\:\mathrm{all}\:\mathrm{x}\in\mathbb{R}\:\mathrm{that}\:\mathrm{are}\:\mathrm{solutions}\:\mathrm{to}\:\mathrm{this} \\ $$$$\mathrm{question}:\: \\ $$$$\mathrm{0}=\left(\mathrm{1}−\mathrm{x}−\mathrm{x}^{\mathrm{2}} −…\right)\centerdot\left(\mathrm{2}−\mathrm{x}−\mathrm{x}^{\mathrm{2}} −…\right) \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$ Commented by mr…
Question Number 115298 by Dwaipayan Shikari last updated on 24/Sep/20 $$\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }+\mathrm{log}\left(\mathrm{y}\right)=\mathrm{0} \\ $$ Commented by mohammad17 last updated on 25/Sep/20 $${y}^{''} +{lny}=\mathrm{0}\Rightarrow{y}^{''} =−{lny}…
Question Number 115285 by mnjuly1970 last updated on 28/Sep/20 $$\:\:\:\:\:\:\:\:…\spadesuit{nice}\:\:\:{topology}\:\spadesuit… \\ $$$${suppose}\:\:\langle{S}\:,\:\tau\:\rangle\:{is}\:\:{Baire}'{s} \\ $$$${space}\:\:\:{and}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{S}\:=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\cup}}{F}_{{n}} \:\:\:{such} \\ $$$${that}\:\:{F}_{{n}} '{s}\:\:{are}\:{closed}\:{sets}\: \\ $$$$\:\:\:\:{prove}\:\:{that}:: \\…
Question Number 180801 by Mastermind last updated on 17/Nov/22 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{Differential}\:\mathrm{equation}\:: \\ $$$$\left(\mathrm{3xy}+\mathrm{6y}^{\mathrm{2}} \right)\mathrm{dx}+\left(\mathrm{2x}^{\mathrm{2}} +\mathrm{9xy}\right)\mathrm{dy}=\mathrm{0} \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$ Answered by qaz last updated…
Question Number 115237 by nisaketto last updated on 24/Sep/20 Answered by nimnim last updated on 24/Sep/20 $$\mathrm{A}=\mathrm{area}\:\mathrm{of}\:\mathrm{regular}\:\mathrm{hexagon}−\mathrm{area}\:\mathrm{of}\:\mathrm{circle} \\ $$$$\:\:\:\:=\frac{\mathrm{3}\sqrt{\mathrm{3}}}{\mathrm{2}}\mathrm{a}^{\mathrm{2}} −\pi\mathrm{r}^{\mathrm{2}} =\left(\frac{\mathrm{3}×\mathrm{1}.\mathrm{732}}{\mathrm{2}}×\mathrm{6}×\mathrm{6}\right)−\left(\frac{\mathrm{22}}{\mathrm{7}}×\mathrm{2}×\mathrm{2}\right) \\ $$$$\:\:\:\:=\mathrm{93}.\mathrm{528}−\mathrm{0}.\mathrm{785}=\mathrm{92}.\mathrm{77cm}^{\mathrm{2}} \\ $$$$\:\:{the}\:{question}\:{said}\:{radius}\:{is}\:\mathrm{2}{cm}\:{while}\:{the}…
Question Number 180713 by Mastermind last updated on 16/Nov/22 Commented by Rasheed.Sindhi last updated on 16/Nov/22 $$\left.\mathrm{b}\left.\right)\:\:\&\:\:\:\mathrm{d}\right)\:{are}\:{same}\:+\mathrm{4}=\mathrm{4} \\ $$$$\sqrt{\mathrm{16}}\:=+\mathrm{4}\:{or}\:\sqrt{\mathrm{16}}\:=\mathrm{4} \\ $$ Commented by Frix last…
Question Number 49637 by Pk1167156@gmail.com last updated on 08/Dec/18 Answered by tanmay.chaudhury50@gmail.com last updated on 09/Dec/18 $$\alpha+\beta=\frac{−{b}}{{a}}\:\:\:\alpha\beta=\frac{{c}}{{a}} \\ $$$$\frac{\alpha+\beta}{\alpha\beta}=\frac{−{b}}{{c}}\:\:\:\:\alpha+\beta=\frac{−{b}}{{a}}\:\:\:\alpha^{\mathrm{2}} +\beta^{\mathrm{2}} =\frac{{b}^{\mathrm{2}} }{{a}^{\mathrm{2}} }−\frac{\mathrm{2}{c}}{{a}}=\frac{{b}^{\mathrm{2}} −\mathrm{2}{ac}}{{a}^{\mathrm{2}} }…
Question Number 180682 by Mastermind last updated on 15/Nov/22 $$\mathrm{Determine}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{k}\:\mathrm{such}\:\mathrm{that}\:\mathrm{the} \\ $$$$\mathrm{following}\:\mathrm{system}\:\mathrm{has}\:\left(\mathrm{i}\right)\:\mathrm{a}\:\mathrm{Unique}\: \\ $$$$\mathrm{solution}\:\left(\mathrm{ii}\right)\:\mathrm{No}\:\mathrm{solution}\:\left(\mathrm{iii}\right)\:\mathrm{More}\:\mathrm{than} \\ $$$$\mathrm{one}\:\mathrm{solution} \\ $$$$ \\ $$$$\left(\mathrm{a}\right)\:\mathrm{Kx}\:+\:\mathrm{y}\:+\:\mathrm{z}\:=\:\mathrm{1} \\ $$$$\:\:\:\:\mathrm{x}\:+\mathrm{Ky}\:+\:\mathrm{z}\:=\:\mathrm{1} \\ $$$$\:\:\:\:\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{Kz}\:=\:\mathrm{1} \\…
Question Number 180683 by Mastermind last updated on 15/Nov/22 $$\left(\mathrm{b}\right)\:\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{Kz}\:=\:\mathrm{2} \\ $$$$\:\:\:\:\mathrm{3x}\:+\:\mathrm{4y}\:+\:\mathrm{2z}\:=\:\mathrm{K} \\ $$$$\:\:\:\:\mathrm{2x}\:+\:\mathrm{3y}\:−\:\mathrm{z}\:=\:\mathrm{1} \\ $$ Answered by manxsol last updated on 15/Nov/22 $$\begin{cases}{\mathrm{1}}&{\mathrm{1}}&{{k}}&{\mathrm{2}}\\{\mathrm{3}}&{\mathrm{4}}&{\mathrm{2}}&{{k}}\\{\mathrm{2}}&{\mathrm{3}}&{−\mathrm{1}}&{\mathrm{1}}\end{cases} \\…
Question Number 180667 by cortano1 last updated on 15/Nov/22 Commented by JDamian last updated on 15/Nov/22 I never expected this from you :( Answered by a.lgnaoui last updated on 15/Nov/22 Commented…