Question Number 11218 by FilupS last updated on 17/Mar/17 $$\mathrm{at}\:\mathrm{tinkutara} \\ $$$$\: \\ $$$$\mathrm{there}\:\mathrm{are}\:\mathrm{major}\:\mathrm{bugs}\:\mathrm{with}\:\mathrm{combining} \\ $$$$\mathrm{brackets}. \\ $$$$\: \\ $$$$\mathrm{e}.\mathrm{g}.\:\mathrm{typing}: \\ $$$$\mid{A}\rangle=\left(\mid{B}^{\ast} \rangle\right)^{\mathrm{T}} \\ $$$$\:…
Question Number 11217 by FilupS last updated on 17/Mar/17 $$\exists{e}_{{i}} :{i}\in\mathbb{N}\:\:\:\:\:\:\:\:{e}_{{i}} \:\mathrm{is}\:\mathrm{a}\:\mathrm{basis}\:\mathrm{vector} \\ $$$$\boldsymbol{{A}}\in\mathbb{C}^{{n}} \\ $$$$\boldsymbol{{A}}=\underset{{i}\in\mathbb{N}} {\sum}{e}_{{i}} {A}_{{i}} =\begin{pmatrix}{{A}_{\mathrm{1}} }\\{{A}_{\mathrm{2}} }\\{\vdots}\\{{A}_{{n}} }\end{pmatrix}\:\:\:=\:\mid{A}\rangle \\ $$$$\langle{B}\mid=\left(\mid{B}^{\ast} \rangle\right)^{\mathrm{T}}…
Question Number 142290 by mnjuly1970 last updated on 29/May/21 $$\:\:\:{evaluate}: \\ $$$$\:\:\:\:\:\:\Theta:=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\zeta\left({n}+\mathrm{1}\right)−\mathrm{1}}{{n}+\mathrm{1}}\:=? \\ $$$$\:\:\:\:\: \\ $$ Answered by Dwaipayan Shikari last updated on…
Question Number 142285 by qaz last updated on 29/May/21 $$\mathscr{L}\left(\frac{\mathrm{1}+\mathrm{2bt}}{\:\sqrt{\mathrm{t}}}\mathrm{e}^{\mathrm{bt}} \right)\left(\mathrm{s}\right)=? \\ $$ Answered by Dwaipayan Shikari last updated on 29/May/21 $$\mathscr{L}\left({f}\left({t}\right)\right)\left({s}\right)=\int_{\mathrm{0}} ^{\infty} {f}\left({t}\right){e}^{−{st}} \:{dt}…
Question Number 11215 by kheleadi11 last updated on 17/Mar/17 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 11214 by uni last updated on 17/Mar/17 Answered by FilupS last updated on 17/Mar/17 $${a}+\frac{{b}}{{a}}=\mathrm{4}\:\:\Rightarrow\:\:{b}={a}\left(\mathrm{4}−{a}\right) \\ $$$$\because{a}\in\mathbb{Z}\:\:\mathrm{and}\:\:\mathrm{RHS}\in\mathbb{Z},\:\therefore{b}\in\mathbb{Z} \\ $$$$\: \\ $$$$\therefore{a}=\frac{{b}}{\mathrm{4}−{a}} \\ $$$$\because{a}\in\mathbb{Z},\:\:\:\frac{{b}}{\mathrm{4}−{a}}\in\mathbb{Z},\:\:\:\:\:\therefore\left(\mathrm{4}−{a}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{factor}…
Question Number 11212 by uni last updated on 17/Mar/17 Answered by mrW1 last updated on 17/Mar/17 $$\mathrm{2}{x}=\mathrm{25}−\mathrm{5}{y}=\mathrm{5}\left(\mathrm{5}−{y}\right) \\ $$$${x}=\frac{\mathrm{5}\left(\mathrm{5}−{y}\right)}{\mathrm{2}} \\ $$$$\mathrm{5}−{y}\:{must}\:{be}\:{even}: \\ $$$$\Rightarrow\mathrm{5}−{y}=\mathrm{2}{k},\:{k}\in\mathbb{N} \\ $$$${y}=\mathrm{5}−\mathrm{2}{k}>\mathrm{0}…
Question Number 142282 by pete last updated on 29/May/21 $$\mathrm{Three}\:\mathrm{interior}\:\mathrm{angles}\:\mathrm{of}\:\mathrm{a}\:\mathrm{polygon}\:\mathrm{are}\:\mathrm{160}° \\ $$$$\mathrm{each}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{other}\:\mathrm{interior}\:\mathrm{angles}\:\mathrm{are}\:\mathrm{120}°\:\mathrm{each}, \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{the}\:\mathrm{polygon}. \\ $$ Answered by som(math1967) last updated on 29/May/21 $$\boldsymbol{{let}}\:\boldsymbol{{no}}\:\boldsymbol{{of}}\:\boldsymbol{{sides}}=\boldsymbol{{n}} \\…
Question Number 142277 by liberty last updated on 29/May/21 $$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−{e}^{\mathrm{sin}\:{x}\:\mathrm{ln}\:\left(\mathrm{cos}\:{x}\right)} }{{x}^{\mathrm{3}} }\:=? \\ $$ Answered by Dwaipayan Shikari last updated on 29/May/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−{e}^{{sinx}\left(−\frac{{x}^{\mathrm{2}}…
Question Number 142276 by mohammad17 last updated on 29/May/21 $$\int_{\mathrm{0}} ^{\:\mathrm{2}} \sqrt{\mathrm{1}+{e}^{\mathrm{2}{x}} }{dx} \\ $$ Answered by mathmax by abdo last updated on 29/May/21 $$\mathrm{I}\int_{\mathrm{1}}…