Question Number 67430 by TawaTawa last updated on 27/Aug/19 Commented by MJS last updated on 27/Aug/19 $$\mathrm{coordinate}\:\mathrm{method} \\ $$$$\mathrm{turn}\:\mathrm{the}\:\mathrm{triangle}\:\rightarrow\:{CA}\:\mathrm{is}\:\mathrm{the}\:\mathrm{base} \\ $$$$\mathrm{side}\:\mathrm{length}\:={s} \\ $$$${s}=\mathrm{8}+{x}\:\Rightarrow\:{x}={s}−\mathrm{8} \\ $$$${C}=\begin{pmatrix}{−\frac{{s}}{\mathrm{2}}}\\{\mathrm{0}}\end{pmatrix}\:\:{A}=\begin{pmatrix}{\frac{{s}}{\mathrm{2}}}\\{\mathrm{0}}\end{pmatrix}\:\:{B}=\begin{pmatrix}{\mathrm{0}}\\{\frac{\sqrt{\mathrm{3}}{s}}{\mathrm{2}}}\end{pmatrix}…
Question Number 1895 by Yozzy last updated on 22/Oct/15 $${Let}\:{us}\:{generalise}\:{the}\:{result}\:{of}\:{taking}\:{the}\:{inverse}\:{tangent}\:{of}\:{a}\:{complex}\:{number} \\ $$$${to}\:{the}\:{form}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{tan}^{−\mathrm{1}} \left({c}+{id}\right)={a}+{ib} \\ $$$${where}\:{a},{b},{c},{d}\in\mathbb{R}\:{and}\:{i}=\sqrt{−\mathrm{1}}.\:{Determine}\:{a}\:{and}\:{b}\:{respectively}\:{in}\:{terms} \\ $$$${of}\:{c}\:{and}\:{d}.\: \\ $$ Commented by Rasheed Soomro…
Question Number 67431 by aliesam last updated on 27/Aug/19 Commented by mathmax by abdo last updated on 27/Aug/19 $${if}\:{a}\:{and}\:{b}\:{from}\:{C}\:{the}\:{question}\:{is}\:{done}\:{by}\:{sir}\:{mjs} \\ $$$${if}\:{a}\:{and}\:{b}\:{from}\:{R}\:\:\:{we}\:{have}\:\:\left(\mid\frac{{a}}{{b}}\mid\right)^{\mathrm{2}} −\left(\frac{\mid{a}\mid}{\mid{b}\mid}\right)^{\mathrm{2}} \: \\ $$$$=\mid\frac{{a}^{\mathrm{2}}…
Question Number 132967 by mohammad17 last updated on 17/Feb/21 $${where}\:{is}\:{function}\:{f}\left({z}\right)={zRez}+\overset{−} {{z}lnz}+\overset{−} {{z}} \\ $$$${derivable}\:,{then}\:{find}\:{the}\:{dervaitive}\:? \\ $$ Commented by mohammad17 last updated on 18/Feb/21 $$????\:\: \\…
Question Number 132961 by danielasebhofoh last updated on 17/Feb/21 Answered by Ar Brandon last updated on 17/Feb/21 $$\mathrm{2n}−\mathrm{3}+\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}−\mathrm{3}} {\sum}}\mathrm{k}=\mathrm{2n}−\mathrm{3}+\frac{\left(\mathrm{n}−\mathrm{3}\right)\left(\mathrm{n}−\mathrm{2}\right)}{\mathrm{2}} \\ $$$$\frac{\mathrm{4n}−\mathrm{6}+\mathrm{n}^{\mathrm{2}} −\mathrm{5n}+\mathrm{6}}{\mathrm{2}}=\frac{\mathrm{n}\left(\mathrm{n}−\mathrm{1}\right)}{\mathrm{2}} \\ $$$$\overset{\mathrm{n}}…
Question Number 1890 by Rasheed Soomro last updated on 21/Oct/15 $${Solve}\:{for}\:{x} \\ $$$$\:\:\:\:\:\:{tan}\:{x}\:+{tan}\:\mathrm{2}{x}\:−{tan}\:\mathrm{3}{x}\:=\mathrm{0} \\ $$$${Some}\:{one}\:{had}\:{posted}\:{this}\:{question}\:{and}\:{I}\:{had}\:{answered}\:{it} \\ $$$${but}\:{then}\:{thread}\:{was}\:{deleted}! \\ $$$${I}\:{think}\:{that}\:{the}\:{question}\:{is}\:{not}\:{importanceless}\:,\:{so}\:{I}\:{hav} \\ $$$${reposted}\:{it}. \\ $$ Commented by…
Question Number 67422 by mr W last updated on 27/Aug/19 Commented by Prithwish sen last updated on 27/Aug/19 $$\bigtriangleup\mathrm{AMN}\:\mathrm{is}\:\mathrm{an}\:\mathrm{isoceles}\:\mathrm{triangle}\:\mathrm{with}\:\mathrm{AM}=\mathrm{AN} \\ $$$$\mathrm{AM}+\mathrm{BM}=\:\mathrm{AN}+\mathrm{D}^{'} \mathrm{N}=\mathrm{16} \\ $$$$\mathrm{Area}\:\mathrm{ABMND}^{'} =\:\mathrm{Area}\:\mathrm{of}\:\mathrm{ABCD}\:−\mathrm{Area}\:\mathrm{of}\:\bigtriangleup\mathrm{AMN}.…
Question Number 1882 by madscientist last updated on 21/Oct/15 $$\underset{−\infty} {\overset{\infty} {\int}}\underset{−\infty} {\overset{\infty} {\int}}\mid\psi\left({r},{t}\right)\mid\in\mid\phi\left({r},{t}\right)\mid\Rightarrow\lambda\left({x}\right)\: \\ $$$${in}\:{quantum}\:{mechanics}\:{would}\:{this}\:{be} \\ $$$${true},\:{if}\:{so}\:{how}? \\ $$$$ \\ $$$$ \\ $$ Terms…
Question Number 132954 by LUFFY last updated on 17/Feb/21 $$\int_{\mathrm{0}} ^{\:\infty} \frac{{cos}\left({x}\right)−{cos}\left(\mathrm{3}{x}\right)}{{x}^{\mathrm{2}} }{dx} \\ $$ Answered by Dwaipayan Shikari last updated on 17/Feb/21 $${I}\left(\alpha\right)=\int_{\mathrm{0}} ^{\infty}…
Question Number 1880 by alib last updated on 20/Oct/15 $${Solve} \\ $$$$ \\ $$$$\left.\mathrm{1}\right)\:\left({sin}\:\mathrm{2}{x}+\:\sqrt{}\mathrm{3}\:{cos}\:\mathrm{2}{x}\right)^{\mathrm{2}} =\mathrm{2}\:−\mathrm{2}\:{cos}\:\left(\frac{\mathrm{2}\pi}{\mathrm{3}}−{x}\right) \\ $$$$\left.\mathrm{2}\right)\:{cos}\:{x}\:−\:{cos}\:\mathrm{2}{x}\:=\:{sin}\:\mathrm{3}{x} \\ $$$$ \\ $$$$\left.\mathrm{3}\right)\:{sin}\:\left(\mathrm{15} °+{x}\right)\:+\:{cos}\:\left(\mathrm{45}°+{x}\right)+\:\frac{\mathrm{1}}{\mathrm{2}}=\mathrm{0} \\ $$$$\left.\mathrm{4}\right)\:{tan}\:\left(\mathrm{70}°+{x}\right)\:+\:{tan}\:\left(\mathrm{20}°−{x}\right)\:=\:\mathrm{2} \\…