Question Number 116611 by gaminghanzo12 last updated on 05/Oct/20 Commented by Dwaipayan Shikari last updated on 05/Oct/20 $$\mathrm{Q}\:\mathrm{116516} \\ $$ Answered by TANMAY PANACEA last…
Question Number 51028 by gunawan last updated on 23/Dec/18 $${f}\left({z}\right)=\sqrt{{r}}\:{e}^{{i}\frac{\theta}{\mathrm{2}}} \\ $$$${f}'\left({z}\right)=…? \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 23/Dec/18 $${df}=\left(\frac{\partial{f}}{\partial{r}}\right)_{\theta} {dr}+\left(\frac{\partial{f}}{\partial\theta}\right)_{{r}} {d}\theta \\…
Question Number 50970 by peter frank last updated on 22/Dec/18 $${Given}\:\mathrm{3}−\mathrm{2}{i}\:{and}\:\mathrm{1}+{i} \\ $$$${are}\:{the}\:{two}\:{of}\:{roots}\:{of} \\ $$$${the}\:{equation} \\ $$$${ax}^{\mathrm{4}} +{bx}^{\mathrm{3}} +{cx}^{\mathrm{3}} +{dx}+{e} \\ $$$${find}\:{the}\:{values}\:{of} \\ $$$${a},{b},{c},{d}\:{and}\:{e} \\…
Question Number 50890 by peter frank last updated on 21/Dec/18 $${Determine}\:{whether} \\ $$$${the}\:{following}\:\:{is}\:{true}\:{for}\:{all} \\ $$$${value}\:{of}\:{x} \\ $$$$\mathrm{0}\leqslant\frac{\left({x}+\mathrm{1}\right)^{\mathrm{2}} }{{x}^{\mathrm{2}} +{x}+\mathrm{1}}\leqslant\frac{\mathrm{4}}{\mathrm{3}} \\ $$ Answered by MJS last…
Question Number 50849 by peter frank last updated on 21/Dec/18 $$\mathrm{solve}\:{for}\:{z}\:\:{in}\:{the}\:{form}\:\:{x}+{iy}\: \\ $$$${if}\:{tanz}=\mathrm{0}.\mathrm{5}\: \\ $$ Answered by ajfour last updated on 21/Dec/18 $${e}^{{iz}} \:=\:\mathrm{cos}\:{z}+{i}\mathrm{sin}\:{z} \\…
Question Number 116359 by bemath last updated on 03/Oct/20 $$\mathrm{If}\:\mathrm{0}\:<\:\theta\:<\:\frac{\pi}{\mathrm{4}}\:\mathrm{such}\:\mathrm{that}\:\mathrm{cosec}\:\theta−\mathrm{sec}\:\theta=\frac{\sqrt{\mathrm{13}}}{\mathrm{6}} \\ $$$$\mathrm{then}\:\mathrm{cot}\:\theta−\mathrm{tan}\:\theta\:\mathrm{equals}\:\mathrm{to}\:\_\_ \\ $$ Answered by bobhans last updated on 03/Oct/20 $$\Rightarrow\:\mathrm{let}\:\mathrm{sin}\:\theta\:\mathrm{cos}\:\theta\:=\:\mathrm{r}\:.\:\mathrm{Then}\:\left(\frac{\mathrm{1}}{\mathrm{sin}\:\theta}\:−\frac{\mathrm{1}}{\mathrm{cos}\:\theta}\right)^{\mathrm{2}} =\:\frac{\mathrm{13}}{\mathrm{36}} \\ $$$$\Rightarrow\:\frac{\left(\mathrm{cos}\:\theta−\mathrm{sin}\:\theta\right)^{\mathrm{2}}…
Question Number 50806 by Tawa1 last updated on 20/Dec/18 $$\mathrm{Determine}\:\mathrm{the}\:\mathrm{fourth}\:\mathrm{roots}\:\mathrm{of}\:\:−\:\mathrm{16}\:,\:\:\mathrm{giving}\:\mathrm{the}\:\mathrm{results}\:\mathrm{in}\:\mathrm{polar} \\ $$$$\mathrm{form}\:\mathrm{and}\:\mathrm{in}\:\mathrm{exponential}\:\mathrm{form} \\ $$$$\boldsymbol{\mathrm{Answers}}:\:\:\:\:\:\sqrt{\mathrm{2}}\:\left(\mathrm{1}\:+\:\boldsymbol{\mathrm{j}}\right)\:,\:\:\sqrt{\mathrm{2}}\:\left(−\:\mathrm{1}\:+\:\boldsymbol{\mathrm{j}}\right)\:,\:\:\:\:\:\sqrt{\mathrm{2}}\:\left(−\:\mathrm{1}\:−\:\boldsymbol{\mathrm{j}}\right),\:\:\:\:\sqrt{\mathrm{2}}\left(\mathrm{1}\:−\:\boldsymbol{\mathrm{j}}\right) \\ $$ Answered by mr W last updated on 20/Dec/18 $${x}={r}\left(\mathrm{cos}\:\theta+{j}\:\mathrm{sin}\:\theta\right)…
Question Number 181841 by mr W last updated on 01/Dec/22 $${what}\:{is}\:{larger},\:\sqrt{\mathrm{11}}+\sqrt{\mathrm{13}}\:{or}\:\mathrm{7}? \\ $$ Answered by hmr last updated on 01/Dec/22 $$ \\ $$$${assume}\:{that}:\: \\ $$$$\sqrt{\mathrm{11}}\:+\:\sqrt{\mathrm{13}\:}\:<\:\mathrm{7}…
Question Number 181722 by Agnibhoo98 last updated on 29/Nov/22 $$\mathrm{Prove}\:\mathrm{that}, \\ $$$$\left(\frac{\mathrm{1}}{{a}\:−\:{b}}\:+\:\frac{\mathrm{1}}{{b}\:−\:{c}}\:+\:\frac{\mathrm{1}}{{c}\:−\:{a}}\right)^{\mathrm{2}} \:=\: \\ $$$$\frac{\mathrm{1}}{\left({a}\:−\:{b}\right)^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\left({b}\:−\:{c}\right)^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\left({c}\:−\:{a}\right)^{\mathrm{2}} } \\ $$ Answered by Rasheed.Sindhi last updated…
Question Number 116113 by Lordose last updated on 01/Oct/20 $$\boldsymbol{\mathrm{what}}'\boldsymbol{\mathrm{s}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{exponent}}\:\boldsymbol{\mathrm{of}}\:\mathrm{12}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{expansion}}\:\boldsymbol{\mathrm{of}}\:\mathrm{100}! \\ $$ Answered by mr W last updated on 01/Oct/20 $$\mathrm{12}=\mathrm{2}^{\mathrm{2}} ×\mathrm{3} \\…