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 $$\mathrm{12}=\mathrm{2}^{\mathrm{2}} ×\mathrm{3} \\…
Question Number 50445 by ANTARES VY last updated on 16/Dec/18 $$\boldsymbol{\mathrm{The}}\:\:\boldsymbol{\mathrm{roots}}\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{fallowing}} \\ $$$$\boldsymbol{\mathrm{functions}}\:\:\boldsymbol{\mathrm{are}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{Sequences}}\:\:\boldsymbol{\mathrm{of}} \\ $$$$\boldsymbol{\mathrm{arithmetic}}\:\:\boldsymbol{\mathrm{progressiyon}} \\ $$$$\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)=\boldsymbol{\mathrm{x}}^{\mathrm{5}} −\mathrm{20}\boldsymbol{\mathrm{x}}^{\mathrm{4}} +\boldsymbol{\mathrm{ax}}^{\mathrm{3}} +\boldsymbol{\mathrm{bx}}^{\mathrm{2}} +\boldsymbol{\mathrm{cx}}+\mathrm{24} \\ $$$$\boldsymbol{\mathrm{f}}\left(\mathrm{8}\right)=? \\ $$…
Question Number 181484 by Linton last updated on 25/Nov/22 $${If}\:{a}\:{hen}\:{and}\:{a}\:{half} \\ $$$${lay}\:{an}\:{egg}\:{and}\:{a}\:{half} \\ $$$${in}\:{a}\:{day}\:{and}\:{a}\:{half} \\ $$$${how}\:{many}\:{eggs}\:{would} \\ $$$${one}\:{hen}\:{lay}\:{in}\:{one} \\ $$$${day}? \\ $$ Commented by MJS_new…
Question Number 115856 by bemath last updated on 29/Sep/20 $${Which}\:{is}\:{greater} \\ $$$${P}\:=\:\left(\mathrm{1983}\right)\left(\mathrm{1}+\mathrm{2}+\mathrm{3}+…+\mathrm{1984}\right)\:,\:{or} \\ $$$${Q}\:=\:\left(\mathrm{1984}\right)\left(\mathrm{1}+\mathrm{2}+\mathrm{3}+…+\mathrm{1983}\right) \\ $$ Answered by bobhans last updated on 29/Sep/20 $${let}\:{z}\:=\:\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}+…+\mathrm{1983} \\…
Question Number 50248 by peter frank last updated on 15/Dec/18 Answered by mr W last updated on 15/Dec/18 $${P}\left({p},\frac{{c}^{\mathrm{2}} }{{p}}\right) \\ $$$${Q}\left({q},\frac{{c}^{\mathrm{2}} }{{q}}\right) \\ $$$${PQ}=\sqrt{\left({p}−{q}\right)^{\mathrm{2}}…