Question Number 83608 by john santu last updated on 04/Mar/20 $$\sqrt[{\mathrm{4}\:\:}]{\mathrm{17}+\mathrm{x}}\:+\:\sqrt[{\mathrm{4}\:\:}]{\mathrm{17}−\mathrm{x}}\:=\:\mathrm{2}\: \\ $$$$\mathrm{find}\:\mathrm{x}\: \\ $$ Commented by mr W last updated on 04/Mar/20 $${LHS}\geqslant\sqrt[{\mathrm{4}}]{\mathrm{2}×\mathrm{17}}>\sqrt[{\mathrm{4}}]{\mathrm{2}×\mathrm{16}}>\sqrt[{\mathrm{4}}]{\mathrm{16}}=\mathrm{2}={RHS} \\…
Question Number 149141 by mathdanisur last updated on 03/Aug/21 $$\frac{{cos}^{\mathrm{2}} \left(\mathrm{70}\right)\:-\:{sin}^{\mathrm{2}} \left(\mathrm{70}\right)}{{sin}\left(\mathrm{100}\right)\:+\:{sin}\left(\mathrm{20}\right)}\:=\:? \\ $$ Commented by liberty last updated on 03/Aug/21 $$=\frac{\left(\mathrm{cos}\:\mathrm{70}°−\mathrm{sin}\:\mathrm{70}°\right)\left(\mathrm{cos}\:\mathrm{70}°+\mathrm{sin}\:\mathrm{70}°\right)}{\mathrm{sin}\:\mathrm{100}°+\mathrm{sin}\:\mathrm{20}°} \\ $$$$=\frac{\left(\mathrm{sin}\:\mathrm{20}°−\mathrm{sin}\:\mathrm{70}°\right)\left(\mathrm{sin}\:\mathrm{20}°+\mathrm{sin}\:\mathrm{70}°\right)}{\mathrm{2sin}\:\mathrm{60}°\mathrm{cos}\:\mathrm{40}°} \\…
Question Number 149140 by mathdanisur last updated on 03/Aug/21 $$\begin{cases}{\mid{x}\mid\:+\:{y}\:-\:\mathrm{1}\:=\:\mathrm{0}}\\{{x}\:-\:{y}\:-\:\mathrm{1}\:=\:\mathrm{0}}\end{cases}\:\:\:\Rightarrow\:\:\mathrm{2}{x}\:-\:\mathrm{3}{y}\:=\:? \\ $$ Commented by liberty last updated on 03/Aug/21 $$\mathrm{y}=\:\mathrm{x}−\mathrm{1} \\ $$$$\Rightarrow\mid\mathrm{x}\mid+\mathrm{x}−\mathrm{2}=\mathrm{0} \\ $$$$\mathrm{case}\left(\mathrm{1}\right)\:\mathrm{x}<\mathrm{0}\:\Rightarrow−\mathrm{x}+\mathrm{x}−\mathrm{2}=\mathrm{0}\:,\mathrm{no}\:\mathrm{solution} \\…
Question Number 149137 by mathdanisur last updated on 03/Aug/21 $${if}\:\:\:{ctg}\boldsymbol{\alpha}\:=\:−\mathrm{2}\:\:\:{and}\:\:\:\frac{\mathrm{3}\pi}{\mathrm{2}}\:<\:\alpha\:<\:\mathrm{2}\pi \\ $$$${find}\:\:\:{sin}\boldsymbol{\alpha}\:=\:? \\ $$ Commented by liberty last updated on 03/Aug/21 $$\mathrm{sin}\:\alpha=−\frac{\mathrm{1}}{\:\sqrt{\mathrm{5}}} \\ $$ Terms…
Question Number 149142 by mathdanisur last updated on 03/Aug/21 $${if}\:\:\:{z}\:+\:\mid{z}\mid\:=\:\mathrm{1}\:+\:\sqrt{\mathrm{3}}\:\boldsymbol{{i}} \\ $$$${find}\:\:\:\boldsymbol{\varphi}\:=\:? \\ $$ Answered by liberty last updated on 03/Aug/21 $$\mathrm{z}=\mathrm{a}+\mathrm{b}{i} \\ $$$$\mid\mathrm{z}\mid=\sqrt{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}}…
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Question Number 149129 by Samimsultani last updated on 03/Aug/21 Commented by ajfour last updated on 03/Aug/21 $${isn}'{t}\:\:\boldsymbol{\div}\:\:{same}\:{as}\:/\: \\ $$ Answered by puissant last updated on…
Question Number 83590 by Tony Lin last updated on 04/Mar/20 $${transform}\:{the}\:{ellipse}\:\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }=\mathrm{1}\:{to} \\ $$$${the}\:{polar}\:{equation}\:{r}=\:\frac{{a}\left(\mathrm{1}−{e}^{\mathrm{2}} \right)}{\mathrm{1}+{ecos}\theta} \\ $$$${a}:\:{semimajor}\:{axis} \\ $$$${e}:\:{eccentricity} \\ $$ Commented…
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Question Number 18053 by mondodotto@gmail.com last updated on 14/Jul/17 Commented by prakash jain last updated on 14/Jul/17 $$\mathrm{can}\:\mathrm{u}\:\mathrm{please}\:\mathrm{type}\:\mathrm{question}?\:\mathrm{it}\:\mathrm{is}\:\mathrm{very} \\ $$$$\mathrm{difficult}\:\mathrm{to}\:\mathrm{read}\:\mathrm{image}. \\ $$ Commented by mondodotto@gmail.com…