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Question-135634

Question Number 135634 by oustmuchiya@gmail.com last updated on 14/Mar/21 Answered by physicstutes last updated on 14/Mar/21 $$\left({i}\right)\:{n}\left({B}\right)\:=\:\mathrm{8}\:+\:\mathrm{5}\:+\:{x}−\mathrm{4}\:=\:\mathrm{11}\:+\:{x} \\ $$$$\:{n}\left(\:{B}\cup{C}\right)\:=\:\mathrm{8}+\:{x}−\mathrm{4}\:+\:\mathrm{5}\:+\:\mathrm{2}{y}\:=\:\mathrm{9}\:+\:{x}\:+\:\mathrm{2}{y} \\ $$$$\Rightarrow\:\:\mathrm{11}\:+\:{x}\:=\:\mathrm{9}\:+{x}\:+\:\mathrm{2}{y}\:\:\Rightarrow\:\:\:\mathrm{2}\:=\:\mathrm{2}{y}\:\Rightarrow\:{y}\:=\:\mathrm{1} \\ $$$$\left({ii}\right)\:{n}\left({C}\right)\:=\:\mathrm{5}\:+\:\mathrm{2}{y}\: \\ $$$$\mathrm{and}\:{n}\left({A}\right)\:=\:\mathrm{15}…

0-4-x-2-1-gt-0-6-x-2-6-

Question Number 4559 by love math last updated on 07/Feb/16 $$\left(\mathrm{0};\left(\mathrm{4}\right)\right)^{{x}^{\mathrm{2}} −\mathrm{1}} >\left(\mathrm{0},\left(\mathrm{6}\right)\right)^{{x}^{\mathrm{2}} +\mathrm{6}} \\ $$ Commented by Yozzii last updated on 07/Feb/16 $${What}\:{is}\:\left(\mathrm{0},\left(\mathrm{6}\right)\right)\:{and}\:\left(\mathrm{0};\left(\mathrm{4}\right)\right)? \\…

Prove-i-i-e-pi-2-i-2-1-

Question Number 4556 by FilupSmith last updated on 07/Feb/16 $$\mathrm{Prove}\:{i}^{{i}} ={e}^{−\pi/\mathrm{2}} ,\:\:{i}^{\mathrm{2}} =−\mathrm{1} \\ $$ Answered by Yozzii last updated on 07/Feb/16 $${i}=\mathrm{0}+{i}×\mathrm{1}={cos}\mathrm{0}.\mathrm{5}\pi+{isin}\mathrm{0}.\mathrm{5}={e}^{\mathrm{0}.\mathrm{5}\pi{i}} \\ $$$$\therefore{i}^{{i}}…

nice-calculus-evaluation-0-pi-2-sin-x-ln-sin-x-dx-solution-cos-x-y-1-2-0-1-ln-1-y-2-dy-

Question Number 135627 by mnjuly1970 last updated on 14/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{nice}\:……………..\:{calculus}\:… \\ $$$$\:\:\:\:\:\:\:{evaluation}:::::\:\:\:\boldsymbol{\phi}\overset{???} {=}\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} {sin}\left({x}\right){ln}\left({sin}\left({x}\right)\right){dx} \\ $$$$\:\:\:\:\:\:\:{solution}::::: \\ $$$$\:\:\:\:\:\:\boldsymbol{\phi}\overset{\langle{cos}\left({x}\right)={y}\rangle} {=}\:\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}} ^{\:\mathrm{1}} {ln}\left(\mathrm{1}−{y}^{\mathrm{2}} \right){dy} \\ $$$$\:\:\:\:\:\:\:\:\:\:=−\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}}…

Question-4548

Question Number 4548 by Yozzii last updated on 07/Feb/16 Commented by Yozzii last updated on 07/Feb/16 $${In}\:{the}\:{diagram}\:{is}\:{a}\:{parallelogram}\:{ABCD} \\ $$$${with}\:{diagonal}\:{CB}. \\ $$$${E}\:{and}\:{F}\:{are}\:{the}\:{midpoints}\:{of}\:{CD}\:{and} \\ $$$${BD}\:{respectively}.\:{Using}\:{vectors},\:{prove} \\ $$$${that}\:{AE}\:{and}\:{AF}\:{trisect}\:{CB}.…