Question Number 65334 by Tawa1 last updated on 28/Jul/19 Answered by mr W last updated on 28/Jul/19 $$\angle{D}=\mathrm{360}−\mathrm{126}−\mathrm{42}×\mathrm{2}=\mathrm{150}° \\ $$$$\frac{{DC}}{\mathrm{sin}\:{x}}=\frac{{AC}}{\mathrm{sin}\:\mathrm{150}} \\ $$$$\Rightarrow{DC}=\frac{\mathrm{sin}\:{x}}{\mathrm{sin}\:\mathrm{150}}×{AC} \\ $$$$\frac{{AC}}{\mathrm{sin}\:\mathrm{126}}=\frac{{AB}}{\mathrm{sin}\:\left[\mathrm{42}−\left(\mathrm{30}−{x}\right)\right]}=\frac{{AB}}{\mathrm{sin}\:\left({x}+\mathrm{12}\right)} \\…
Question Number 65333 by aliesam last updated on 28/Jul/19 Commented by Prithwish sen last updated on 28/Jul/19 $$\mathrm{log}_{\mathrm{y}} \mathrm{x}=\mathrm{v}\Rightarrow\frac{\mathrm{v}^{\mathrm{2}} +\mathrm{1}}{\mathrm{v}}\:=\:\frac{\mathrm{17}}{\mathrm{4}}\Rightarrow\mathrm{4v}^{\mathrm{2}} −\mathrm{17v}+\mathrm{4}=\mathrm{0} \\ $$$$\mathrm{4v}^{\mathrm{2}} −\mathrm{16v}−\mathrm{v}+\mathrm{4}=\mathrm{0}\Rightarrow\mathrm{4v}\left(\mathrm{v}−\mathrm{4}\right)−\mathrm{1}\left(\mathrm{v}−\mathrm{4}\right)=\mathrm{0} \\…
Question Number 130869 by EDWIN88 last updated on 30/Jan/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{\mathrm{tan}\:{x}}{{x}}\right)^{\frac{\mathrm{tan}\:{x}}{{x}−\mathrm{tan}\:{x}\:}} ? \\ $$ Answered by benjo_mathlover last updated on 30/Jan/21 $$\:\mathrm{ln}\:\mathrm{L}\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{tan}\:\mathrm{x}}{\mathrm{x}−\mathrm{tan}\:\mathrm{x}}\right)\mathrm{ln}\:\left(\frac{\mathrm{tan}\:\mathrm{x}}{\mathrm{x}}\right) \\ $$$$\:\mathrm{ln}\:\mathrm{L}=\:\underset{{x}\rightarrow\mathrm{0}}…
Question Number 65332 by aliesam last updated on 28/Jul/19 Commented by mathmax by abdo last updated on 29/Jul/19 $${let}\:{suppose}\:{n}\:{inter}\:{let}\:{decompose}\:{the}\:{fraction} \\ $$$${F}\left({x}\right)\:=\frac{{x}}{{x}^{{n}} \:+\mathrm{1}} \\ $$$${z}^{{n}} \:+\mathrm{1}\:=\mathrm{0}\:\Rightarrow{z}^{{n}}…
Question Number 65325 by Tawa1 last updated on 28/Jul/19 Commented by Tony Lin last updated on 28/Jul/19 $$\left({a}\right)\left({i}\right) \\ $$$$\left({i}\right){O}\overset{\rightarrow} {{E}}=\lambda{O}\overset{\rightarrow} {{D}}+\left(\mathrm{1}−\lambda\right){O}\overset{\rightarrow} {{C}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:=\lambda\left(\mathrm{4}\overset{\rightarrow}…
Question Number 65324 by hovea cw last updated on 28/Jul/19 Commented by mathmax by abdo last updated on 28/Jul/19 $${we}\:{have}\:\mathrm{1}\leqslant{k}\leqslant{n}^{\mathrm{2}} \:\Rightarrow\mathrm{1}+{n}^{\mathrm{2}} \leqslant{k}+{n}^{\mathrm{2}} \leqslant\mathrm{2}{n}^{\mathrm{2}} \:\Rightarrow\sqrt{\mathrm{1}+{n}^{\mathrm{2}} }\leqslant\sqrt{{k}+{n}^{\mathrm{2}}…
Question Number 130858 by mathlove last updated on 29/Jan/21 $$\mathrm{log}\:\left[\sqrt{\boldsymbol{{mx}}^{\mathrm{2}} +\mathrm{3}}\:+\boldsymbol{{x}}\right]=? \\ $$The following subject is a node subject with a value of m Terms…
Question Number 65321 by hovea cw last updated on 28/Jul/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 65320 by hovea cw last updated on 28/Jul/19 Commented by mathmax by abdo last updated on 28/Jul/19 $${let}\:{I}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}+{x}}{lnxdx}\:{changement}\:\sqrt{\mathrm{1}+{x}}={t}\:{give}\:\mathrm{1}+{x}\:={t}^{\mathrm{2}} \:\Rightarrow \\ $$$${x}\:={t}^{\mathrm{2}}…
Question Number 130854 by mathlove last updated on 29/Jan/21 $$\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\frac{{x}^{{x}} \centerdot{x}!−\mathrm{4}\left(\mathrm{3}{x}−\mathrm{4}\right)!}{\mathrm{3}{x}!−\mathrm{6}} \\ $$ Answered by Dwaipayan Shikari last updated on 29/Jan/21 $$\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\frac{{x}^{{x}} \left(\mathrm{1}+{logx}\right){x}!+{x}^{{x}}…