Question Number 226558 by hardmath last updated on 04/Dec/25 Answered by mr W last updated on 04/Dec/25 Commented by mr W last updated on 04/Dec/25…
Question Number 226561 by Spillover last updated on 04/Dec/25 Answered by Spillover last updated on 04/Dec/25 Answered by Spillover last updated on 04/Dec/25 Answered by…
Question Number 226562 by thetpainghtun_111 last updated on 04/Dec/25 $$\mathrm{If}\:\mathrm{x}\:+\:\mathrm{y}\:{i}\:=\:\frac{\mathrm{a}\:+\:{i}}{\mathrm{a}\:−\:{i}}\:,\:\mathrm{prove}\:\mathrm{that}\:\mathrm{ay}\:−\:\mathrm{1}\:=\:\mathrm{x}. \\ $$$$\:\left(\mathrm{x}+\mathrm{y}{i}\right)\left(\mathrm{a}−{i}\right)=\mathrm{a}+{i} \\ $$$$\:\:\:\mathrm{ax}\:−\:\mathrm{x}{i}\:+\:\mathrm{ay}{i}\:−\:\mathrm{y}{i}^{\mathrm{2}} \:=\:\mathrm{a}\:+\:{i} \\ $$$$\:\:\left(\mathrm{ax}\:+\:\mathrm{y}\right)\:+\:\left(\mathrm{ay}\:−\:\mathrm{x}\right){i}\:=\:\mathrm{a}\:+\:{i} \\ $$$$\:\:\mathrm{ay}\:−\:\mathrm{x}\:=\:\mathrm{1} \\ $$$$\:\:\mathrm{x}\:=\:\mathrm{ay}\:−\mathrm{1} \\ $$ Terms of…
Question Number 226542 by Lara2440 last updated on 03/Dec/25 Commented by Lara2440 last updated on 04/Dec/25 $$\: \\ $$$$\mathrm{Smooth}\:\mathrm{Manifold}\:{M},{N}\:\mathrm{and}\:\mathrm{differentiable}\:\mathrm{Smooth}\:\mathrm{function}\: \\ $$$$\overset{\rightarrow} {\phi}\left({u},{v}\right);{M}\rightarrow{N} \\ $$$$\: \\…
Question Number 226554 by Spillover last updated on 03/Dec/25 Answered by peace2 last updated on 03/Dec/25 $$=\frac{\mathrm{1}}{{n}}\int\frac{{nx}^{{n}−\mathrm{1}} {dx}}{{x}^{{n}} \left(\mathrm{1}+{x}^{{n}} \right)}=\frac{\mathrm{1}}{{n}}\int\frac{{dy}}{{y}\left(\mathrm{1}+{y}\right)}=\frac{\mathrm{1}}{{n}}\int\frac{\mathrm{1}}{{y}}−\frac{\mathrm{1}}{\mathrm{1}+{y}}{dy} \\ $$$$=\frac{\mathrm{1}}{{n}}{ln}\left(\frac{{y}}{\mathrm{1}+{y}}\right)+\mathrm{c};{y}={x}^{{n}} \\ $$ Answered…
Question Number 226550 by gregori last updated on 03/Dec/25 $$\:\:\:\: {a}+{b}+{c}\:=\:{x}\: \\ $$$$\:\:\:\: \underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{a}^{\mathrm{3}} +{b}^{\mathrm{3}} +{c}^{\mathrm{3}} }{{abc}}\:=? \\ $$ Answered by peace2 last updated…
Question Number 226524 by wongb1506 last updated on 02/Dec/25 Answered by som(math1967) last updated on 02/Dec/25 $$\:\alpha=\mathrm{3}{x}\:\:\beta=\mathrm{2}{x} \\ $$$$\mathrm{5}{x}=\mathrm{90}\Rightarrow{x}=\mathrm{18}=\alpha−\beta \\ $$$$\:\:\left({D}\right) \\ $$ Terms of…
Question Number 226525 by wongb1506 last updated on 02/Dec/25 Answered by som(math1967) last updated on 02/Dec/25 $${AF}=\sqrt{\mathrm{160}}\:,{AE}=\sqrt{\mathrm{180}}\:,\:{EF}=\sqrt{\mathrm{100}} \\ $$$${Cosx}=\frac{\mathrm{160}+\mathrm{180}−\mathrm{100}}{\mathrm{2}×\sqrt{\mathrm{180}×\mathrm{160}}}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}} \\ $$$$\:{x}=\mathrm{45}° \\ $$ Answered by…
Question Number 226526 by wongb1506 last updated on 02/Dec/25 Answered by som(math1967) last updated on 02/Dec/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 226536 by hardmath last updated on 02/Dec/25 $$\mathrm{If}\:\:\:\left(\mathrm{x}+\left(\mathrm{2a}^{\mathrm{2}} +\mathrm{5}\right)\right)\left(\mathrm{x}−\left(\mathrm{2a}^{\mathrm{2}} +\mathrm{7}\right)\right)\:\leqslant\:\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\mathrm{x}\in\left[−\left(\mathrm{a}^{\mathrm{2}} +\mathrm{8a}−\mathrm{10}\right)\:;\:\left(\mathrm{a}^{\mathrm{2}} +\mathrm{9a}−\mathrm{11}\right)\right] \\ $$$$\mathrm{Find}:\:\boldsymbol{\mathrm{a}}\:=\:? \\ $$ Answered by gregori last updated…