Category: Algebra

Question Number 151300 by mathdanisur last updated on 19/Aug/21 $$5\cdot 6,02\cdot {10}^{23}=?\left(\mathrm{solution}\right)$$$$\mathrm{a})3,01\cdot {10}^{24}\mathrm{b})3,01\cdot {10}^{22}$$ Answered by puissant last updated on 19/Aug/21 $$\mathrm{5}×\mathrm{6},\mathrm{02}.\mathrm{10}^{\mathrm{23}} =\mathrm{3},\mathrm{1}.\mathrm{10}^{\mathrm{24}}…

Question Number 151284 by mathdanisur last updated on 19/Aug/21 $$\mathrm{if}\frac{\mathrm{a}}{3^{\mathbf{x}-1}}=\frac{\mathrm{b}}{3^{\mathbf{y}+2}}=\frac{\mathrm{c}}{3^{\mathbf{z}-1}}=\frac{1}{5}$$$$\mathrm{find}\mathrm{abc}=?$$ Answered by Rasheed.Sindhi last updated on 19/Aug/21 $$\mathrm{a}=\frac{\mathrm{3}^{\mathrm{x}−\mathrm{1}}…

Question Number 151276 by peter frank last updated on 19/Aug/21 $${\int }_0^{2\pi }{\cos }^{-1}\left(\cos \mathrm{x}\right)\mathrm{dx}$$ Commented by tabata last updated on 19/Aug/21 $$=\int_{\mathrm{0}} ^{\:\mathrm{2}\pi}…

Question Number 151278 by mathdanisur last updated on 19/Aug/21 $$\int \frac{{\mathbf{e}}^{\sqrt{\mathbf{x}-1}}}{\sqrt{\mathbf{x}-1}}\mathrm{dx}=?$$ Answered by Ar Brandon last updated on 19/Aug/21 $$\mathrm{I}=\int \frac{e^{\sqrt{x-1}}}{\sqrt{x-1}}dx,u=\sqrt{x-1}\Rightarrow du=\frac{dx}{2\sqrt{x-1}}$$$$\:\:=\mathrm{2}\int{e}^{{u}}…

Question Number 151248 by mathdanisur last updated on 19/Aug/21 Answered by EDWIN88 last updated on 19/Aug/21 $$4\sin (4x-60°)\sin (6x-60°)\sin (480°-10x)+\frac{\sqrt{3}}{2}=0$$$$\left\{2\sin (4x-60°)\sin (6x-60°)\right\}2\sin (120°-10x)+\sin 60°=0$$$$\{\cos 2x-\cos (10x-120°)\}2\sin (120°-10x)+\sin 60°=0$$$$2\cos 2x\sin (120°-10x)-\sin (240°-20x)+\sin 60°=0$$$$\mathrm{sin}\:\left(\mathrm{120}°−\mathrm{8}{x}\right)−\mathrm{sin}\:\left(\mathrm{12}{x}−\mathrm{120}°\right)+\mathrm{sin}\:\left(\mathrm{60}°−\mathrm{20}{x}\right)+\mathrm{sin}\:\mathrm{60}°=\mathrm{0}…