Category: Algebra

Question Number 91377 by A8;15: last updated on 30/Apr/20 Commented by Tony Lin last updated on 30/Apr/20 $$\int \frac{1}{\sqrt{sinx}}dx$$$$=\int \frac{1}{\sqrt{cos(x-\frac{\pi }{2})}}dx$$$$=\int \frac{1}{\sqrt{1-2{sin}^2\left(\frac{2x-\pi }{4}\right)}}dx$$$${let}\:\frac{\mathrm{2}{x}−\pi}{\mathrm{4}}={u},\:\frac{{du}}{{dx}}=\frac{\mathrm{1}}{\mathrm{2}}…

Question Number 156905 by JSM last updated on 16/Oct/21 $$findthevalueofxandy,x:3:5=8:y:9$$ Answered by Rasheed.Sindhi last updated on 16/Oct/21 $$9x:27:45=40:5y:45$$$$9x=40\Rightarrow x=\frac{40}{9}$$$$\mathrm{5}{y}=\mathrm{27}\Rightarrow{y}=\frac{\mathrm{27}}{\mathrm{5}} \…

Question Number 156904 by JSM last updated on 16/Oct/21 $$findthevalueofxandy,x:3:5=2:y:10$$ Answered by Rasheed.Sindhi last updated on 16/Oct/21 $$x:3:5=2:y:10$$$$\Rightarrow 2x:6:10=2:y:10$$$$\mathrm{2}{x}=\mathrm{2}\Rightarrow{x}=\mathrm{1} \…

Question Number 156900 by MathSh last updated on 16/Oct/21 $${\mathrm{\Omega }}_1=1-\frac{\pi }{2}+\underset{\mathbf{n}=2}{\sum ^{\mathrm{\infty }}}{(-\frac{1}{\mathit{\pi }})}^{\mathbf{n}}\cdot \frac{1}{\mathrm{n}+1}$$$${\mathrm{\Omega }}_2=1-\frac{\pi }{2}+\underset{\mathbf{n}=2}{\sum ^{\mathrm{\infty }}}{(-\frac{1}{\mathbf{e}})}^{\mathbf{n}}\cdot \frac{1}{\mathrm{n}+1}$$$$\left.\mathrm{A}\left.\right)\left.\:\Omega_{\mathrm{1}} \:<\:\Omega_{\mathrm{2}} \:\:\:\mathrm{B}\right)\:\Omega_{\mathrm{1}} \:=\:\Omega_{\mathrm{2}}…

Question Number 25823 by ajfour last updated on 15/Dec/17 $$z_1=4-3i$$$$z_2=9+2i$$$$Find\left(a\right)z_1{oz}_2$$$$\left(b\right)z_1\times z_2$$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left({c}\right)\:{angle}\:{between}\:{z}_{\mathrm{1}} {and}\:{z}_{\mathrm{2}} . \…