Category: Algebra

Question Number 212361 by Ari last updated on 11/Oct/24 Commented by Ari last updated on 11/Oct/24 $$howisthisequationsolved?$$ Commented by Ghisom last updated on…

Question Number 212341 by Spillover last updated on 10/Oct/24 Answered by Ghisom last updated on 10/Oct/24 $$\underset{0}{\stackrel{\pi /4}{\int }}\frac{\sin x+\cos x}{9+16\sin 2x}dx=$$$$[t=\frac{4\sqrt{2}}{5}\cos (x+\frac{\pi }{4})]$$$$=−\frac{\mathrm{1}}{\mathrm{20}}\underset{\mathrm{0}} {\overset{\mathrm{4}/\mathrm{5}} {\int}}\frac{{dt}}{{t}^{\mathrm{2}}…

Question Number 212342 by hardmath last updated on 10/Oct/24 $$\mathrm{The}\mathrm{number}\overline{\mathrm{abc}}\mathrm{is}\mathrm{divisible}\mathrm{by}37.$$$$\mathrm{Prove}\mathrm{that}\overline{\mathrm{bca}}+\overline{\mathrm{cab}}\mathrm{is}\mathrm{divisible}\mathrm{by}37.$$ Answered by A5T last updated on 10/Oct/24 $$\mathrm{100}{a}+\mathrm{10}{b}+{c}\equiv−\mathrm{11}{a}−\mathrm{27}{b}+{c}=−\left(\mathrm{11}{a}+\mathrm{27}{b}−{c}\right)…

Question Number 212339 by Spillover last updated on 10/Oct/24 Answered by Ghisom last updated on 10/Oct/24 $$\underset{0}{\stackrel{3}{\int }}\frac{x^{3/4}{(3-x)}^{1/4}}{{(5-x)}^3}dx=$$$$\:\:\:\:\:\left[{t}=\left(\frac{\mathrm{2}{x}}{\mathrm{5}\left(\mathrm{3}−{x}\right)}\right)^{\mathrm{1}/\mathrm{4}} ;\:{C}=\frac{\mathrm{9}\sqrt[{\mathrm{4}}]{\mathrm{2}}}{\mathrm{5}\sqrt[{\mathrm{4}}]{\mathrm{5}}}\right]…

Question Number 212314 by Spillover last updated on 09/Oct/24 Answered by mehdee7396 last updated on 09/Oct/24 $$f\left(x\right)=ln\left(\frac{2-sinx}{2+sinx}\right)$$$$f(-x)=ln\left(\frac{2+sinx}{2-sinx}\right)=-f\left(x\right)$$$$\Rightarrow ;f;is;odd\Rightarrow {\int }_{-\frac{\pi }{2}}^{\frac{\pi }{2}}f\left(x\right)dx=0✓$$$$…