Category: Algebra

Question Number 218163 by hardmath last updated on 31/Mar/25 $$\mathrm{Find}:\int \frac{\mathrm{x}}{\sqrt{48-2\mathrm{x}-{\mathrm{x}}^2}}\mathrm{dx}=?$$ Answered by efronzo1 last updated on 31/Mar/25 $$\mathrm{I}=\int \frac{\mathrm{x}}{\sqrt{49-{(\mathrm{x}+1)}^2}}\mathrm{dx}$$$$\:\mathrm{x}+\mathrm{1}\:=\:\mathrm{7sin}\:\:\mathrm{u}\: \…

Question Number 218185 by hardmath last updated on 31/Mar/25 $$\mathrm{Find}:$$$$\underset{\mathbf{n}\to \mathrm{\infty }}{\lim }\sin \left(\mathrm{n}\pi \sqrt{{\mathrm{n}}^2+2\mathrm{n}+2\cdot (\mathrm{k}+1)}\right)=?$$$$\mathrm{k}\in \mathbb{Z}-\mathrm{fixed}$$ Answered by vnm last updated on 01/Apr/25…

Question Number 218183 by hardmath last updated on 31/Mar/25 $$\mathrm{Find}:$$$$\sqrt{{33}^2+{544}^2}+\sqrt{{333}^2+{55444}^2}=?$$ Answered by Hanuda354 last updated on 01/Apr/25…

Question Number 218119 by MrGaster last updated on 30/Mar/25 $$\left|\begin{array}{cccccc}\epsilon & 1& 0& 0& 0& 1\\ 1& \epsilon & 1& 0& 0& 0\\ 0& 1& \epsilon & 1& 0& 0\\ 0& 0& 1& \epsilon & 1& 0\\ 0& 0& 0& 1& \epsilon & 1\\ 1& 0& 0& 0& 1& \epsilon \end{array}\right|=?$$$$$$ Answered by SdC355 last updated on 30/Mar/25 $$\mathrm{Holy}\mathrm{shit}\dots .\mathrm{what}\mathrm{is}\mathrm{that}\mathrm{Lol}$$$$\mathrm{But}\:\mathrm{that}\:\mathrm{det}\left\{\mathrm{A}\right\}\:\mathrm{is}\:\varepsilon^{\mathrm{6}} −\mathrm{6}\varepsilon^{\mathrm{4}}…

Question Number 218103 by ArshadS last updated on 29/Mar/25 $$x+\frac{1}{x}=3,x^5+\frac{1}{x^5}=?$$ Answered by Rasheed.Sindhi last updated on 29/Mar/25 $${x}+\frac{\mathrm{1}}{{x}}=\mathrm{3}\:,\:{x}^{\mathrm{5}} +\frac{\mathrm{1}}{{x}^{\mathrm{5}} }=? \…