Category: Algebra

Question Number 217299 by peter frank last updated on 09/Mar/25 Answered by mr W last updated on 10/Mar/25 $$x=r\cos \theta$$$$y=r\sin \theta$$$$\left({r}\:\mathrm{cos}\:\theta−\mathrm{1}\right)^{\mathrm{2}} +\left({r}\:\mathrm{sin}\:\theta\right)^{\mathrm{2}} =\mathrm{16}…

Question Number 217262 by ArshadS last updated on 07/Mar/25 $$Solve:$$$$\frac{x^2+3x}{x^3-4x}-\frac{2}{x^2+2x}=\frac{1}{x-2}$$ Answered by ibrahimmatematic last updated on 07/Mar/25 $$\frac{{x}\left({x}+\mathrm{3}\right)}{{x}\left({x}−\mathrm{2}\right)\left({x}+\mathrm{2}\right)}−\frac{\mathrm{2}}{{x}\left({x}+\mathrm{2}\right)}=\frac{\mathrm{1}}{{x}−\mathrm{2}}…

Question Number 217197 by hardmath last updated on 05/Mar/25 $$\mathrm{Find}:$$$$\sqrt[5]{-32}+\sqrt[8]{{(-3)}^8}=?$$ Answered by Rasheed.Sindhi last updated on 05/Mar/25 $$\sqrt[{\mathrm{5}}]{−\mathrm{32}}\:\:+\:\:\sqrt[{\mathrm{8}}]{\left(−\mathrm{3}\right)^{\mathrm{8}} }\: \…

Question Number 217205 by peter frank last updated on 05/Mar/25 Answered by som(math1967) last updated on 06/Mar/25 $$\cos {\tan }^{-1}\left(\sin {\cot }^{-1}x\right)$$$$=\mathrm{cos}\:\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{sin}\:\mathrm{sin}^{−\mathrm{1}} \frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}\right)…

Question Number 217178 by hardmath last updated on 04/Mar/25 $$\mathrm{Find}:$$$$100-99+98-97+96-95+\dots +2-1=?$$ Answered by MathematicalUser2357 last updated on 04/Mar/25 $$=(100+98+96+\dots choegangcheckiscute\dots +6+4+2)-(99+97+95+\dots sorryforaggro\dots +5+3+1)$$$$=\mathrm{2}\left(\mathrm{50}+\mathrm{49}+\mathrm{48}+…+\mathrm{3}+\mathrm{2}+\mathrm{1}\right)−\left\{\mathrm{2}\left(\mathrm{50}+\mathrm{49}+\mathrm{48}+…+\mathrm{3}+\mathrm{2}+\mathrm{1}\right)−\mathrm{50}\right\} \…