Category: Algebra

Question Number 118634 by ajfour last updated on 18/Oct/20 $$Provethattheequationofthecircle$$$$passingthroughthepointsof$$$$intersectionofthesetwocurves:$$$$y=1+\frac{c}{x};y=x^2(c<\frac{2}{3\sqrt{3}})$$$$is{(x-\frac{c}{2})}^2+{(y-1)}^2=1+\frac{c^2}{4}.$$ Commented…

Question Number 53051 by Abror last updated on 16/Jan/19 $$\int \sin \left(2x\right)\cos xd\left(x\right)=$$ Answered by tanmay.chaudhury50@gmail.com last updated on 16/Jan/19 $$\frac{1}{2}\int 2sin2xcosxdx$$$$=\frac{1}{2}\int (sin3x+sinx)dx$$$$=\frac{\mathrm{1}}{\mathrm{2}}\left[\frac{−{cos}\mathrm{3}{x}}{\mathrm{3}}+\frac{−{cosx}}{}\right]+{c} \…

Question Number 184085 by Shrinava last updated on 02/Jan/23 $$({\mathrm{y}}^2+{\mathrm{xy}}^2){\mathrm{y}}^{{}^{\prime }}+{\mathrm{x}}^2-{\mathrm{yx}}^2=0$$$$$$ Answered by mr W last updated…

Question Number 184083 by mnjuly1970 last updated on 02/Jan/23 $$$$$$f\left(x\right)=x^3+3x^2-axis$$$$decreasingon[-1,2]$$$$thenwhichiscorrect\dots$$$$1:[-3,24]$$$$2:[24,+\mathrm{\infty })$$$$\:\:\:\:\:\:\mathrm{3}:\:\left(−\infty\:,−\mathrm{3}\right] \…

Question Number 118482 by peter frank last updated on 17/Oct/20 $$\mathrm{If}\mathrm{the}\mathrm{tangents}\mathrm{at}\mathrm{the}$$$$\mathrm{end}\mathrm{of}\mathrm{a}\mathrm{focal}\mathrm{chord}\mathrm{of}$$$$\mathrm{parabola}\mathrm{meet}\mathrm{the}$$$$\mathrm{tangent}\mathrm{at}\mathrm{the}\mathrm{vertex}$$$$\mathrm{in}\mathrm{C},\mathrm{D}.\mathrm{prove}\mathrm{that}\mathrm{CD}$$$$\mathrm{substends}\mathrm{a}\mathrm{right}\mathrm{angle}$$$$\mathrm{at}\mathrm{the}\mathrm{focus}$$…