Category: Coordinate Geometry

Question Number 217084 by maths_plus last updated on 28/Feb/25 $$\mathbf{Geometr}\mathrm{i}\mathbf{e}\mathbf{dans}\mathbf{le}\mathbf{plan}.$$$$\overrightarrow{\mathrm{AB}}\mathrm{et}\overrightarrow{\mathrm{CD}}\mathrm{sont}\mathrm{deux}\mathrm{vecteurs}\mathrm{du}\mathrm{plan}.$$$$\overrightarrow{\mathrm{AB}}{\mathrm{n}}^{\prime }\mathrm{est}\mathrm{pas}\mathrm{nul}.$$$$\mathrm{Demontre}\mathrm{que}\mathrm{si}\overrightarrow{\mathrm{AB}}\mathrm{et}\overrightarrow{\mathrm{CD}}\mathrm{sont}\mathrm{colineaires}$$$$\mathrm{alors}\mathrm{il}\mathrm{existe}\mathrm{un}\mathrm{nombre}\mathrm{reel}\mathrm{k}\mathrm{tel}\mathrm{que}$$$$\overset{\rightarrow}…

Question Number 217088 by alcohol last updated on 28/Feb/25 $$showthat{\int }_n^{n+1}ln\left(t\right)dt⩽ln(n+\frac{1}{2})$$$$Given{u}_n=\frac{{\left(4n\right)}^{n}n!e^{-n}}{\left(2n\right)!},\mathrm{\forall }n⩾1$$$$prove,usingtheprecedingquestionthat$$$$u_{n}isdecreasingandconvergent$$ Answered…

Question Number 216750 by sniper237 last updated on 17/Feb/25 $$Ifa-b=\sqrt{ab}findthevalueof\frac{a-b}{a+b}$$ Answered by mr W last updated on 17/Feb/25 $${(a+b)}^2={(a-b)}^2+4ab=ab+4ab=5ab$$$$\Rightarrow{a}+{b}=\pm\sqrt{\mathrm{5}{ab}}…

Question Number 216607 by Tawa11 last updated on 12/Feb/25 Answered by Rasheed.Sindhi last updated on 12/Feb/25 $$4x^2+bx-45=(hx+k)(x+j);h,k,j\in \mathbb{Z}$$$$={hx}^2+(hj+k)x+kj$$$$kj=-45\Rightarrow j=-\frac{45}{k}$$$$\frac{\mathrm{45}}{{k}}=−{j}\:\in\:\mathbb{Z}\:\rightarrow\left({D}\right)…

Question Number 216387 by Tawa11 last updated on 06/Feb/25 Answered by mr W last updated on 06/Feb/25 $$(6,0)$$$${(6-6)}^2+{(0-3+a)}^2=5^2$$$$\Rightarrow−\mathrm{3}+{a}=\mathrm{5}\:\Rightarrow{a}=\mathrm{8} \…