Category: Algebra

Question Number 26207 by pieroo last updated on 22/Dec/17 $$\mathrm{I}\mathrm{think}\mathrm{of}\mathrm{a}\mathrm{two}\mathrm{digit}\mathrm{number}.\mathrm{The}\mathrm{sum}\mathrm{of}\mathrm{the}\mathrm{digits}\mathrm{is}9.$$$$\mathrm{When}\mathrm{the}\mathrm{number}\mathrm{is}\mathrm{reversed}\mathrm{and}\mathrm{subtracted}\mathrm{from}\mathrm{the}$$$$\mathrm{original},\mathrm{the}\mathrm{result}\mathrm{is}45.\mathrm{Find}\mathrm{the}\mathrm{original}\mathrm{number}$$ Answered by peileng8802 last updated on 22/Dec/17 $$\mathrm{let}\:\mathrm{x}\:\mathrm{be}\:\mathrm{tens}\:\:\:\mathrm{y}\:\mathrm{be}\:\mathrm{ones} \…

Question Number 157265 by MathSh last updated on 21/Oct/21 $$\mathrm{Solve}\mathrm{for}\mathrm{real}\mathrm{numbers}:$$$$\sin \left(\mathrm{x}\right)+\cos \left(\mathrm{x}\right)+\sec \left(\mathrm{x}\right)\cdot \csc \left(\mathrm{x}\right)=2+\sqrt{2}$$ Answered by TheSupreme last updated on 21/Oct/21 $$sin\left(x\right)+cos\left(x\right)-\frac{1}{sin\left(x\right)cos\left(x\right)}=A$$$$\pm{s}\sqrt{\mathrm{1}−{s}^{\mathrm{2}} }−\left(\pm\frac{\mathrm{1}}{{s}\sqrt{\mathrm{1}−{s}^{\mathrm{2}}…

Question Number 157258 by MathSh last updated on 21/Oct/21 $$\mathrm{Solve}\mathrm{for}\mathrm{real}\mathrm{numbers}:$$$$\frac{1}{{\sin }^{2\mathbf{k}}\left(\mathrm{x}\right)}+\frac{1}{{\cos }^{2\mathbf{k}}\left(\mathrm{x}\right)}=8;\mathrm{k}\in \mathbb{Z}$$ Commented by mr W last updated on 21/Oct/21 $$\left(\frac{\mathrm{1}}{\mathrm{sin}^{\mathrm{2}}…

Question Number 91688 by s.ayeni14@yahoo.com last updated on 02/May/20 $$solveequations{x}^x+y^y=31andx+y=5$$ Commented by mr W last updated on 02/May/20 $$ithinkyouknowbyyourselfx=2,y=3$$$${since}\:\mathrm{2}^{\mathrm{2}}…

Question Number 157222 by amin96 last updated on 21/Oct/21 Answered by Dimitri_01 last updated on 21/Oct/21 $$\mathrm{A}=\underset{n=1}{\sum ^{25}}\frac{1}{n(n+100)}=\frac{1}{100}\underset{n=1}{\sum ^{25}}\frac{(n+100)-n}{n(n+100)}$$$$\:\:\:\:=\frac{\mathrm{1}}{\mathrm{100}}\underset{{n}=\mathrm{1}} {\overset{\mathrm{25}} {\sum}}\left(\frac{\mathrm{1}}{{n}}−\frac{\mathrm{1}}{{n}+\mathrm{100}}\right)=\frac{\mathrm{1}}{\mathrm{100}}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{101}}+\frac{\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{102}}+\frac{\mathrm{1}}{\mathrm{3}}−\frac{\mathrm{1}}{\mathrm{103}}+\centerdot\centerdot\centerdot+\frac{\mathrm{1}}{\mathrm{25}}−\frac{\mathrm{1}}{\mathrm{125}}\right)…