Category: Arithmetic

Question Number 117007 by TANMAY PANACEA last updated on 08/Oct/20 $$findunitdigitof$$$$1!+2!+3!+4!+5!+\dots .+100!$$ Answered by mindispower last updated on 08/Oct/20 $$ifn⩾5n!=0\left(10\right)$$$$\mathrm{1}+\mathrm{2}!+\mathrm{3}!+\mathrm{4}!=\mathrm{24}+\mathrm{6}+\mathrm{4}+\mathrm{1}=\mathrm{35}…

Question Number 51028 by gunawan last updated on 23/Dec/18 $$f\left(z\right)=\sqrt{r}{e}^{i\frac{\theta }{2}}$$$$f^{\prime }\left(z\right)=\dots ?$$ Answered by tanmay.chaudhury50@gmail.com last updated on 23/Dec/18 $${df}=\left(\frac{\partial{f}}{\partial{r}}\right)_{\theta} {dr}+\left(\frac{\partial{f}}{\partial\theta}\right)_{{r}} {d}\theta \…

Question Number 50890 by peter frank last updated on 21/Dec/18 $$Determinewhether$$$$thefollowingistrueforall$$$$valueofx$$$$0⩽\frac{{(x+1)}^2}{x^2+x+1}⩽\frac{4}{3}$$ Answered by MJS last…

Question Number 116359 by bemath last updated on 03/Oct/20 $$\mathrm{If}0<\theta <\frac{\pi }{4}\mathrm{such}\mathrm{that}\mathrm{cosec}\theta -\sec \theta =\frac{\sqrt{13}}{6}$$$$\mathrm{then}\cot \theta -\tan \theta \mathrm{equals}\mathrm{to}\mathrm{\_}\mathrm{\_}$$ Answered by bobhans last updated on 03/Oct/20 $$\Rightarrow \mathrm{let}\sin \theta \cos \theta =\mathrm{r}.\mathrm{Then}{(\frac{1}{\sin \theta }-\frac{1}{\cos \theta })}^2=\frac{13}{36}$$$$\Rightarrow\:\frac{\left(\mathrm{cos}\:\theta−\mathrm{sin}\:\theta\right)^{\mathrm{2}}…

Question Number 181841 by mr W last updated on 01/Dec/22 $$whatislarger,\sqrt{11}+\sqrt{13}or7?$$ Answered by hmr last updated on 01/Dec/22 $$$$$$assumethat:$$$$\sqrt{\mathrm{11}}\:+\:\sqrt{\mathrm{13}\:}\:<\:\mathrm{7}…