Menu Close

Author: Tinku Tara

f-0-R-g-0-R-f-ux-f-uf-x-g-ux-g-u-f-x-f-x-g-x-

Question Number 3886 by 123456 last updated on 23/Dec/15 $${f}:\left[\mathrm{0},+\infty\right)\rightarrow\mathbb{R} \\ $$$${g}:\left[\mathrm{0},+\infty\right)\rightarrow\mathbb{R} \\ $$$${f}\left({ux}\right)={f}\left({uf}\left({x}\right)\right) \\ $$$${g}\left({ux}\right)={g}\left({u}+{f}\left({x}\right)\right) \\ $$$${f}\left({x}\right)+{g}\left({x}\right)=? \\ $$ Commented by Yozzii last updated…

Prove-that-there-are-n-r-1-n-1-ways-of-placing-r-identical-objects-in-n-compartments-where-n-gt-r-

Question Number 3884 by Yozzii last updated on 23/Dec/15 $${Prove}\:{that}\:{there}\:{are}\:\begin{pmatrix}{{n}+{r}−\mathrm{1}}\\{{n}−\mathrm{1}}\end{pmatrix}\: \\ $$$${ways}\:{of}\:{placing}\:{r}\:{identical}\:{objects} \\ $$$${in}\:{n}\:{compartments},\:{where}\:{n}>{r}. \\ $$ Commented by RasheedSindhi last updated on 24/Dec/15 $${Let}\:{r}\:{objects}\:{are}\:{denoted}\:{as}\: \\…

Four-integers-are-chosen-at-random-from-0-to-9-inclusive-Find-the-probability-that-no-more-than-2-integers-are-the-same-

Question Number 3881 by Yozzii last updated on 23/Dec/15 $${Four}\:{integers}\:{are}\:{chosen}\:{at}\:{random} \\ $$$${from}\:\mathrm{0}\:{to}\:\mathrm{9},\:{inclusive}.\:{Find}\:{the} \\ $$$${probability}\:{that}\:{no}\:{more}\:{than} \\ $$$$\mathrm{2}\:{integers}\:{are}\:{the}\:{same}.\: \\ $$$$ \\ $$ Commented by RasheedSindhi last updated…

Question-134949

Question Number 134949 by rexford last updated on 08/Mar/21 Answered by bobhans last updated on 30/Jan/22 $$\overset{\rightarrow} {\mathrm{b}}\:=\:\mathrm{2}\overset{\rightarrow} {\mathrm{c}}+\lambda\overset{\rightarrow} {\mathrm{a}}\:;\:\mid\overset{\rightarrow} {\mathrm{b}}\mid\:=\:\mid\mathrm{2}\overset{\rightarrow} {\mathrm{c}}+\lambda\overset{\rightarrow} {\mathrm{a}}\mid \\ $$$$\Rightarrow\:\mathrm{4}\:=\:\sqrt{\mid\mathrm{2}\overset{\rightarrow}…