Question Number 12998 by 1630321995 last updated on 10/May/17 $$\frac{{a}\:\underset{−} {+}\sqrt{\mathrm{2}{a}.\mathrm{1}.\mathrm{1}}}{\mathrm{2}} \\ $$ Answered by Joel577 last updated on 10/May/17 $$\frac{{a}\:\pm\:\sqrt{\mathrm{2}{a}}}{\mathrm{2}}\: \\ $$ Terms of…
Question Number 78493 by Rio Michael last updated on 18/Jan/20 $${the}\:{sum}\:{to}\:{infinity}\:{of}\:{a}\:{Geometric}\:{series}\:{is}\:{S} \\ $$$${the}\:{sum}\:{to}\:{infinty}\:{of}\:{the}\:{squares}\:{of}\:{the}\:{terms} \\ $$$${of}\:{the}\:{series}\:{is}\:\mathrm{2}{S} \\ $$$${the}\:{sum}\:{to}\:{infinity}\:{of}\:{the}\:{cubes}\:{of}\:{the}\:{terms} \\ $$$${of}\:{the}\:{series}\:{is}\:\frac{\mathrm{64}}{\mathrm{13}}{S}. \\ $$$${find}\:{the}\:{value}\:{of}\:{S}\:{and}\:{write}\:{iut}\:{the}\:{first} \\ $$$$\mathrm{3}\:{terms}\:{if}\:{the}\:{series}. \\ $$…
Question Number 12829 by tawa last updated on 03/May/17 Answered by mrW1 last updated on 03/May/17 $$\left(\mathrm{1}\right) \\ $$$${let}'{s}\:{say}\:{the}\:{mean}\:{mark}\:{of}\:{the}\:\mathrm{6}\:{students} \\ $$$${who}\:{passed}\:{is}\:{x}. \\ $$$${the}\:{total}\:{mark}\:{of}\:{the}\:\mathrm{2}\:{students}\:{who} \\ $$$${failed}\:{is}\:{y}.…
Question Number 12796 by tawa last updated on 01/May/17 $$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{two}\:\mathrm{positive}\:\:\mathrm{numbers}\:\mathrm{is}\:\mathrm{20}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{numbers} \\ $$$$\left(\mathrm{i}\right)\:\:\mathrm{If}\:\mathrm{their}\:\mathrm{product}\:\mathrm{is}\:\mathrm{maximum} \\ $$$$\left(\mathrm{ii}\right)\:\:\mathrm{If}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{their}\:\mathrm{square}\:\mathrm{is}\:\mathrm{maximum} \\ $$$$\left(\mathrm{iii}\right)\:\mathrm{If}\:\mathrm{the}\:\mathrm{product}\:\mathrm{of}\:\mathrm{the}\:\mathrm{square}\:\mathrm{of}\:\mathrm{one}\:\mathrm{and}\:\mathrm{the}\:\mathrm{cube}\:\mathrm{of}\:\mathrm{the}\:\mathrm{other}\:\mathrm{is}\:\mathrm{maximum} \\ $$ Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 01/May/17…
Question Number 12760 by tawa last updated on 30/Apr/17 Answered by mrW1 last updated on 01/May/17 $${Q}\mathrm{5} \\ $$$${total}\:{number}\:{of}\:{ways}\:{for}\:{Sofia}\:{and}\:{Tesa}\: \\ $$$${each}\:{to}\:{choose}\:{one}\:{integer}\:{from}\:\mathrm{1}\:{to}\:\mathrm{10}: \\ $$$$\mathrm{10}×\mathrm{10}=\mathrm{100} \\ $$$$…
Question Number 143794 by Huy last updated on 18/Jun/21 $$\mathrm{Prove}\:\:\:\:\:\:\:\:\:\mathrm{3}^{\mathrm{111}} +\mathrm{1}\vdots\mathrm{223} \\ $$ Commented by TheHoneyCat last updated on 18/Jun/21 $${sorry}\:{for}\:{my}\:{ignorance}; \\ $$$${what}\:{does}\:{a}\vdots{b}\:{means}? \\ $$$${I}'{ve}\:{notices}\:{it}\:{is}\:{defined}\:{on}\:{integers}…
Question Number 12605 by tawa last updated on 26/Apr/17 Answered by ajfour last updated on 26/Apr/17 $${let}\:{painter}\:{worked}\:{for}\:{N}\:{days}\:. \\ $$$$\mathrm{40}{N}+\mathrm{10}\left({N}−\mathrm{10}\right)=\mathrm{2000} \\ $$$$\mathrm{50}{N}=\mathrm{2100}\:\:\:\Rightarrow\:\:{N}=\mathrm{42} \\ $$$${assistant}\:{worked}\:{N}−\mathrm{10}\:=\mathrm{32}\:{days} \\ $$$${he}\:{received}\:=#\mathrm{320}\:.…
Question Number 77953 by pete last updated on 12/Jan/20 $$\mathrm{Given}\:\mathrm{that}\:\underset{\mathrm{r}=\mathrm{0}} {\overset{\mathrm{4}} {\sum}}\mathrm{6r}\:=\mathrm{2}\underset{\mathrm{r}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mathrm{5r},\:\mathrm{work}\:\mathrm{out}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:\mathrm{n}. \\ $$ Answered by john santu last updated on…
Question Number 12326 by sin (x) last updated on 19/Apr/17 $$\underset{{n}=\mathrm{1}} {\overset{{x}} {\prod}}{a}_{{n}} =\mathrm{9}^{{x}!} \\ $$$${a}_{\mathrm{4}} =? \\ $$ Answered by nume1114 last updated on…
Question Number 77848 by jagoll last updated on 11/Jan/20 Commented by jagoll last updated on 11/Jan/20 $${dear}\:{sir}\:{W} \\ $$$${look}\:{picture}\: \\ $$$${correct}\:{a}\:=\:\sqrt{{b}×{c}}? \\ $$ Commented by…