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Category: Arithmetic

find-the-solution-6-x-gt-x-4-

Question Number 117641 by bemath last updated on 13/Oct/20 $$\mathrm{find}\:\mathrm{the}\:\mathrm{solution}\:\sqrt{\mathrm{6}−\mathrm{x}}\:>\:\mathrm{x}−\mathrm{4} \\ $$ Answered by Don08q last updated on 13/Oct/20 $$\left(\mathrm{6}−{x}\right)\:>\:\left({x}−\mathrm{4}\right)^{\mathrm{2}} \:{or}\:\left(\mathrm{6}−{x}\right)\:<\:\left({x}−\mathrm{4}\right)^{\mathrm{2}} \\ $$$$\:\:\:\:\:\:{when}\:\:\mathrm{6}\:−\:{x}\:>\:{x}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{16} \\…

It-takes-man-A-6-days-to-a-piece-of-work-It-takes-man-B-4-days-to-do-the-same-piece-of-work-How-many-days-will-A-and-B-take-to-do-the-same-piece-of-work-

Question Number 51649 by byaw last updated on 29/Dec/18 $$\mathrm{It}\:\mathrm{takes}\:\mathrm{man}\:\mathrm{A}\:\mathrm{6}\:\mathrm{days}\:\mathrm{to}\:\mathrm{a}\:\mathrm{piece}\:\mathrm{of} \\ $$$$\mathrm{work}.\:\mathrm{It}\:\mathrm{takes}\:\mathrm{man}\:\mathrm{B}\:\mathrm{4}\:\mathrm{days}\:\mathrm{to}\:\mathrm{do}\: \\ $$$$\mathrm{the}\:\mathrm{same}\:\mathrm{piece}\:\mathrm{of}\:\mathrm{work}.\:\mathrm{How}\:\mathrm{many} \\ $$$$\mathrm{days}\:\mathrm{will}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{take}\:\mathrm{to}\:\mathrm{do}\:\mathrm{the} \\ $$$$\mathrm{same}\:\mathrm{piece}\:\mathrm{of}\:\mathrm{work}? \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated…

x-y-z-t-Z-x-and-y-are-x-are-respectively-the-divisor-of-y-and-t-Justify-the-existence-of-k-Z-such-that-yt-xzk-Deduct-that-x-m-is-a-divisor-of-y-m-where-m-N-

Question Number 117116 by mathocean1 last updated on 10/Oct/20 $${x}\:,\:{y}\:,{z}\:,\:{t}\:\in\:\mathbb{Z}. \\ $$$${x}\:{and}\:{y}\:{are}\:{x}\:{are}\:{respectively}\:{the} \\ $$$${divisor}\:{of}\:{y}\:{and}\:{t}. \\ $$$${Justify}\:{the}\:{existence}\:{of}\:{k}\:\in\:\mathbb{Z}\:{such} \\ $$$${that}\:{yt}={xzk}. \\ $$$${Deduct}\:{that}\:{x}^{{m}\:} {is}\:{a}\:{divisor}\:{of}\:{y}^{{m}} \\ $$$${where}\:{m}\:\in\:\mathbb{N}. \\ $$…

find-unit-digit-of-1-2-3-4-5-100-

Question Number 117007 by TANMAY PANACEA last updated on 08/Oct/20 $${find}\:{unit}\:{digit}\:{of} \\ $$$$\mathrm{1}!+\mathrm{2}!+\mathrm{3}!+\mathrm{4}!+\mathrm{5}!+….+\mathrm{100}! \\ $$ Answered by mindispower last updated on 08/Oct/20 $${if}\:{n}\geqslant\mathrm{5}\:{n}!=\mathrm{0}\left(\mathrm{10}\right) \\ $$$$\mathrm{1}+\mathrm{2}!+\mathrm{3}!+\mathrm{4}!=\mathrm{24}+\mathrm{6}+\mathrm{4}+\mathrm{1}=\mathrm{35}…

f-z-r-e-i-2-f-z-

Question Number 51028 by gunawan last updated on 23/Dec/18 $${f}\left({z}\right)=\sqrt{{r}}\:{e}^{{i}\frac{\theta}{\mathrm{2}}} \\ $$$${f}'\left({z}\right)=…? \\ $$ 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 \\…

Given-3-2i-and-1-i-are-the-two-of-roots-of-the-equation-ax-4-bx-3-cx-3-dx-e-find-the-values-of-a-b-c-d-and-e-

Question Number 50970 by peter frank last updated on 22/Dec/18 $${Given}\:\mathrm{3}−\mathrm{2}{i}\:{and}\:\mathrm{1}+{i} \\ $$$${are}\:{the}\:{two}\:{of}\:{roots}\:{of} \\ $$$${the}\:{equation} \\ $$$${ax}^{\mathrm{4}} +{bx}^{\mathrm{3}} +{cx}^{\mathrm{3}} +{dx}+{e} \\ $$$${find}\:{the}\:{values}\:{of} \\ $$$${a},{b},{c},{d}\:{and}\:{e} \\…