Question Number 131259 by Tinku Tara last updated on 03/Feb/21 $$\mathrm{Important}\:\mathrm{Information}: \\ $$$$\mathrm{If}\:\mathrm{you}\:\mathrm{are}\:\mathrm{a}\:\mathrm{student}\:\mathrm{and}\:\mathrm{not}\:\mathrm{able}\:\mathrm{to} \\ $$$$\mathrm{pay}/\mathrm{afford}\:\mathrm{premium}\:\mathrm{version}\:\mathrm{please} \\ $$$$\mathrm{send}\:\mathrm{us}\:\mathrm{an}\:\mathrm{email}\:\mathrm{with}\:\mathrm{your}\:\mathrm{forum} \\ $$$$\mathrm{user}\:\mathrm{id}\:\mathrm{to}\:\mathrm{get}\:\mathrm{free}\:\mathrm{premium}\:\mathrm{access} \\ $$$$\mathrm{for}\:\mathrm{1}\:\mathrm{year}. \\ $$$$\mathrm{Please}\:\mathrm{make}\:\mathrm{sure}\:\mathrm{you}\:\mathrm{include}\:\mathrm{your} \\ $$$$\mathrm{user}\:\mathrm{id}\:\mathrm{used}\:\mathrm{in}\:\mathrm{Q\&A}\:\mathrm{Forum}.…
Question Number 185 by 123456 last updated on 25/Jan/15 $$\mathrm{solve}\:\mathrm{10x}\equiv\mathrm{25}\left(\mathrm{mod}\:\mathrm{15}\right) \\ $$ Answered by mreddy last updated on 14/Dec/14 $$\mathrm{gcd}\left(\mathrm{10},\mathrm{15}\right)=\mathrm{5}\:\mathrm{and}\:\mathrm{5}\:\mathrm{divided}\:\mathrm{25}\:\mathrm{so}\: \\ $$$$\mathrm{there}\:\mathrm{are}\:\mathrm{5}\:\mathrm{solutions} \\ $$$$\mathrm{Solutions}\:\mathrm{are}\:\mathrm{given}\:\mathrm{by}\:\mathrm{equation} \\…
Question Number 131253 by bramlexs22 last updated on 03/Feb/21 $${Solve}\:\left({D}^{\mathrm{2}} −\mathrm{3}{D}+\mathrm{2}\right){y}\:=\:\mathrm{2}{x}^{\mathrm{3}} \\ $$$${by}\:{operator}\:{D}\:{method}\: \\ $$ Answered by liberty last updated on 03/Feb/21 $$\mathrm{y}_{\mathrm{h}} \left(\mathrm{x}\right)=\:\mathrm{C}_{\mathrm{1}} \mathrm{e}^{\mathrm{x}}…
Question Number 131252 by bramlexs22 last updated on 03/Feb/21 $$\:\int\:\mathrm{sin}\:^{\mathrm{3}} {t}\:\sqrt{\mathrm{9}{t}^{\mathrm{2}} +\mathrm{4cos}\:^{\mathrm{2}} {t}}\:{dt}\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 182 by sudhanshur last updated on 25/Jan/15 $$\mathrm{solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation} \\ $$$$\left({e}^{{y}} +\mathrm{1}\right)\mathrm{cos}\:{x}\:{dx}+{e}^{{y}} \mathrm{sin}\:{x}\:{dy}=\mathrm{0} \\ $$ Answered by 123456 last updated on 14/Dec/14 $$\mathrm{we}\:\mathrm{have}\:\left({e}^{{y}} +\mathrm{1}\right)\mathrm{cos}\:{x}\:{dx}+{e}^{{y}}…
Question Number 178 by 123456 last updated on 14/Dec/14 $$\mathrm{proof}\:\mathrm{that} \\ $$$$\mid\mathrm{sin}\:\mathrm{1sin}\:\mathrm{2}…\mathrm{sin}\:{n}\mid\leqslant\mathrm{sin}\:\frac{\pi}{{n}}\mathrm{sin}\:\frac{\mathrm{2}\pi}{{n}}…\mathrm{sin}\:\frac{\left({n}−\mathrm{1}\right)\pi}{{n}} \\ $$$$\mathrm{for}\:\forall{n}\in\mathbb{N}\backslash\left\{\mathrm{0},\mathrm{1}\right\} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 131248 by bramlexs22 last updated on 03/Feb/21 $${If}\:\alpha\:{and}\:\beta\:{are}\:{the}\:{coefficient}\: \\ $$$${of}\:{x}^{\mathrm{8}} \:{and}\:{x}^{−\mathrm{24}} \:{respectively}\: \\ $$$${in}\:{the}\:{expansion}\:{of}\:\left[\:{x}^{\mathrm{4}} +\mathrm{2}+\frac{\mathrm{1}}{{x}^{\mathrm{4}} }\:\right]^{\mathrm{10}} \\ $$$${in}\:{powers}\:{of}\:{x}\:{then}\:\frac{\alpha}{\beta}\:{is}\:{equal}\:{to}\: \\ $$ Answered by EDWIN88…
Question Number 177 by 123456 last updated on 25/Jan/15 $$\mathrm{solve}\:\mathrm{12x}\equiv\mathrm{34}\left(\mathrm{mod}\:\mathrm{56}\right) \\ $$ Answered by prakash jain last updated on 14/Dec/14 $$\mathrm{gcd}\left(\mathrm{12},\mathrm{56}\right)=\mathrm{4}\: \\ $$$$\mathrm{4}\:\mathrm{does}\:\mathrm{not}\:\mathrm{divide}\:\mathrm{34}\:\mathrm{so}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{has}\:\mathrm{no}\:\mathrm{solutions}. \\ $$…
Question Number 176 by 123456 last updated on 25/Jan/15 $$\mathrm{find}\:\mathrm{the}\:\mathrm{integer}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{3x}+\mathrm{4y}=\mathrm{5} \\ $$ Answered by prakash jain last updated on 14/Dec/14 $$\mathrm{gcd}\left(\mathrm{3},\mathrm{4}\right)=\mathrm{1}\:\mathrm{and}\:\mathrm{1}\:\mathrm{divides}\:\mathrm{5}\:\mathrm{so}\:\mathrm{it}\:\mathrm{is}\:\mathrm{solvable}. \\ $$$$\mathrm{Particular}\:\mathrm{solution}\:{x}=\mathrm{3},\:{y}=−\mathrm{1} \\ $$$$\mathrm{General}\:\mathrm{solution}…
Question Number 131245 by Ahmed1hamouda last updated on 02/Feb/21 $$\:\mathrm{Find}\: \\ $$$$\:\:\:\:\int_{−\mathrm{b}} ^{\mathrm{b}} \int_{−\mathrm{a}} ^{\mathrm{a}} \frac{\mathrm{d}{xdy}}{\:\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{h}^{\mathrm{2}} \right)^{\mathrm{3}/\mathrm{2}} } \\ $$ Answered by Ar…