Question Number 75987 by Ajao yinka last updated on 21/Dec/19 Answered by MJS last updated on 22/Dec/19 $${m}=\sqrt{{x}}\wedge{n}=\sqrt{{y}} \\ $$$${x}^{\mathrm{3}} +\left(\mathrm{375}{y}\right){x}+\left({y}^{\mathrm{3}} −\mathrm{1953125}\right)=\mathrm{0} \\ $$$$\mathrm{Cardano}\:\mathrm{with}\:{p}=\mathrm{375}{y}\wedge{q}={y}^{\mathrm{3}} −\mathrm{1953125}…
Question Number 10364 by Joel575 last updated on 05/Feb/17 $$\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}+\mathrm{5}+\mathrm{6}+\mathrm{7}+\mathrm{8}+\mathrm{9}+\mathrm{10}+\mathrm{11}\:=\:{x}^{{y}} \\ $$$$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{possible}\:\mathrm{solutions}\:\mathrm{of}\:{x}\:\mathrm{and}\:{y}\:\mathrm{is}\:… \\ $$ Answered by mrW1 last updated on 05/Feb/17 $$\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}+\mathrm{5}+\mathrm{6}+\mathrm{7}+\mathrm{8}+\mathrm{9}+\mathrm{10}+\mathrm{11}=\frac{\mathrm{11}×\mathrm{12}}{\mathrm{2}}=\mathrm{66} \\ $$$${x}^{{y}} =\mathrm{66}…
Question Number 75771 by Ajao yinka last updated on 16/Dec/19 Commented by mind is power last updated on 17/Dec/19 $$\tau\left(\mathrm{n}^{\mathrm{2}} \right)=\underset{\mathrm{d}\mid\mathrm{n}} {\sum}\mathrm{2}^{\omega\left(\mathrm{d}\right)} ? \\ $$…
Question Number 10142 by 0942679167 last updated on 26/Jan/17 Commented by prakash jain last updated on 27/Jan/17 $$\underset{{i}={x}} {\overset{{x}+\mathrm{7}} {\sum}}{i}^{\mathrm{3}} =\underset{{i}=\mathrm{1}} {\overset{{x}+\mathrm{7}} {\sum}}{i}^{\mathrm{3}} −\underset{{i}=\mathrm{1}} {\overset{{x}−\mathrm{1}}…
Question Number 10070 by Tawakalitu ayo mi last updated on 23/Jan/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{of}\:, \\ $$$$\mathrm{3333333334}^{\mathrm{2}} \\ $$ Answered by ridwan balatif last updated on 23/Jan/17 $$\mathrm{3}^{\mathrm{2}}…
Question Number 9790 by tawakalitu last updated on 04/Jan/17 $$\mathrm{prove}\:\mathrm{by}\:\mathrm{mathematical}\:\mathrm{induction} \\ $$$$\mathrm{n}!\:\leqslant\:\mathrm{n}^{\mathrm{n}} \\ $$ Commented by FilupSmith last updated on 04/Jan/17 $${n}=\mathrm{1} \\ $$$$\mathrm{1}!\leqslant\mathrm{1}^{\mathrm{1}} \\…
Question Number 140833 by liberty last updated on 13/May/21 $$\mathrm{Determine}\:\mathrm{if}\:\mathrm{the}\:\mathrm{series}\:\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\mathrm{a}_{\mathrm{n}} \\ $$$$\mathrm{defined}\:\mathrm{by}\:\mathrm{the}\:\:\mathrm{formula}\:\mathrm{converges}\:\mathrm{or} \\ $$$$\mathrm{diverges}\:.\:\mathrm{a}_{\mathrm{1}} =\:\mathrm{4}\:,\:\mathrm{a}_{\mathrm{n}+\mathrm{1}} \:=\:\frac{\mathrm{10}+\mathrm{sin}\:\mathrm{n}}{\mathrm{n}}.\:\mathrm{a}_{\mathrm{n}} \\ $$ Commented by liberty last updated…
Question Number 9485 by Joel575 last updated on 10/Dec/16 $${a}_{{n}} \:=\:{a}_{{n}−\mathrm{1}} ^{\mathrm{2}} \:+\:{a}_{{n}−\mathrm{2}} ^{\mathrm{2}} \\ $$$$\mathrm{If}\:{a}_{\mathrm{1}} =\mathrm{1}\:\mathrm{and}\:{a}_{\mathrm{2}} =\mathrm{1},\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{of}\:{a}_{\mathrm{2016}} \:\mathrm{when}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{10}\:? \\ $$ Commented by sou1618 last…
Question Number 140449 by byaw last updated on 07/May/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{first}\:\mathrm{four}\:\mathrm{values}\:\mathrm{of} \\ $$$$\mathrm{2}{x}+\mathrm{5}=\mathrm{1}\left(\mathrm{mod}\:\mathrm{7}\right) \\ $$ Answered by Rasheed.Sindhi last updated on 08/May/21 $$\mathrm{2}{x}+\mathrm{5}=\mathrm{1}\left(\mathrm{mod}\:\mathrm{7}\right) \\ $$$$\mathrm{2}{x}\equiv\mathrm{1}−\mathrm{5}=−\mathrm{4}\left({mod}\mathrm{7}\right) \\…
Question Number 140428 by byaw last updated on 07/May/21 $$\mathrm{If}\:\mathrm{4}{x}=\mathrm{3}\left(\mathrm{Mod}\:\mathrm{6}\right),\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{first}\:\mathrm{four}\:\mathrm{values}\:\mathrm{of}\:{x}. \\ $$ Commented by mr W last updated on 07/May/21 $$\mathrm{4}{x}\:{is}\:{even}. \\ $$$${but}\:{when}\:{it}\:{is}\:{divided}\:{by}\:\mathrm{6}\:{and}\:{the}…