Question Number 9004 by mrW last updated on 12/Nov/16 $$\mathrm{prove} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\centerdot\frac{\mathrm{3}}{\mathrm{4}}\centerdot\frac{\mathrm{5}}{\mathrm{6}}\centerdot\centerdot\centerdot\centerdot\centerdot\frac{\mathrm{2n}−\mathrm{1}}{\mathrm{2n}}\leqslant\frac{\mathrm{1}}{\:\sqrt{\mathrm{3n}+\mathrm{1}}} \\ $$ Answered by mrW last updated on 15/Nov/16 $$\mathrm{Using}\:\mathrm{mathematical}\:\mathrm{induction} \\ $$$$\mathrm{prove}\:{P}\left(\mathrm{n}\right)=\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}}…
Question Number 8998 by tawakalitu last updated on 11/Nov/16 $$\mathrm{If}\:\:\mathrm{2}^{\mathrm{x}} \:=\:\mathrm{3}^{\mathrm{y}} \:=\:\mathrm{6}^{−\mathrm{z}} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\::\:\:\frac{\mathrm{1}}{\mathrm{x}}\:+\:\frac{\mathrm{1}}{\mathrm{y}}\:+\:\frac{\mathrm{1}}{\mathrm{z}} \\ $$ Answered by Rasheed Soomro last updated on 12/Nov/16 $$\mathrm{If}\:\:\mathrm{2}^{\mathrm{x}}…
Question Number 8985 by j.masanja06@gmail.com last updated on 10/Nov/16 $$\mathrm{solve}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x} \\ $$$$\mathrm{log}_{\mathrm{x}} \mathrm{3}=\mathrm{81} \\ $$ Answered by Rasheed Soomro last updated on 10/Nov/16 $$\mathrm{log}_{\mathrm{x}} \mathrm{3}=\mathrm{81}…
Question Number 140042 by denzel last updated on 03/May/21 Answered by MJS_new last updated on 03/May/21 $$\mathrm{254}=\frac{\mathrm{1269}}{\mathrm{4}+\mathrm{46e}^{−.\mathrm{3}{t}} } \\ $$$$\mathrm{just}\:\mathrm{transform}\:\mathrm{it} \\ $$$$\mathrm{e}^{−.\mathrm{3}{t}} =\frac{\frac{\mathrm{1269}}{\mathrm{254}}−\mathrm{4}}{\mathrm{46}}=\frac{\mathrm{11}}{\mathrm{508}} \\ $$$$−.\mathrm{3}{t}=\mathrm{ln}\:\frac{\mathrm{11}}{\mathrm{508}}…
Question Number 140040 by bobhans last updated on 03/May/21 $$\:\sqrt[{\mathrm{3}}]{\mathrm{45}+\mathrm{29}\sqrt{\mathrm{2}}}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{45}−\mathrm{29}\sqrt{\mathrm{2}}}\:=?\: \\ $$ Answered by cherokeesay last updated on 05/May/21 $${U}\:=\:\sqrt[{\mathrm{3}}]{\mathrm{45}\:+\mathrm{29}\sqrt{\mathrm{2}}}\:\:\:\:\:{V}\:=\:\sqrt[{\mathrm{3}}]{\mathrm{45}−\mathrm{29}\sqrt{\mathrm{2}}} \\ $$$${U}^{\:\mathrm{3}} \:=\:\mathrm{45}\:+\mathrm{29}\sqrt{\mathrm{2}}\:\:\:\:{V}^{\:\mathrm{3}} \:=\:\mathrm{45}\:−\mathrm{29}\sqrt{\mathrm{2}}\:\: \\…
Question Number 8965 by Joel575 last updated on 08/Nov/16 $${If} \\ $$$${xy}\:−\:{x}\:=\:{yz}\:−\:\mathrm{2}{y}\:=\:{xz}\:+\:\mathrm{3}{z}\:=\:\mathrm{3} \\ $$$${and} \\ $$$${xyz}\:>\:\mathrm{0} \\ $$$${What}\:{is}\:{the}\:{value}\:{of}\:{xyz}\:? \\ $$ Commented by sou1618 last updated…
Question Number 140030 by mathdanisur last updated on 03/May/21 Answered by mr W last updated on 03/May/21 Commented by mathdanisur last updated on 03/May/21 $${cool}\:{thanks}\:{sir}…
Question Number 8956 by j.masanja06@gmail.com last updated on 07/Nov/16 $$\mathrm{prove}\:\mathrm{that}; \\ $$$$\mathrm{log}_{\mathrm{ab}} \mathrm{x}=\frac{\mathrm{log}_{\mathrm{a}} \mathrm{x}−\mathrm{log}_{\mathrm{b}} \mathrm{x}}{\mathrm{log}_{\mathrm{a}} \mathrm{x}+\mathrm{log}_{\mathrm{b}} \mathrm{x}} \\ $$ Commented by sou1618 last updated on…
Question Number 8934 by j.masanja06@gmail.com last updated on 06/Nov/16 $$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\mathrm{x}. \\ $$$$\mathrm{3}^{\mathrm{x}+\mathrm{1}} =\mathrm{2}^{\mathrm{x}+\mathrm{2}} \\ $$ Answered by Rasheed Soomro last updated on 08/Nov/16 $$\mathrm{3}^{\mathrm{x}+\mathrm{1}} =\mathrm{2}^{\mathrm{x}+\mathrm{2}}…
Question Number 139998 by bramlexs22 last updated on 03/May/21 Commented by bramlexs22 last updated on 03/May/21 $$\mathrm{find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\Delta\mathrm{ABC} \\ $$ Answered by som(math1967) last updated on…