Menu Close

Category: Algebra

Question-83262

Question Number 83262 by peter frank last updated on 29/Feb/20 Answered by mr W last updated on 29/Feb/20 $${curve}\:\mathrm{1}:\:{x}^{\mathrm{2}} +\mathrm{4}{y}^{\mathrm{2}} =\mathrm{8}\:\:\:…\left({i}\right) \\ $$$${curve}\:\mathrm{2}:\:{x}^{\mathrm{2}} −\mathrm{2}{y}^{\mathrm{2}} =\mathrm{4}\:\:\:…\left({ii}\right)…

Evaluate-3-2-

Question Number 17713 by tawa tawa last updated on 09/Jul/17 $$\mathrm{Evaluate}:\:\:\:\:\left(−\sqrt{\mathrm{3}}\right)^{\left(−\sqrt{\mathrm{2}}\right)} \\ $$ Commented by b.e.h.i.8.3.417@gmail.com last updated on 09/Jul/17 $${a}=\left(−\sqrt{\mathrm{3}}\right)^{\left(−\sqrt{\mathrm{2}}\right)} \\ $$$${lna}=−\sqrt{\mathrm{2}}{ln}\left(−\sqrt{\mathrm{3}}\right)=−\sqrt{\mathrm{2}}{ln}\left({i}^{\mathrm{2}} \sqrt{\mathrm{3}}\right)= \\…

Question-148776

Question Number 148776 by liberty last updated on 31/Jul/21 Answered by mathmax by abdo last updated on 31/Jul/21 $$\mathrm{P}=\prod_{\mathrm{k}=\mathrm{2}} ^{\mathrm{2020}} \:\frac{\mathrm{k}^{\mathrm{2}} }{\mathrm{k}^{\mathrm{2}} −\mathrm{1}}=\prod_{\mathrm{k}=\mathrm{2}} ^{\mathrm{2020}} \:\frac{\mathrm{k}}{\mathrm{k}−\mathrm{1}}×\frac{\mathrm{k}}{\mathrm{k}+\mathrm{1}}…

Question-83229

Question Number 83229 by peter frank last updated on 28/Feb/20 Commented by jagoll last updated on 28/Feb/20 $$\left(\mathrm{iii}\right)\:\frac{\mathrm{cos}\:\mathrm{3A}−\mathrm{cos}\:\mathrm{9A}+\mathrm{cos}\:\mathrm{A}−\mathrm{cos}\:\mathrm{3A}}{\mathrm{sin}\:\mathrm{9A}−\mathrm{sin}\:\mathrm{3A}+\mathrm{sin}\:\mathrm{3A}−\mathrm{sin}\:\mathrm{A}} \\ $$$$=\frac{\mathrm{cos}\:\mathrm{A}−\mathrm{cos}\:\mathrm{9A}}{\mathrm{sin}\:\mathrm{9A}−\mathrm{sin}\:\mathrm{A}}\:=\:\frac{\mathrm{2sin}\:\mathrm{5Asin}\:\mathrm{4A}}{\mathrm{2cos}\:\mathrm{5Asin}\:\mathrm{4A}} \\ $$$$=\:\mathrm{tan}\:\mathrm{5A} \\ $$ Commented…