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Category: Algebra

Question-58853

Question Number 58853 by cesar.marval.larez@gmail.com last updated on 30/Apr/19 Answered by MJS last updated on 01/May/19 $$\frac{\frac{\mathrm{3}}{\mathrm{2}}\mathrm{sin}^{\mathrm{3}} \:\frac{\pi}{\mathrm{2}}\:+\mathrm{cos}\:\frac{\mathrm{2}\pi}{\mathrm{3}}}{\mathrm{tan}\:\frac{\pi}{\mathrm{3}}\:+\mathrm{cos}\:−\mathrm{2}\pi}=\frac{\frac{\mathrm{3}}{\mathrm{2}}×\mathrm{1}^{\mathrm{3}} −\frac{\mathrm{1}}{\mathrm{2}}}{\:\sqrt{\mathrm{3}}+\mathrm{1}}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}+\mathrm{1}}=−\frac{\mathrm{1}}{\mathrm{2}}+\frac{\sqrt{\mathrm{3}}}{\mathrm{2}} \\ $$ Terms of Service Privacy…

If-x-y-are-real-numbers-satisfy-x-40-y-569-xy-26-y-x-then-xy-

Question Number 189919 by horsebrand11 last updated on 24/Mar/23 $$\:{If}\:{x},{y}\:{are}\:{real}\:{numbers}\:{satisfy} \\ $$$$\:\frac{{x}+\mathrm{40}}{{y}}+\frac{\mathrm{569}}{{xy}}=\frac{\mathrm{26}−{y}}{{x}}\:,\:{then}\:{xy}=? \\ $$ Answered by cortano12 last updated on 24/Mar/23 $$\Rightarrow\left(\mathrm{x}+\mathrm{20}\right)^{\mathrm{2}} +\left(\mathrm{y}−\mathrm{13}\right)^{\mathrm{2}} =\mathrm{0} \\…

e-x-gt-1-x-x-gt-0-set-x-pi-e-1-e-pi-e-1-gt-pi-e-e-pi-e-gt-pi-e-pi-e-e-gt-pi-e-e

Question Number 189886 by mnjuly1970 last updated on 23/Mar/23 $$ \\ $$$$\:\:{e}^{\:{x}} \:>\:\mathrm{1}+\:{x}\:\:\:\:\left(\forall\:{x}\:>\mathrm{0}\:\right) \\ $$$$\:\:\:{set}:\:{x}=\sqrt{\frac{\pi}{{e}}}\:−\mathrm{1} \\ $$$$\:\:\:\:{e}^{\:\frac{\sqrt{\pi}}{\:\sqrt{{e}}}\:−\mathrm{1}} >\:\frac{\sqrt{\pi}}{\:\sqrt{{e}}}\:\Rightarrow\:{e}^{\:\frac{\sqrt{\pi}}{\:\sqrt{{e}}}} \:>\:\sqrt{\pi}\: \\ $$$$\:\:\:\:\:\:\left(\:{e}^{\:\frac{\sqrt{\pi}}{\:\sqrt{{e}}}} \right)^{\:\sqrt{{e}}} >\:\sqrt{\pi}\:^{\:\sqrt{{e}}} \:\Rightarrow\:{e}^{\:\sqrt{\pi}} \:>\:\sqrt{\pi\:}\:^{\:\sqrt{{e}}}…

Question-58816

Question Number 58816 by Tawa1 last updated on 30/Apr/19 Answered by Kunal12588 last updated on 30/Apr/19 $${from}\:{looking}\:{the}\:{graph}\:{we}\:{can}\:{say}\:{that} \\ $$$${maxima}\:{of}\:{function}\:{is}\:{at}\:\:{x}=\mathrm{2} \\ $$$$\left.{for}\:{A}\right) \\ $$$$\frac{{d}\left({f}\left({x}\right)\right)}{{dx}}=\mathrm{0}\:\:\:\:\:\left[{for}\:{minima}\:{or}\:{maxima}\right] \\ $$$$−\frac{\mathrm{1}}{\mathrm{3}}×\mathrm{2}\left({x}−\mathrm{2}\right)\left(\mathrm{1}\right)=\mathrm{0}…