Question Number 140193 by mathdanisur last updated on 05/May/21 $${Solve}\:{for}\:{real}\:{numbers} \\ $$$$\mathrm{4}{sin}\frac{\pi}{\mathrm{26}}\:+\:\mathrm{4}{xsin}\frac{\mathrm{3}\pi}{\mathrm{26}}\:+\:\mathrm{4}{sin}\frac{\mathrm{9}\pi}{\mathrm{26}}\:=\:{x}+\sqrt{\mathrm{13}} \\ $$ Answered by Dwaipayan Shikari last updated on 05/May/21 $${x}\left(\mathrm{1}−\mathrm{4}{sin}\frac{\mathrm{3}\pi}{\mathrm{26}}\right)=\mathrm{4}\left({sin}\frac{\mathrm{9}\pi}{\mathrm{26}}+{sin}\frac{\pi}{\mathrm{26}}\right)−\sqrt{\mathrm{13}} \\ $$$${x}=\frac{\mathrm{4}\left({sin}\frac{\mathrm{9}\pi}{\mathrm{26}}+{sin}\frac{\pi}{\mathrm{16}}\right)−\sqrt{\mathrm{13}}}{\left(\mathrm{1}−\mathrm{4}{sin}\frac{\mathrm{3}\pi}{\mathrm{26}}\right)}…
Question Number 9119 by tawakalitu last updated on 19/Nov/16 $$\mathrm{If}\:\:\mathrm{x}\:=\:\mathrm{5}^{\mathrm{1}/\mathrm{4}} \:+\:\mathrm{5}^{−\mathrm{1}/\mathrm{4}} \:\:\:\mathrm{and}\:\:\mathrm{y}\:=\:\mathrm{5}^{\mathrm{1}/\mathrm{4}} \:−\:\mathrm{5}^{−\mathrm{1}/\mathrm{4}} \\ $$$$\mathrm{Show}\:\mathrm{that}\::\:\mathrm{5}^{\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \right)^{\mathrm{2}} \:} =\:\mathrm{144} \\ $$ Answered by mrW last…
Question Number 140187 by mathsuji last updated on 05/May/21 $${Solution}\:{equation}: \\ $$$${sin}\mathrm{2}{x}=\mathrm{1}+\sqrt{\mathrm{2}}\:{cosx}+{cos}\mathrm{2}{x} \\ $$ Answered by Ankushkumarparcha last updated on 05/May/21 $${Solution}:\:\mathrm{sin}\left(\mathrm{2}{x}\right)\:=\:\mathrm{2cos}^{\mathrm{2}} \left({x}\right)+\sqrt{\mathrm{2}}\mathrm{cos}\left({x}\right)\:\left(\because\:\mathrm{cos}\left(\mathrm{2}{x}\right)\:=\:\mathrm{2cos}^{\mathrm{2}} \left({x}\right)−\mathrm{1}\right) \\…
Question Number 9096 by tawakalitu last updated on 17/Nov/16 Answered by mrW last updated on 19/Nov/16 $${let}\:{R}_{\mathrm{1}} \:{and}\:{R}_{\mathrm{2}} \:{be}\:{the}\:{rent}\:{of}\:{the}\:{first} \\ $$$${and}\:{second}\:{house}\:{last}\:{year}. \\ $$$$\frac{{R}_{\mathrm{1}} }{{R}_{\mathrm{2}} }=\frac{\mathrm{16}}{\mathrm{23}}…
Question Number 140166 by mathdanisur last updated on 04/May/21 $$\frac{\mathrm{7}−\mathrm{8}\sqrt{\mathrm{7}}{cos}\left(\frac{{arcsin}\left(\frac{\mathrm{3}\sqrt{\mathrm{21}}}{\mathrm{14}}\right)+\mathrm{4}\pi}{\mathrm{3}}\right)}{\mathrm{3}}\:+\:\mathrm{8}{cos}\left(\frac{\mathrm{4}\pi}{\mathrm{7}}\right)=\mathrm{1} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 74614 by chess1 last updated on 27/Nov/19 Answered by mind is power last updated on 27/Nov/19 $$\mathrm{we}\:\mathrm{can}\:\mathrm{extend}\:\mathrm{without} \\ $$$$\mathrm{and}\:\mathrm{U}_{\mathrm{i}+\mathrm{n}} =\mathrm{a}_{\mathrm{i}} ,\forall\mathrm{i}\in\left[\mathrm{1},\mathrm{n}\right] \\ $$$$\mathrm{U}_{\mathrm{i}}…
Question Number 74615 by chess1 last updated on 27/Nov/19 Answered by mind is power last updated on 27/Nov/19 $$\mathrm{a}=\mathrm{8}−\mathrm{b} \\ $$$$\left(\mathrm{2}\right)\Leftrightarrow\left(\mathrm{8}−\mathrm{b}\right)^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} +\mathrm{c}^{\mathrm{2}} =\mathrm{32} \\…
Question Number 74609 by TawaTawa last updated on 27/Nov/19 $$. \\ $$ Commented by TawaTawa last updated on 27/Nov/19 The force F acting along an inclined plane is just sufficient to maintain a body on the plane, the angle of friction M being less than Y, the angle of plane. prove that the least force acting along the plane, sufficient to drag the body up the plane is : F sin( M + Y )/sin( M - Y) Terms of Service Privacy Policy…
Question Number 74611 by chess1 last updated on 27/Nov/19 Answered by mind is power last updated on 27/Nov/19 $$\mathrm{et}\:\mathrm{x}=\mathrm{a}+\mathrm{1},\mathrm{y}=\mathrm{b}+\mathrm{1},\mathrm{z}=\mathrm{c}+\mathrm{1} \\ $$$$\mathrm{x}+\mathrm{y}+\mathrm{z}=\mathrm{11} \\ $$$$\frac{\mathrm{81}}{\mathrm{x}.\mathrm{y}.\mathrm{z}}\geqslant\frac{\mathrm{1}}{\:\sqrt[{\mathrm{4}}]{\mathrm{27}}} \\ $$$$\Leftrightarrow\mathrm{xyz}\leqslant\mathrm{81}.\sqrt[{\mathrm{4}}]{\mathrm{27}}…
Question Number 74604 by TawaTawa last updated on 27/Nov/19 $$. \\ $$ Commented by TawaTawa last updated on 27/Nov/19 Six balls are identical in size; 2 are red,2 white and 2 green. In how many different ways can they be arranged in a circle touching each other? Commented by mr W last…