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Category: Algebra

Question-9128

Question Number 9128 by tawakalitu last updated on 20/Nov/16 Commented by tawakalitu last updated on 20/Nov/16 $$\mathrm{Note}:\:\:#\:\mathrm{means}\:\:\mathrm{Naira}\:\mathrm{in}\:\mathrm{Nigeria}. \\ $$$$\mathrm{while}:\:\:\mathrm{K}\:\mathrm{means}\:\:\mathrm{Kobo}\:\mathrm{in}\:\mathrm{Nigeria} \\ $$$$\mathrm{and} \\ $$$$\mathrm{100}\:\mathrm{kobo}\:=\:\mathrm{1}\:\mathrm{Naira}\:\:\:\:\left(\mathrm{100k}\:=\:#\mathrm{1}\right) \\ $$…

Let-a-gt-0-and-z-1-z-a-z-0-is-a-complex-number-Then-the-maximum-and-minimum-values-of-z-are-A-a-a-2-4-2-B-2a-a-2-4-2-C-a-2-4-

Question Number 140198 by EnterUsername last updated on 05/May/21 $$\mathrm{Let}\:{a}>\mathrm{0}\:\mathrm{and}\:\mid{z}+\left(\mathrm{1}/{z}\right)\mid={a}\:\left({z}\neq\mathrm{0}\:\mathrm{is}\:\mathrm{a}\:\mathrm{complex}\:\mathrm{number}\right). \\ $$$$\mathrm{Then}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{and}\:\mathrm{minimum}\:\mathrm{values}\:\mathrm{of}\:\mid{z}\mid\:\mathrm{are} \\ $$$$\left(\mathrm{A}\right)\:\frac{{a}+\sqrt{{a}^{\mathrm{2}} +\mathrm{4}}}{\mathrm{2}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{B}\right)\:\frac{\mathrm{2}{a}+\sqrt{{a}^{\mathrm{2}} +\mathrm{4}}}{\mathrm{2}} \\ $$$$\left(\mathrm{C}\right)\:\frac{\sqrt{{a}^{\mathrm{2}} +\mathrm{4}}−{a}}{\mathrm{2}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{D}\right)\:\frac{\sqrt{{a}^{\mathrm{2}} +\mathrm{4}}−\mathrm{2}{a}}{\mathrm{2}} \\ $$ Answered by Dwaipayan…

If-x-x-y-y-z-z-c-show-that-at-x-y-z-2-z-x-y-x-log-ex-1-

Question Number 74663 by TawaTawa last updated on 28/Nov/19 $$\mathrm{If}\:\:\:\:\mathrm{x}^{\mathrm{x}} \:\mathrm{y}^{\mathrm{y}} \:\mathrm{z}^{\mathrm{z}} \:\:\:=\:\:\:\mathrm{c}\:\:\:\:\:\:\:\mathrm{show}\:\mathrm{that}\:\mathrm{at}\:\:\:\:\:\mathrm{x}\:\:=\:\:\mathrm{y}\:\:=\:\:\mathrm{z} \\ $$$$\:\:\:\:\:\:\frac{\partial^{\mathrm{2}} \mathrm{z}}{\partial\mathrm{x}\partial\mathrm{y}}\:\:\:=\:\:\:−\:\left(\mathrm{x}\:\mathrm{log}\:\mathrm{ex}\right)^{−\mathrm{1}} \\ $$ Answered by mind is power last updated…

simplify-x-2-x-1-1-2-x-1-1-2-x-2-

Question Number 9123 by j.masanja06@gmail.com last updated on 20/Nov/16 $$\mathrm{simplify} \\ $$$$\left(\mathrm{x}^{\mathrm{2}} \left(\mathrm{x}+\mathrm{1}\right)^{−\mathrm{1}/\mathrm{2}} −\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{1}/\mathrm{2}} \right)/\mathrm{x}^{\mathrm{2}} \\ $$ Commented by tawakalitu last updated on 20/Nov/16 $$\frac{\mathrm{x}^{\mathrm{2}}…

Solve-for-real-numbers-4sin-pi-26-4xsin-3pi-26-4sin-9pi-26-x-13-

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)}…

If-x-5-1-4-5-1-4-and-y-5-1-4-5-1-4-Show-that-5-x-2-y-2-2-144-

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…

Solution-equation-sin2x-1-2-cosx-cos2x-

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-9096

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-74614

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}}…