Menu Close

Category: Algebra

If-z-1-z-2-and-z-3-are-the-vertices-of-an-equilateral-triangle-described-in-counterclock-sense-and-w-1-is-a-cube-root-of-unity-then-A-z-1-z-3-z-3-z-2-w-B-z-1-z-2-w-z-3-w-2-0-C-1-z

Question Number 140107 by EnterUsername last updated on 04/May/21 $$\mathrm{If}\:{z}_{\mathrm{1}} ,\:{z}_{\mathrm{2}} ,\:\mathrm{and}\:{z}_{\mathrm{3}} \:\mathrm{are}\:\mathrm{the}\:\mathrm{vertices}\:\mathrm{of}\:\mathrm{an}\:\mathrm{equilateral}\:\mathrm{triangle} \\ $$$$\mathrm{described}\:\mathrm{in}\:\mathrm{counterclock}\:\mathrm{sense}\:\mathrm{and}\:{w}\neq\mathrm{1}\:\mathrm{is}\:\mathrm{a}\:\mathrm{cube}\:\mathrm{root} \\ $$$$\mathrm{of}\:\mathrm{unity},\:\mathrm{then} \\ $$$$\left(\mathrm{A}\right)\:{z}_{\mathrm{1}} −{z}_{\mathrm{3}} =\left({z}_{\mathrm{3}} −{z}_{\mathrm{2}} \right){w} \\ $$$$\left(\mathrm{B}\right)\:{z}_{\mathrm{1}}…

2cos-x-4-cos-x-4-

Question Number 9029 by rzagung last updated on 15/Nov/16 $$ \\ $$$$\mathrm{2}{cos}\left({x}+\Pi/\mathrm{4}\right)={cos}\left({x}−\Pi/\mathrm{4}\right) \\ $$ Answered by Rasheed Soomro last updated on 15/Nov/16 $$\mathrm{2}{cos}\left({x}+\pi/\mathrm{4}\right)={cos}\left({x}−\pi/\mathrm{4}\right) \\ $$$$\mathrm{cos}\left(\mathrm{x}+\pi/\mathrm{4}\right)+\mathrm{cos}\left(\mathrm{x}+\pi/\mathrm{4}\right)−\mathrm{cos}\left(\mathrm{x}−\pi/\mathrm{4}\right)=\mathrm{0}…

Question-9020

Question Number 9020 by tawakalitu last updated on 14/Nov/16 Commented by RasheedSoomro last updated on 20/Nov/16 $$\mathrm{By}\:\left[\frac{\mathrm{ax}^{\mathrm{2}} +\mathrm{bx}+\mathrm{c}}{\mathrm{2x}+\mathrm{b}}\right]\:\mathrm{do}\:\mathrm{you}\:\mathrm{mean}\:\mathrm{bracket}\:\mathrm{function}? \\ $$ Answered by Rasheed Soomro last…

Find-the-superimum-of-the-set-n-2-2-n-

Question Number 74554 by shubham90412@gmail.com last updated on 26/Nov/19 $$\boldsymbol{{Find}}\:\boldsymbol{{the}}\:\boldsymbol{{superimum}}\:\boldsymbol{{of}}\:\boldsymbol{{the}}\:\boldsymbol{{set}}\:\left\{\frac{\boldsymbol{{n}}^{\mathrm{2}} }{\mathrm{2}^{\boldsymbol{{n}}} }\right\} \\ $$ Answered by MJS last updated on 26/Nov/19 $$\mathrm{trying} \\ $$$${S}=\left\{\mathrm{0},\:\frac{\mathrm{1}}{\mathrm{2}},\:\mathrm{1},\:\frac{\mathrm{9}}{\mathrm{8}},\:\mathrm{1},\:\frac{\mathrm{25}}{\mathrm{32}},\:\frac{\mathrm{9}}{\mathrm{16}},\:…\right\} \\…

1-2-1-3-2-3-5-2-5-7-2-7-

Question Number 140090 by mathdanisur last updated on 04/May/21 $$\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{1}} }+\frac{\mathrm{3}}{\mathrm{2}^{\mathrm{3}} }+\frac{\mathrm{5}}{\mathrm{2}^{\mathrm{5}} }+\frac{\mathrm{7}}{\mathrm{2}^{\mathrm{7}} }+..=? \\ $$ Answered by qaz last updated on 04/May/21 $${S}=\underset{{n}=\mathrm{0}} {\overset{\infty}…

If-x-3y-6z-7z-2-and-y-1-2-z-6y-3-2-z-6y-Find-x-3-y-3-

Question Number 9009 by tawakalitu last updated on 13/Nov/16 $$\mathrm{If}\::\:\:\mathrm{x}\:=\:\frac{\mathrm{3y}\:+\:\mathrm{6z}}{\mathrm{7z}\:−\:\mathrm{2}}\:\:\mathrm{and}\:\:\mathrm{y}\:=\:\frac{\frac{\mathrm{1}}{\mathrm{2}}\mathrm{z}\:+\:\mathrm{6y}}{\frac{\mathrm{3}}{\mathrm{2}}\mathrm{z}\:+\:\mathrm{6y}} \\ $$$$\mathrm{Find}\::\:\:\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{y}^{\mathrm{3}} \\ $$ Answered by Rasheed Soomro last updated on 14/Nov/16 $$\mathrm{If}\::\:\:\mathrm{x}\:=\:\frac{\mathrm{3y}\:+\:\mathrm{6z}}{\mathrm{7z}\:−\:\mathrm{2}}\:\:\mathrm{and}\:\:\mathrm{y}\:=\:\frac{\frac{\mathrm{1}}{\mathrm{2}}\mathrm{z}\:+\:\mathrm{6y}}{\frac{\mathrm{3}}{\mathrm{2}}\mathrm{z}\:+\:\mathrm{6y}}=\frac{\mathrm{z}+\mathrm{12y}}{\mathrm{3z}+\mathrm{12y}} \\…

prove-1-2-3-4-5-6-2n-1-2n-1-3n-1-

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}}…

If-2-x-3-y-6-z-find-the-value-of-1-x-1-y-1-z-

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}}…