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Category: Algebra

Question-191283

Question Number 191283 by Shrinava last updated on 22/Apr/23 Answered by amin96 last updated on 22/Apr/23 $$\boldsymbol{\mathrm{this}}\:\boldsymbol{\mathrm{problem}}\:\boldsymbol{\mathrm{new}}\:\boldsymbol{\mathrm{RMM}}\:\boldsymbol{\mathrm{problem}} \\ $$$$\boldsymbol{\mathrm{solution}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{on}}\:\boldsymbol{\mathrm{my}}\:\boldsymbol{\mathrm{instagram}}\:\boldsymbol{\mathrm{page}}\: \\ $$$$ \\ $$@mathematics.azerbaijan Terms of…

x-y-z-simple-numbers-y-lt-x-lt-z-y-x-z-68-y-x-x-z-z-y-1121-y-x-

Question Number 125743 by MathSh last updated on 13/Dec/20 $$\boldsymbol{{x}}\:;\:\boldsymbol{{y}}\:;\:\boldsymbol{{z}}\:\rightarrow\:\boldsymbol{{simple}}\:\boldsymbol{{numbers}}\:, \\ $$$$\boldsymbol{{y}}<\boldsymbol{{x}}<\boldsymbol{{z}}\:, \\ $$$$\boldsymbol{{y}}+\boldsymbol{{x}}+\boldsymbol{{z}}=\mathrm{68}\:, \\ $$$$\boldsymbol{{y}}\:\centerdot\:\boldsymbol{{x}}\:+\:\boldsymbol{{x}}\:\centerdot\:\boldsymbol{{z}}\:+\:\boldsymbol{{z}}\:\centerdot\:\boldsymbol{{y}}\:=\:\mathrm{1121}\:, \\ $$$$\boldsymbol{{y}}\:\centerdot\:\boldsymbol{{x}}\:=\:? \\ $$ Commented by MJS_new last updated…

solving-u-v-w-with-u-v-w-C-finding-all-possible-solutions-I-tested-this-with-several-values-and-found-no-mistake-please-review-and-comment-I-hope-this-will-help-at-least-some-of-you-

Question Number 60175 by MJS last updated on 18/May/19 $$\mathrm{solving}\:{u}^{{v}} ={w}\:\mathrm{with}\:{u},\:{v},\:{w}\:\in\mathbb{C} \\ $$$$\mathrm{finding}\:\mathrm{all}\:\mathrm{possible}\:\mathrm{solutions} \\ $$$$\mathrm{I}\:\mathrm{tested}\:\mathrm{this}\:\mathrm{with}\:\mathrm{several}\:\mathrm{values}\:\mathrm{and}\:\mathrm{found} \\ $$$$\mathrm{no}\:\mathrm{mistake}.\:\mathrm{please}\:\mathrm{review}\:\mathrm{and}\:\mathrm{comment}. \\ $$$$\mathrm{I}\:\mathrm{hope}\:\mathrm{this}\:\mathrm{will}\:\mathrm{help}\:\mathrm{at}\:\mathrm{least}\:\mathrm{some}\:\mathrm{of}\:\mathrm{you}. \\ $$ Commented by MJS last…

Prove-by-principle-of-mathematical-induction-sin-x-sin-2x-sin-3x-sin-nx-cos-1-2-x-cos-n-1-2-x-2-sin-1-2-x-

Question Number 60156 by Tawa1 last updated on 18/May/19 $$\mathrm{Prove}\:\mathrm{by}\:\mathrm{principle}\:\mathrm{of}\:\mathrm{mathematical}\:\mathrm{induction} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{sin}\left(\mathrm{x}\right)\:+\:\mathrm{sin}\left(\mathrm{2x}\right)\:+\:\mathrm{sin}\left(\mathrm{3x}\right)\:+\:…\:+\:\mathrm{sin}\left(\mathrm{nx}\right)\:\:=\:\:\frac{\mathrm{cos}\left(\frac{\mathrm{1}}{\mathrm{2}}\mathrm{x}\right)\:−\:\mathrm{cos}\left(\mathrm{n}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\right)\mathrm{x}}{\mathrm{2}\:\mathrm{sin}\left(\frac{\mathrm{1}}{\mathrm{2}}\mathrm{x}\right)} \\ $$ Commented by Smail last updated on 19/May/19 $${sinx}+{sin}\mathrm{2}{x}+…+{sin}\left({nx}\right)=\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}{sin}\left({kx}\right) \\…

show-that-cos-4pi-5-cos-2pi-5-1-0-

Question Number 125686 by mathocean1 last updated on 12/Dec/20 $${show}\:{that} \\ $$$${cos}\frac{\mathrm{4}\pi}{\mathrm{5}}+{cos}\frac{\mathrm{2}\pi}{\mathrm{5}}+\mathrm{1}=\mathrm{0} \\ $$ Commented by bramlexs22 last updated on 13/Dec/20 $$\mathrm{cos}\:\frac{\mathrm{4}\pi}{\mathrm{5}}\:=\:\mathrm{cos}\:\left(\pi−\frac{\pi}{\mathrm{5}}\right)=−\mathrm{cos}\:\frac{\pi}{\mathrm{5}} \\ $$$$\mathrm{cos}\:\frac{\mathrm{4}\pi}{\mathrm{5}}\:=\:−\mathrm{cos}\:\mathrm{36}°\: \\…

N-lt-10200-N-has-five-digits-N-22-23-and-N-5-17-Determinate-the-integer-N-

Question Number 125670 by mathocean1 last updated on 12/Dec/20 $${N}<\mathrm{10200}\:,\:{N}\:{has}\:{five}\:{digits}. \\ $$$${N}\equiv\mathrm{22}\left[\mathrm{23}\right]\:{and}\:{N}\equiv\mathrm{5}\left[\mathrm{17}\right]. \\ $$$${Determinate}\:{the}\:{integer}\:{N}. \\ $$ Answered by floor(10²Eta[1]) last updated on 12/Dec/20 $$\mathrm{10000}\leqslant\mathrm{N}<\mathrm{10200} \\…

we-are-in-C-solve-z-5-1-show-that-the-sum-of-its-solutions-is-null-the-deduct-that-cos-2pi-5-cos-4pi-5-1-2-

Question Number 125669 by mathocean1 last updated on 12/Dec/20 $${we}\:{are}\:{in}\:\mathbb{C}. \\ $$$${solve}\:{z}^{\mathrm{5}} =\mathrm{1}. \\ $$$${show}\:{that}\:{the}\:{sum}\:{of}\:{its}\:{solutions}\:{is} \\ $$$${null}\:{the}\:{deduct}\:{that}\:{cos}\left(\frac{\mathrm{2}\pi}{\mathrm{5}}\right)+{cos}\left(\frac{\mathrm{4}\pi}{\mathrm{5}}\right)=−\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Answered by mr W last updated…