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Question Number 52086 Answers: 1 Comments: 3

If 1,a_(1,) a_2 ,...,a_(n−1) are n^(th) roots of unity, then prove that. (1+a_1 )(1+a_2 )..(1+a_(n−1) )= n if n is even 0 if n is odd

$$\mathrm{If}\:\mathrm{1},{a}_{\mathrm{1},} {a}_{\mathrm{2}} ,...,{a}_{{n}−\mathrm{1}} \:\mathrm{are}\:{n}^{{th}} \:\mathrm{roots}\:\mathrm{of} \\ $$$$\mathrm{unity},\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that}. \\ $$$$\left(\mathrm{1}+{a}_{\mathrm{1}} \right)\left(\mathrm{1}+{a}_{\mathrm{2}} \right)..\left(\mathrm{1}+{a}_{{n}−\mathrm{1}} \right)= \\ $$$${n}\:\:\mathrm{if}\:{n}\:\mathrm{is}\:\mathrm{even} \\ $$$$\mathrm{0}\:\mathrm{if}\:{n}\:\mathrm{is}\:\mathrm{odd} \\ $$

Question Number 52082 Answers: 1 Comments: 1

Question Number 52079 Answers: 1 Comments: 1

Sum to the n terms of the series whose n^(th ) term is 2^(n−1 ) + 8n^3 −6n^2

$${Sum}\:{to}\:{the}\:{n}\:{terms}\:{of}\:{the}\:{series}\:{whose}\:{n}^{{th}\:} \:{term}\:{is}\:\mathrm{2}^{{n}−\mathrm{1}\:} \:+\:\mathrm{8}{n}^{\mathrm{3}} \:−\mathrm{6}{n}^{\mathrm{2}} \\ $$

Question Number 52075 Answers: 0 Comments: 0

Question Number 52072 Answers: 0 Comments: 0

Question Number 52061 Answers: 2 Comments: 3

Question Number 52059 Answers: 0 Comments: 1

Question Number 52058 Answers: 1 Comments: 0

Question Number 52052 Answers: 0 Comments: 1

Question Number 52038 Answers: 1 Comments: 0

(6x+8)+3=(8x−5)−6 sir plz help me

$$\left(\mathrm{6x}+\mathrm{8}\right)+\mathrm{3}=\left(\mathrm{8x}−\mathrm{5}\right)−\mathrm{6}\:\:\: \\ $$$$\mathrm{sir}\:\mathrm{plz}\:\mathrm{help}\:\mathrm{me} \\ $$

Question Number 52034 Answers: 1 Comments: 1

Question Number 52043 Answers: 1 Comments: 1

Question Number 52031 Answers: 2 Comments: 1

Question Number 52030 Answers: 1 Comments: 0

given that log2=0.3010 log3=0.477 log5=0.699 find the values of log(√((0.2)))

$${given}\:{that}\:{log}\mathrm{2}=\mathrm{0}.\mathrm{3010}\:{log}\mathrm{3}=\mathrm{0}.\mathrm{477}\:{log}\mathrm{5}=\mathrm{0}.\mathrm{699} \\ $$$${find}\:{the}\:{values}\:{of}\:{log}\sqrt{\left(\mathrm{0}.\mathrm{2}\right)} \\ $$$$ \\ $$

Question Number 52449 Answers: 0 Comments: 0

let j=e^((i2π)/3) and P(x)=(1+jx)^n −(1−jx)^n with n integr natural 1) find roots of P(x) 2)factorize P(x) inside C[x] 3) calculate ∫_0 ^1 P(x)dx. 4) decompose inside C(x) the fraction F(x)=(1/(P(x)))

$${let}\:{j}={e}^{\frac{{i}\mathrm{2}\pi}{\mathrm{3}}} \:\:\:{and}\:{P}\left({x}\right)=\left(\mathrm{1}+{jx}\right)^{{n}} −\left(\mathrm{1}−{jx}\right)^{{n}} \:\:{with}\:{n}\:{integr}\:{natural} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{roots}\:{of}\:{P}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){factorize}\:{P}\left({x}\right)\:{inside}\:{C}\left[{x}\right] \\ $$$$\left.\mathrm{3}\right)\:\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {P}\left({x}\right){dx}. \\ $$$$\left.\mathrm{4}\right)\:{decompose}\:{inside}\:{C}\left({x}\right)\:{the}\:{fraction}\:{F}\left({x}\right)=\frac{\mathrm{1}}{{P}\left({x}\right)} \\ $$

Question Number 52025 Answers: 4 Comments: 8

Question Number 52016 Answers: 1 Comments: 1

Question Number 52012 Answers: 0 Comments: 2

Question Number 52138 Answers: 1 Comments: 0

Question Number 52137 Answers: 0 Comments: 0

Question Number 52007 Answers: 2 Comments: 0

Solve: ((x/4))^(log_5 50x) = x^6

$$\mathrm{Solve}:\:\:\:\:\:\:\:\:\:\:\left(\frac{\boldsymbol{\mathrm{x}}}{\mathrm{4}}\right)^{\boldsymbol{\mathrm{log}}_{\mathrm{5}} \mathrm{50}\boldsymbol{\mathrm{x}}} \:\:\:=\:\:\:\:\boldsymbol{\mathrm{x}}^{\mathrm{6}} \\ $$

Question Number 52006 Answers: 1 Comments: 1

Differentiate sin^(−1) [((ln x)/(cos x))] with respect to tan x^2

$${Differentiate}\:\mathrm{sin}^{−\mathrm{1}} \left[\frac{\mathrm{ln}\:{x}}{\mathrm{cos}\:{x}}\right] \\ $$$${with}\:{respect}\:{to}\:\mathrm{tan}\:{x}^{\mathrm{2}} \\ $$

Question Number 51998 Answers: 0 Comments: 1

let U ={(x,y)∈R^2 / 1≤x^2 +2y^2 ≤3} calculate ∫∫_U ((x−y)/(x^2 +y^2 ))dxdxy

$${let}\:{U}\:=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\:\mathrm{1}\leqslant{x}^{\mathrm{2}} \:+\mathrm{2}{y}^{\mathrm{2}} \leqslant\mathrm{3}\right\} \\ $$$${calculate}\:\int\int_{{U}} \:\:\:\:\frac{{x}−{y}}{{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} }{dxdxy} \\ $$

Question Number 51997 Answers: 1 Comments: 2

let f(x)=∫_0 ^(π/2) (dt/(1+xsint)) with x>−1 1) calculate f(o) ,f(1) and f(2) 2) give f at form of function

$${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\:\frac{{dt}}{\mathrm{1}+{xsint}}\:\:{with}\:{x}>−\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({o}\right)\:,{f}\left(\mathrm{1}\right)\:{and}\:{f}\left(\mathrm{2}\right) \\ $$$$\left.\mathrm{2}\right)\:{give}\:{f}\:{at}\:{form}\:{of}\:{function}\: \\ $$$$ \\ $$

Question Number 51996 Answers: 1 Comments: 1

calculate S_n =Σ_(k=0) ^(n−1) sin((π/(4n)) +((kπ)/(2n)))

$${calculate}\:{S}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:{sin}\left(\frac{\pi}{\mathrm{4}{n}}\:+\frac{{k}\pi}{\mathrm{2}{n}}\right)\: \\ $$$$ \\ $$

Question Number 51995 Answers: 1 Comments: 0

let f defined on [0,1] by f(0)=0 and f(x)=(1/(2[(1/(2x))]+1)) calculate ∫_0 ^1 f(x)dx

$${let}\:\:{f}\:{defined}\:{on}\:\left[\mathrm{0},\mathrm{1}\right]\:{by}\:\:{f}\left(\mathrm{0}\right)=\mathrm{0}\:{and}\:{f}\left({x}\right)=\frac{\mathrm{1}}{\mathrm{2}\left[\frac{\mathrm{1}}{\mathrm{2}{x}}\right]+\mathrm{1}} \\ $$$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({x}\right){dx} \\ $$

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