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Question Number 29123 Answers: 0 Comments: 0

Question Number 29049 Answers: 1 Comments: 0

Prove that e^(iπ) +1=0

$${Prove}\:{that} \\ $$$$\:\:\:\:\:{e}^{{i}\pi} +\mathrm{1}=\mathrm{0} \\ $$

Question Number 28921 Answers: 1 Comments: 0

Question Number 28857 Answers: 1 Comments: 0

Question Number 28856 Answers: 0 Comments: 0

Question Number 28739 Answers: 1 Comments: 0

if S_n =((a(r^n −1))/(r−1)) make r the subject of formula

$${if}\:{S}_{{n}} =\frac{{a}\left({r}^{{n}} −\mathrm{1}\right)}{{r}−\mathrm{1}}\: \\ $$$$ \\ $$$${make}\:{r}\:{the}\:{subject}\:{of}\:{formula} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 28642 Answers: 0 Comments: 0

f(x)=4x−1for0<x<4 find f(0) ,f(1) f(1.2),f(4),f(−1)

$${f}\left({x}\right)=\mathrm{4}{x}−\mathrm{1}{for}\mathrm{0}<{x}<\mathrm{4}\:{find}\:{f}\left(\mathrm{0}\right)\:,{f}\left(\mathrm{1}\right) \\ $$$${f}\left(\mathrm{1}.\mathrm{2}\right),{f}\left(\mathrm{4}\right),{f}\left(−\mathrm{1}\right) \\ $$

Question Number 28554 Answers: 2 Comments: 0

(((a − b))/((c − d))) = 3 (((a − c))/((b − d))) = 4 (((a − d))/((b − c))) = ?

$$\frac{\left({a}\:−\:{b}\right)}{\left({c}\:−\:{d}\right)}\:\:=\:\:\mathrm{3} \\ $$$$\frac{\left({a}\:−\:{c}\right)}{\left({b}\:−\:{d}\right)}\:\:=\:\:\mathrm{4} \\ $$$$\frac{\left({a}\:−\:{d}\right)}{\left({b}\:−\:{c}\right)}\:\:=\:\:? \\ $$$$ \\ $$

Question Number 28546 Answers: 0 Comments: 0

let give w=e^(i((2π)/n)) and S= Σ_(k=0) ^(n−1) w^k^2 1) prove that S= Σ_(k=0) ^(n−1) w^((q+k)^2 ) 2) find ∣S∣.

$${let}\:{give}\:{w}={e}^{{i}\frac{\mathrm{2}\pi}{{n}}} \:\:\:{and}\:\:{S}=\:\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:\:{w}^{{k}^{\mathrm{2}} } \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:\:\:{S}=\:\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:\:{w}^{\left({q}+{k}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{2}\right)\:{find}\:\mid{S}\mid. \\ $$

Question Number 28544 Answers: 0 Comments: 2

if a_1 ,a_2 ,...a_(14 ) are roots of the polynomial p(x)=x^(14) +x^8 2x+1 calculate Σ_(i=1) ^(14) (1/((a_i −1)^2 )) .

$${if}\:\:{a}_{\mathrm{1}} \:,{a}_{\mathrm{2}} ,...{a}_{\mathrm{14}\:} {are}\:{roots}\:{of}\:{the}\:{polynomial} \\ $$$${p}\left({x}\right)={x}^{\mathrm{14}} +{x}^{\mathrm{8}} \:\mathrm{2}{x}+\mathrm{1}\:\:\:{calculate}\:\:\sum_{{i}=\mathrm{1}} ^{\mathrm{14}} \:\:\frac{\mathrm{1}}{\left({a}_{{i}} −\mathrm{1}\right)^{\mathrm{2}} }\:\:. \\ $$

Question Number 28534 Answers: 0 Comments: 1

find n from N in ordre tohave x^2 +x+1 divide (x+1)^n −x^n −1.

$${find}\:{n}\:{from}\:{N}\:\:{in}\:{ordre}\:{tohave}\:{x}^{\mathrm{2}} +{x}+\mathrm{1}\:{divide} \\ $$$$\left({x}+\mathrm{1}\right)^{{n}} −{x}^{{n}} −\mathrm{1}. \\ $$

Question Number 28533 Answers: 0 Comments: 1

let give the matrice A= (((1 2 )),((2 1)) ) calculate A^n then find e^A .

$${let}\:{give}\:{the}\:{matrice}\:\:{A}=\:\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:\:\:\mathrm{2}\:\:\:}\\{\mathrm{2}\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}}\end{pmatrix} \\ $$$${calculate}\:\:{A}^{{n}} \:\:{then}\:{find}\:\:{e}^{{A}} \:. \\ $$

Question Number 28532 Answers: 0 Comments: 1

let give A_n = ( C_n ^0 .C_n ^1 ....C_n ^n )^(1/(n+1)) find^n (√A) _n .

$${let}\:{give}\:\:{A}_{{n}} =\:\left(\:{C}_{{n}} ^{\mathrm{0}} \:.{C}_{{n}} ^{\mathrm{1}} \:....{C}_{{n}} ^{{n}} \right)^{\frac{\mathrm{1}}{{n}+\mathrm{1}}} \:\:\:{find}\:^{{n}} \sqrt{{A}}\:_{{n}} . \\ $$

Question Number 28506 Answers: 0 Comments: 3

Question Number 28435 Answers: 0 Comments: 0

find Q(x) / nx^(n+1) −(n+1)x^n +1 =(x−1)^2 Q(x).

$${find}\:{Q}\left({x}\right)\:/\:{nx}^{{n}+\mathrm{1}} −\left({n}+\mathrm{1}\right){x}^{{n}} +\mathrm{1}\:=\left({x}−\mathrm{1}\right)^{\mathrm{2}} {Q}\left({x}\right). \\ $$

Question Number 28434 Answers: 0 Comments: 0

let give the polynomial p(x)=(x+1)^n −(x−1)^n with n from N^∗ 1) give the factorisation of p(x) inside C[x] 2) prove that Π_(k=0) ^(n−1) cotan(((kπ)/(2p+1)))=(1/(√(2p+1)))

$${let}\:{give}\:{the}\:{polynomial}\:{p}\left({x}\right)=\left({x}+\mathrm{1}\right)^{{n}} −\left({x}−\mathrm{1}\right)^{{n}} {with}\:{n} \\ $$$${from}\:{N}^{\ast} \\ $$$$\left.\mathrm{1}\right)\:{give}\:{the}\:{factorisation}\:{of}\:{p}\left({x}\right)\:{inside}\:{C}\left[{x}\right] \\ $$$$\left.\mathrm{2}\right)\:{prove}\:{that}\:\prod_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} {cotan}\left(\frac{{k}\pi}{\mathrm{2}{p}+\mathrm{1}}\right)=\frac{\mathrm{1}}{\sqrt{\mathrm{2}{p}+\mathrm{1}}} \\ $$

Question Number 28433 Answers: 0 Comments: 0

let give T_n (x)= cos(narcosx) decompose (1/(T_n (x))).

$${let}\:{give}\:{T}_{{n}} \left({x}\right)=\:{cos}\left({narcosx}\right)\:\:{decompose}\:\frac{\mathrm{1}}{{T}_{{n}} \left({x}\right)}. \\ $$

Question Number 28432 Answers: 0 Comments: 1

let put w=e^(i((2π)/n)) calculate S_n = Σ_(k=0) ^(n−1) (1/(x−w^k )) and W_n = Σ_(k=0) ^(n−1) (1/((x−w^k )^2 )) .

$${let}\:{put}\:{w}={e}^{{i}\frac{\mathrm{2}\pi}{{n}}} \:{calculate}\:\:{S}_{{n}} =\:\:\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:\:\:\frac{\mathrm{1}}{{x}−{w}^{{k}} }\:\:{and} \\ $$$${W}_{{n}} =\:\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:\:\frac{\mathrm{1}}{\left({x}−{w}^{{k}} \right)^{\mathrm{2}} }\:. \\ $$

Question Number 28393 Answers: 0 Comments: 0

Find the value of Σ_(i = 0) ^(33) (((99)),((3k)) )

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\underset{{i}\:=\:\mathrm{0}} {\overset{\mathrm{33}} {\sum}}\:\begin{pmatrix}{\mathrm{99}}\\{\mathrm{3}{k}}\end{pmatrix} \\ $$

Question Number 28382 Answers: 1 Comments: 0

A boat of mass m, traveling with v of Vo at t=0. A power is shut off assuming water resistance is proportioal to Vn^ and V is instantaneous velocity find V as a function of the distance travelled

$${A}\:{boat}\:{of}\:{mass}\:{m},\:{traveling}\:{with}\:{v}\:{of}\:{Vo}\:{at} \\ $$$${t}=\mathrm{0}.\:{A}\:{power}\:{is}\:{shut}\:{off}\:{assuming}\:{water}\: \\ $$$${resistance}\:{is}\:{proportioal}\:{to}\:{V}\hat {{n}}\:\:{and}\:{V}\:{is}\: \\ $$$${instantaneous}\:{velocity}\:{find}\:{V}\:{as}\:{a}\:{function} \\ $$$${of}\:{the}\:{distance}\:{travelled} \\ $$

Question Number 28381 Answers: 0 Comments: 0

Question Number 28375 Answers: 1 Comments: 0

4kg ball falls from rest at time t =0 in a medium offering a resistance in kg numerically equal to twice its instantaneous velocity in m/s. find; (a) the velocity and distance travelled at any time t>0 (b) the limiting velocity

$$\:\mathrm{4}{kg}\:{ball}\:{falls}\:{from}\:{rest}\:{at}\:{time}\:{t}\:=\mathrm{0}\:{in}\:{a}\: \\ $$$${medium}\:{offering}\:\:{a}\:{resistance}\:{in}\:{kg}\: \\ $$$${numerically}\:{equal}\:{to}\:{twice}\:{its}\:{instantaneous} \\ $$$${velocity}\:{in}\:{m}/{s}. \\ $$$${find}; \\ $$$$\left({a}\right)\:{the}\:{velocity}\:{and}\:{distance}\:{travelled}\:{at}\:{any}\: \\ $$$${time}\:{t}>\mathrm{0}\: \\ $$$$\left({b}\right)\:{the}\:{limiting}\:{velocity}\: \\ $$

Question Number 28372 Answers: 0 Comments: 0

let give w=e^(i2(π/n)) .calculate Π_(l=0_(l≠k) ) ^(n−1) (w^k −w^l ) .

$${let}\:{give}\:{w}={e}^{{i}\mathrm{2}\frac{\pi}{{n}}} \:\:\:\:.{calculate}\:\:\prod_{{l}=\mathrm{0}_{{l}\neq{k}} } ^{{n}−\mathrm{1}} \:\:\:\left({w}^{{k}} \:\:−{w}^{{l}} \right)\:. \\ $$

Question Number 28371 Answers: 0 Comments: 1

prove that x^2 −2x cosθ +1 divide x^(2n) −2x^n cos(nθ)+1

$${prove}\:{that}\:{x}^{\mathrm{2}} −\mathrm{2}{x}\:{cos}\theta\:+\mathrm{1}\:{divide}\:{x}^{\mathrm{2}{n}} \:−\mathrm{2}{x}^{{n}} {cos}\left({n}\theta\right)+\mathrm{1} \\ $$

Question Number 28370 Answers: 0 Comments: 1

1) factorizse p(x) =x^n −1 inside C[x] 2) find the value of Π_(k=1) ^(n−1) sin(((kπ)/n)) 3)find also the value of Π_(k=0) ^(n−1) sin(((kπ)/n) +θ).

$$\left.\mathrm{1}\right)\:{factorizse}\:{p}\left({x}\right)\:={x}^{{n}} \:−\mathrm{1}\:\:{inside}\:{C}\left[{x}\right] \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\prod_{{k}=\mathrm{1}} ^{{n}−\mathrm{1}} \:{sin}\left(\frac{{k}\pi}{{n}}\right) \\ $$$$\left.\mathrm{3}\right){find}\:{also}\:{the}\:{value}\:{of}\:\:\:\:\prod_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:\:{sin}\left(\frac{{k}\pi}{{n}}\:+\theta\right). \\ $$

Question Number 28369 Answers: 0 Comments: 0

let give the matrice A = (((1 0 0)),((0 1 1)) ) [ (1 0 1 A ∈ M_3 (R) write A at form A= I +J and calculate A^n .

$${let}\:{give}\:{the}\:{matrice}\:\:\:{A}\:=\:\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\mathrm{0}\:\:\:\:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\mathrm{1}}\end{pmatrix} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left[\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{1}\:\:\:\:\:\:\:\:\mathrm{0}\:\:\:\:\:\:\mathrm{1}\right.\right. \\ $$$${A}\:\in\:{M}_{\mathrm{3}} \left({R}\right)\:\:{write}\:\:{A}\:{at}\:{form}\:\:{A}=\:{I}\:+{J}\:\:\:\:{and}\:{calculate} \\ $$$${A}^{{n}} . \\ $$

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