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Question Number 67234 Answers: 2 Comments: 3

factorise p(x)=1+x+x^2 +x^3 +x^5 inside C[x] and R[x] calculate p(e^(i(π/5)) ) and p(cos((π/5)))

$${factorise}\:{p}\left({x}\right)=\mathrm{1}+{x}+{x}^{\mathrm{2}} \:+{x}^{\mathrm{3}} \:+{x}^{\mathrm{5}} \\ $$$${inside}\:{C}\left[{x}\right]\:{and}\:{R}\left[{x}\right] \\ $$$${calculate}\:{p}\left({e}^{{i}\frac{\pi}{\mathrm{5}}} \right)\:{and}\:{p}\left({cos}\left(\frac{\pi}{\mathrm{5}}\right)\right) \\ $$

Question Number 67233 Answers: 0 Comments: 1

calculate ∫_0 ^1 ((xdx)/(√(1+x^4 )))

$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{xdx}}{\sqrt{\mathrm{1}+{x}^{\mathrm{4}} }} \\ $$

Question Number 67232 Answers: 1 Comments: 1

calculate Σ_(n=1) ^∞ ((cos(n(π/3)))/n)

$${calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{{cos}\left({n}\frac{\pi}{\mathrm{3}}\right)}{{n}} \\ $$

Question Number 67231 Answers: 2 Comments: 0

find ∫x/x^5 −1) dx

$$\left.{find}\:\int{x}/{x}^{\mathrm{5}} −\mathrm{1}\right)\:{dx} \\ $$

Question Number 67298 Answers: 0 Comments: 2

Find the third degree polynomial which vanishes when x =−1 and x = 2, which has a value 8 when x =0 and leaves a remainder ((16)/3) when divided by 3x + 2.

$${Find}\:\:{the}\:{third}\:{degree}\:{polynomial}\:{which}\:{vanishes}\:{when} \\ $$$${x}\:=−\mathrm{1}\:{and}\:{x}\:=\:\mathrm{2},\:{which}\:{has}\:{a}\:{value}\:\mathrm{8}\:{when}\:{x}\:=\mathrm{0}\:{and}\:{leaves}\:{a}\:{remainder}\:\frac{\mathrm{16}}{\mathrm{3}}\:{when} \\ $$$${divided}\:{by}\:\:\mathrm{3}{x}\:+\:\mathrm{2}. \\ $$

Question Number 67294 Answers: 0 Comments: 3

solve for x and y the simultaneous equation log_3 x = y = log(2x − 1)

$${solve}\:{for}\:\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}\:{the}\:{simultaneous}\:{equation} \\ $$$$\:\mathrm{log}_{\mathrm{3}} {x}\:=\:{y}\:=\:\mathrm{log}\left(\mathrm{2}{x}\:−\:\mathrm{1}\right) \\ $$

Question Number 67215 Answers: 1 Comments: 1

Question Number 67208 Answers: 1 Comments: 6

Find the times in a day when the hour′s, minute′s and second′s hand of a clock occupy the same angular position. [old question reposted]

$${Find}\:{the}\:{times}\:{in}\:{a}\:{day}\:{when} \\ $$$${the}\:{hour}'{s},\:{minute}'{s}\:{and}\:{second}'{s} \\ $$$${hand}\:{of}\:{a}\:{clock}\:{occupy}\:{the}\:{same} \\ $$$${angular}\:{position}. \\ $$$$\left[{old}\:{question}\:{reposted}\right] \\ $$

Question Number 67197 Answers: 1 Comments: 0

∫_0 ^2 x^5 (1−(x/2))^4 dx

$$\int_{\mathrm{0}} ^{\mathrm{2}} {x}^{\mathrm{5}} \left(\mathrm{1}−\frac{{x}}{\mathrm{2}}\right)^{\mathrm{4}} {dx} \\ $$

Question Number 67193 Answers: 0 Comments: 7

Question Number 67189 Answers: 1 Comments: 0

solve inside R^3 the system { ((2x+y+z =1)),((x+2y+z =2)) :} {x+y+2z =3

$${solve}\:{inside}\:{R}^{\mathrm{3}} \:{the}\:{system}\:\begin{cases}{\mathrm{2}{x}+{y}+{z}\:=\mathrm{1}}\\{{x}+\mathrm{2}{y}+{z}\:=\mathrm{2}}\end{cases} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left\{{x}+{y}+\mathrm{2}{z}\:=\mathrm{3}\right. \\ $$

Question Number 67187 Answers: 0 Comments: 1

let f(x) =arctan(x^3 ) 1)calculate f^((n)) (x)and f^((n)) (0) 2) developp f at integr serie 3) calculate ∫_0 ^1 arctan(x^3 )dx

$${let}\:{f}\left({x}\right)\:={arctan}\left({x}^{\mathrm{3}} \right) \\ $$$$\left.\mathrm{1}\right){calculate}\:{f}^{\left({n}\right)} \left({x}\right){and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{arctan}\left({x}^{\mathrm{3}} \right){dx} \\ $$

Question Number 67167 Answers: 4 Comments: 2

solve for real x and y:[a,b∈R] a. { ((x^3 +1=y^3 )),((x^2 +1=y^2 )) :} b. { ((x^3 +x^2 +1=y^3 )),((x^2 +x+1=y^2 )) :} c. { ((x^3 +y^2 =9xy)),((x^2 +y^3 =8xy)) :} d. { ((ax+by=2ab)),((x^2 +y^2 =4abxy)) :}

Question Number 67153 Answers: 2 Comments: 0

find ∫(v^3 −2)/(v^4 +v )dv

$${find}\:\int\left({v}^{\mathrm{3}} −\mathrm{2}\right)/\left({v}^{\mathrm{4}} +{v}\:\:\right){dv} \\ $$

Question Number 67148 Answers: 0 Comments: 6

explicitez la suite u_n definie par la relation; { ((u_0 =0, u_1 =1)),((u_(n+2) =u_(n+1) +u_n ∀n∈∤N)) :} u_n =???????? −calculer la lim _(n→∞) (u_(n+1) /u_n )=??? −montre que Σ_(k=0) ^n u_k =u_(n+2) −1 voila^′

$$\mathrm{explicitez}\:\:\:\mathrm{la}\:\mathrm{suite}\:\mathrm{u}_{\mathrm{n}} \mathrm{definie}\:\mathrm{par}\:\mathrm{la}\:\mathrm{relation}; \\ $$$$\begin{cases}{\mathrm{u}_{\mathrm{0}} =\mathrm{0},\:\mathrm{u}_{\mathrm{1}} =\mathrm{1}}\\{\mathrm{u}_{\mathrm{n}+\mathrm{2}} =\mathrm{u}_{\mathrm{n}+\mathrm{1}} +\mathrm{u}_{\mathrm{n}} \:\:\:\forall\mathrm{n}\in\nmid\boldsymbol{\mathrm{N}}}\end{cases} \\ $$$$\boldsymbol{{u}}_{\boldsymbol{{n}}} =???????? \\ $$$$−\mathrm{calculer}\:\mathrm{la}\:\mathrm{lim}\underset{\mathrm{n}\rightarrow\infty} {\:}\frac{\mathrm{u}_{\mathrm{n}+\mathrm{1}} }{\mathrm{u}_{\mathrm{n}} }=??? \\ $$$$−\mathrm{montre}\:\mathrm{que}\:\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\mathrm{u}_{\mathrm{k}} =\mathrm{u}_{\mathrm{n}+\mathrm{2}} −\mathrm{1} \\ $$$$\:\:\:\:\:\:\mathrm{voila}^{'} \\ $$

Question Number 67138 Answers: 0 Comments: 1

find the area abounded y=(√x) and y=x−2?

$${find}\:{the}\:{area}\:{abounded}\:{y}=\sqrt{{x}} \\ $$$${and}\:{y}={x}−\mathrm{2}? \\ $$

Question Number 67136 Answers: 2 Comments: 0

factorize 2x^3 −1

$${factorize}\:\mathrm{2}{x}^{\mathrm{3}} −\mathrm{1} \\ $$

Question Number 67122 Answers: 1 Comments: 0

Question Number 67116 Answers: 4 Comments: 1

Question Number 67108 Answers: 2 Comments: 2

Three school children share some oranges as follows: Akwasi gets (1/3) of the total and the remainder is shared between Abena and Juana in the ratio 2: 3 . If Abena gets 24 oranges , how many does Akwasi get.

$$\mathrm{Three}\:\mathrm{school}\:\mathrm{children}\:\mathrm{share}\:\mathrm{some}\: \\ $$$$\mathrm{oranges}\:\mathrm{as}\:\mathrm{follows}:\:\mathrm{Akwasi}\:\mathrm{gets}\:\frac{\mathrm{1}}{\mathrm{3}}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{total}\:\mathrm{and}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{is}\:\mathrm{shared} \\ $$$$\mathrm{between}\:\mathrm{Abena}\:\mathrm{and}\:\mathrm{Juana}\:\mathrm{in}\:\mathrm{the}\:\mathrm{ratio} \\ $$$$\mathrm{2}:\:\mathrm{3}\:.\:\mathrm{If}\:\mathrm{Abena}\:\mathrm{gets}\:\mathrm{24}\:\mathrm{oranges}\:,\:\mathrm{how} \\ $$$$\mathrm{many}\:\mathrm{does}\:\mathrm{Akwasi}\:\mathrm{get}. \\ $$

Question Number 67106 Answers: 0 Comments: 1

find the area abounded y=(√x) afind y=x−2?

$${find}\:{the}\:{area}\:{abounded}\:{y}=\sqrt{{x}} \\ $$$${afind}\:{y}={x}−\mathrm{2}? \\ $$

Question Number 67105 Answers: 0 Comments: 0

find the area abounded y=(√x) afind y=x−2?

$${find}\:{the}\:{area}\:{abounded}\:{y}=\sqrt{{x}} \\ $$$${afind}\:{y}={x}−\mathrm{2}? \\ $$

Question Number 67102 Answers: 2 Comments: 0

Question Number 67083 Answers: 1 Comments: 0

CosA+CosB+CosC=1+4Cos(((B+C)/2)).Cos(((C+A)/2)).Cos(((A+B)/2))=1+4Cos(((Π−A)/4)).Cos(((Π−B)/4)).Cos(((Π−C)/4)) prove that if A+B+C=Π

$$\mathrm{CosA}+\mathrm{CosB}+\mathrm{CosC}=\mathrm{1}+\mathrm{4Cos}\left(\frac{\mathrm{B}+\mathrm{C}}{\mathrm{2}}\right).\mathrm{Cos}\left(\frac{\mathrm{C}+\mathrm{A}}{\mathrm{2}}\right).\mathrm{Cos}\left(\frac{\mathrm{A}+\mathrm{B}}{\mathrm{2}}\right)=\mathrm{1}+\mathrm{4Cos}\left(\frac{\Pi−\mathrm{A}}{\mathrm{4}}\right).\mathrm{Cos}\left(\frac{\Pi−\mathrm{B}}{\mathrm{4}}\right).\mathrm{Cos}\left(\frac{\Pi−\mathrm{C}}{\mathrm{4}}\right) \\ $$$$\mathrm{prove}\:\mathrm{that}\:\mathrm{if}\:\mathrm{A}+\mathrm{B}+\mathrm{C}=\Pi \\ $$

Question Number 67072 Answers: 1 Comments: 0

Question Number 67071 Answers: 0 Comments: 7

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