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Question Number 196070 Answers: 1 Comments: 0

During an invasion In the amazon dominion Every evening , every invader kills an amazon warrior Every morning , every amazon kills an invader soldier The 8^(th) day evening , there remains only one amazon and no invader How many were they in each part ?

$${During}\:{an}\:{invasion}\: \\ $$$${In}\:{the}\:{amazon}\:{dominion} \\ $$$${Every}\:{evening}\:,\:{every}\:\:{invader}\: \\ $$$${kills}\:\:{an}\:\:{amazon}\:{warrior}\: \\ $$$${Every}\:{morning}\:,\:{every}\:{amazon} \\ $$$${kills}\:\:\:{an}\:{invader}\:{soldier} \\ $$$${The}\:\mathrm{8}^{{th}} \:{day}\:{evening}\:,\:{there}\:{remains}\: \\ $$$${only}\:{one}\:{amazon}\:\:{and}\:{no}\:{invader} \\ $$$$ \\ $$$${How}\:{many}\:\:{were}\:{they}\:{in}\:{each}\:{part}\:? \\ $$

Question Number 196066 Answers: 2 Comments: 0

((( 1 −1)),((−1 2)) )^(−8) = ?

$$\begin{pmatrix}{\:\:\mathrm{1}\:\:\:\:\:\:\:\:\:−\mathrm{1}}\\{−\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}}\end{pmatrix}^{−\mathrm{8}} =\:\:? \\ $$

Question Number 196063 Answers: 1 Comments: 0

calcul ∫_0 ^(+∞) (((√u) .arctan(u))/(1+u^2 )) du

$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$\mathrm{calcul}\:\:\:\:\int_{\mathrm{0}} ^{+\infty} \:\frac{\sqrt{\mathrm{u}}\:.\mathrm{arctan}\left(\mathrm{u}\right)}{\mathrm{1}+\mathrm{u}^{\mathrm{2}} }\:\mathrm{du} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 196062 Answers: 1 Comments: 1

Σ_(i=1) ^n Σ_(j=1) ^n [gcd(i,j)=1]=? ,[D]= { ((1, D is ture.)),((0, D is false. )) :}

$$\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\underset{{j}=\mathrm{1}} {\overset{{n}} {\sum}}\left[{gcd}\left({i},{j}\right)=\mathrm{1}\right]=?\:\:\:\:\:\:\:\:\:,\left[{D}\right]=\begin{cases}{\mathrm{1},\:\:\:{D}\:{is}\:{ture}.}\\{\mathrm{0},\:\:\:\:{D}\:{is}\:{false}.\:\:\:}\end{cases} \\ $$

Question Number 196056 Answers: 5 Comments: 0

solve (√(2x+3))−(√(3x+8))=(√(3x+4))−(√(2x+7))

$${solve} \\ $$$$\sqrt{\mathrm{2}{x}+\mathrm{3}}−\sqrt{\mathrm{3}{x}+\mathrm{8}}=\sqrt{\mathrm{3}{x}+\mathrm{4}}−\sqrt{\mathrm{2}{x}+\mathrm{7}} \\ $$

Question Number 196053 Answers: 1 Comments: 0

faind n terme 4,−2,((16)/9),−2,......

$${faind}\:{n}\:{terme} \\ $$$$\mathrm{4},−\mathrm{2},\frac{\mathrm{16}}{\mathrm{9}},−\mathrm{2},...... \\ $$

Question Number 196049 Answers: 1 Comments: 1

a, b, c > 0. Find the min value of Σ_(cyc) (√((a+b)/(a+b+c))) .

$${a},\:{b},\:{c}\:>\:\mathrm{0}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{min}\:\mathrm{value}\:\mathrm{of} \\ $$$$\underset{\mathrm{cyc}} {\sum}\:\sqrt{\frac{{a}+{b}}{{a}+{b}+{c}}}\:. \\ $$

Question Number 196046 Answers: 0 Comments: 0

∫e^x^2 ln^(24) (x)dx

$$\int{e}^{{x}^{\mathrm{2}} } \:{ln}^{\mathrm{24}} \left({x}\right){dx} \\ $$

Question Number 196037 Answers: 2 Comments: 0

∫ ((sin 2x)/(sin^3 x+cos^3 x)) dx =?

$$\:\:\:\int\:\frac{\mathrm{sin}\:\mathrm{2x}}{\mathrm{sin}\:^{\mathrm{3}} \mathrm{x}+\mathrm{cos}\:^{\mathrm{3}} \mathrm{x}}\:\mathrm{dx}\:=? \\ $$

Question Number 196035 Answers: 0 Comments: 0

Question Number 196024 Answers: 1 Comments: 0

lim_(x→0^+ ) [xΣ_(n=1) ^∞ ((1/n^(x+1) ))]=λ , evalute λ

$$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\left[{x}\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{{n}^{{x}+\mathrm{1}} }\right)\right]=\lambda\:,\:{evalute}\:\lambda \\ $$

Question Number 196023 Answers: 1 Comments: 0

find the domain of definition of this function for t∈]0;1[ 𝛒(x)=∫_x ^(2x) (1/(lnt))dt ptiCantor

$${find}\:{the}\:{domain}\:{of}\:{definition}\:{of}\:{this} \\ $$$$\left.{function}\:{for}\:{t}\in\right]\mathrm{0};\mathrm{1}\left[\right. \\ $$$$\:\:\:\:\:\boldsymbol{\rho}\left({x}\right)=\int_{{x}} ^{\mathrm{2}{x}} \frac{\mathrm{1}}{{lnt}}{dt} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{ptiCantor} \\ $$

Question Number 196021 Answers: 1 Comments: 0

Question Number 196015 Answers: 0 Comments: 1

Question Number 196014 Answers: 0 Comments: 2

∫_0 ^(π/2) t.(√(tan(t))) dt = ???

$$\:\:\:\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{t}.\sqrt{{tan}\left({t}\right)}\:{dt}\:\:=\:??? \\ $$

Question Number 196013 Answers: 1 Comments: 0

quel est la transformer de Fourier de la fonction suivante: f(x)=e^(−(x^2 /2)) Find the Fourier transform of the following fonction.

$${quel}\:{est}\:{la}\:{transformer}\:{de}\:{Fourier}\:{de}\:{la}\:{fonction} \\ $$$${suivante}: \\ $$$${f}\left({x}\right)=\boldsymbol{{e}}^{−\frac{\boldsymbol{{x}}^{\mathrm{2}} }{\mathrm{2}}} \\ $$$$\boldsymbol{{F}}{ind}\:{the}\:{Fourier}\:{transform}\:{of}\:{the}\: \\ $$$${following}\:{fonction}. \\ $$

Question Number 196008 Answers: 1 Comments: 2

Question Number 196007 Answers: 1 Comments: 0

Question Number 196000 Answers: 2 Comments: 0

lim_(x→+∞) (lnx)^2 −(√x) ????

$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\:\:\mathrm{lim}_{{x}\rightarrow+\infty} \:\left({lnx}\right)^{\mathrm{2}} −\sqrt{{x}}\:\:\:\:\:???? \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 195998 Answers: 0 Comments: 0

We can transform to get rid of the ((...))^(1/3) a^(1/3) +b^(1/3) =c^(1/3) (a^(1/3) +b^(1/3) )^3 =c a+b+3a^(1/3) b^(1/3) (a^(1/3) +b^(1/3) )=c 3a^(1/3) b^(1/3) c^(1/3) =c−a−b 27abc=(c−a−b)^3 Is it possible to do the same for a^(1/3) +b^(1/3) =c^(1/3) +d^(1/3) I found no path yet...

Question Number 195997 Answers: 0 Comments: 0

Question Number 195995 Answers: 1 Comments: 0

Δ={(x^ y z), x^2 +y^2 ≤1, x≥0,0<z<y+1} calculer I=∫∫∫_Δ xyzdxdydz please i need help

$$\Delta=\left\{\left(\bar {{x}}\:{y}\:{z}\right),\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \leqslant\mathrm{1},\:{x}\geqslant\mathrm{0},\mathrm{0}<{z}<{y}+\mathrm{1}\right\} \\ $$$${calculer}\:\boldsymbol{{I}}=\int\int\int_{\Delta} {xyzdxdydz} \\ $$$${please}\:{i}\:{need}\:{help} \\ $$

Question Number 195996 Answers: 2 Comments: 0

Question Number 195982 Answers: 2 Comments: 0

lim_(x→1) [(1/(2(1−(√x))))−(1/(3(1−(x)^(1/3) )))]=? with out l′pital rule

$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\left[\frac{\mathrm{1}}{\mathrm{2}\left(\mathrm{1}−\sqrt{{x}}\right)}−\frac{\mathrm{1}}{\mathrm{3}\left(\mathrm{1}−\sqrt[{\mathrm{3}}]{{x}}\right)}\right]=? \\ $$$${with}\:{out}\:{l}'{pital}\:{rule} \\ $$

Question Number 196026 Answers: 1 Comments: 0

∫^( +∞) _( 0) (((lnt)^2 )/(1+t^2 ))dt

$$\underset{\:\mathrm{0}} {\int}^{\:+\infty} \frac{\left({lnt}\right)^{\mathrm{2}} }{\mathrm{1}+{t}^{\mathrm{2}} }{dt} \\ $$

Question Number 195964 Answers: 1 Comments: 0

the family A has 5 members and the family B has 4 members. there are 6 personsfrom other families. in how many ways can you arrange these 15 persons around a round table such that no member from family A and no member from family B are next to each other?

$${the}\:{family}\:{A}\:{has}\:\mathrm{5}\:{members}\:{and}\:{the} \\ $$$${family}\:{B}\:{has}\:\mathrm{4}\:{members}.\:{there}\:{are}\: \\ $$$$\mathrm{6}\:{personsfrom}\:{other}\:{families}. \\ $$$${in}\:{how}\:{many}\:{ways}\:{can}\:{you}\:{arrange} \\ $$$${these}\:\mathrm{15}\:{persons}\:{around}\:{a}\:{round}\:{table} \\ $$$${such}\:{that}\:{no}\:{member}\:{from}\:{family}\:{A} \\ $$$${and}\:{no}\:{member}\:{from}\:{family}\:{B}\:{are} \\ $$$${next}\:{to}\:{each}\:{other}? \\ $$

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