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Question Number 218199    Answers: 1   Comments: 0

describes the rupture body onQ of polynomials. a) X^5 +1 b) X^6 −X^3 +1

$${describes}\:{the}\:{rupture}\:{body}\:{onQ} \\ $$$${of}\:{polynomials}. \\ $$$$\left.{a}\left.\right)\:{X}^{\mathrm{5}} +\mathrm{1}\:\:\:\:\:\:\:\:\:{b}\right)\:{X}^{\mathrm{6}} −{X}^{\mathrm{3}} +\mathrm{1} \\ $$

Question Number 218191    Answers: 0   Comments: 0

exercises algebra. all algebraically closed fields ares finite. prouve it .

$${exercises}\:{algebra}. \\ $$$${all}\:\:{algebraically}\:\:{closed}\:\:{fields} \\ $$$${ares}\:{finite}. \\ $$$${prouve}\:\:{it}\:. \\ $$

Question Number 218189    Answers: 0   Comments: 0

Question Number 218188    Answers: 0   Comments: 0

Question Number 218187    Answers: 1   Comments: 0

Question Number 218185    Answers: 1   Comments: 0

Find: lim_(n→∞) sin (nπ (√(n^2 + 2n + 2∙(k + 1)))) = ? k ∈ Z - fixed

$$\mathrm{Find}: \\ $$$$\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{sin}\:\left(\mathrm{n}\pi\:\sqrt{\mathrm{n}^{\mathrm{2}} \:+\:\mathrm{2n}\:+\:\mathrm{2}\centerdot\left(\mathrm{k}\:+\:\mathrm{1}\right)}\right)\:=\:? \\ $$$$\mathrm{k}\:\in\:\mathbb{Z}\:-\:\mathrm{fixed} \\ $$

Question Number 218184    Answers: 1   Comments: 0

− 2025 : 7 Residue = ?

$$−\:\mathrm{2025}\:\::\:\:\mathrm{7} \\ $$$$\mathrm{Residue}\:=\:? \\ $$

Question Number 218196    Answers: 3   Comments: 0

lim _(n→∞) (1/n) ( (((2n)!)/(n!)) )^(1/n) = ?

$$ \\ $$$$ \\ $$$$\:\:\:\:\mathrm{lim}\:_{\mathrm{n}\rightarrow\infty} \frac{\mathrm{1}}{{n}}\:\left(\:\frac{\left(\mathrm{2}{n}\right)!}{{n}!}\:\right)^{\frac{\mathrm{1}}{{n}}} =\:?\:\:\:\:\:\:\:\: \\ $$$$ \\ $$

Question Number 218195    Answers: 1   Comments: 0

P=((ΣFz)/(Npil))

$${P}=\frac{\Sigma{Fz}}{{Npil}} \\ $$

Question Number 218183    Answers: 1   Comments: 0

Find: (√(33^2 + 544^2 )) + (√(333^2 + 55444^2 )) = ?

$$\mathrm{Find}: \\ $$$$\sqrt{\mathrm{33}^{\mathrm{2}} \:\:+\:\:\mathrm{544}^{\mathrm{2}} }\:\:+\:\:\sqrt{\mathrm{333}^{\mathrm{2}} \:\:+\:\:\mathrm{55444}^{\mathrm{2}} }\:\:=\:\:? \\ $$

Question Number 218169    Answers: 0   Comments: 0

P(5,6)=((15!)/((15−6))) = ((15!)/(9!)) =((15×14×131×2×11×10×9×8×7×6×5×4×3×2×1)/(9×8×7×6×5×4×3×2×)) =15×14×13×12×11×10 =3,603,600

$${P}\left(\mathrm{5},\mathrm{6}\right)=\frac{\mathrm{15}!}{\left(\mathrm{15}−\mathrm{6}\right)}\:=\:\frac{\mathrm{15}!}{\mathrm{9}!}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\frac{\mathrm{15}×\mathrm{14}×\mathrm{131}×\mathrm{2}×\mathrm{11}×\mathrm{10}×\mathrm{9}×\mathrm{8}×\mathrm{7}×\mathrm{6}×\mathrm{5}×\mathrm{4}×\mathrm{3}×\mathrm{2}×\mathrm{1}}{\mathrm{9}×\mathrm{8}×\mathrm{7}×\mathrm{6}×\mathrm{5}×\mathrm{4}×\mathrm{3}×\mathrm{2}×} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{15}×\mathrm{14}×\mathrm{13}×\mathrm{12}×\mathrm{11}×\mathrm{10} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{3},\mathrm{603},\mathrm{600} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$

Question Number 218165    Answers: 2   Comments: 0

λ > 0 x , y , z ∈ C Solve the system: { ((xy = z^2 + 2λz − λx − λy)),((yz = x^2 + 2λx − λy − λz )),((zx = y^2 + 2λy − λz − λx)) :}

$$\lambda\:>\:\mathrm{0} \\ $$$$\mathrm{x}\:,\:\mathrm{y}\:,\:\mathrm{z}\:\in\:\mathrm{C} \\ $$$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{system}:\:\:\:\begin{cases}{\mathrm{xy}\:=\:\mathrm{z}^{\mathrm{2}} \:+\:\mathrm{2}\lambda\mathrm{z}\:−\:\lambda\mathrm{x}\:−\:\lambda\mathrm{y}}\\{\mathrm{yz}\:=\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{2}\lambda\mathrm{x}\:−\:\lambda\mathrm{y}\:−\:\lambda\mathrm{z}\:\:\:\:\:\:\:\:}\\{\mathrm{zx}\:=\:\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{2}\lambda\mathrm{y}\:−\:\lambda\mathrm{z}\:−\:\lambda\mathrm{x}}\end{cases} \\ $$

Question Number 218153    Answers: 3   Comments: 0

x+y =12 minimum value of (√(x^2 +4)) +(√(y^2 +9)) =?

$$\:{x}+{y}\:=\mathrm{12} \\ $$$$\:{minimum}\:{value}\:{of} \\ $$$$\:\sqrt{{x}^{\mathrm{2}} +\mathrm{4}}\:+\sqrt{{y}^{\mathrm{2}} +\mathrm{9}}\:=? \\ $$

Question Number 218150    Answers: 1   Comments: 0

∫_0 ^1 (1/(1−x^2 ))ln(((1+x)/(2x)))dx

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

Question Number 218162    Answers: 1   Comments: 0

Each edge of a parallelepiped is 1 cm long. At one of its vertices, all three face angles are acute, and each measures 2α. Find the volume of the parallepiped. Help me, please

$$\:\:\: \\ $$$$\:\:\:{Each}\:{edge}\:{of}\:{a}\:{parallelepiped}\:{is}\:\mathrm{1}\:{cm}\:{long}. \\ $$$$\:\:\:{At}\:{one}\:{of}\:{its}\:{vertices},\:{all}\:{three}\:{face}\:{angles} \\ $$$$\:\:\:{are}\:{acute},\:{and}\:{each}\:{measures}\:\mathrm{2}\alpha. \\ $$$$\:\:\:{Find}\:{the}\:{volume}\:{of}\:{the}\:{parallepiped}. \\ $$$$\:\:\:{Help}\:{me},\:\:{please} \\ $$

Question Number 218163    Answers: 1   Comments: 0

Find: ∫ (x/( (√(48 − 2x − x^2 )))) dx = ?

$$\mathrm{Find}:\:\:\:\int\:\frac{\mathrm{x}}{\:\sqrt{\mathrm{48}\:−\:\mathrm{2x}\:−\:\mathrm{x}^{\mathrm{2}} }}\:\mathrm{dx}\:=\:? \\ $$

Question Number 218138    Answers: 2   Comments: 0

((629 − x))^(1/4) + ((77 + x))^(1/4) = 8 Find: x = ?

$$\sqrt[{\mathrm{4}}]{\mathrm{629}\:−\:\mathrm{x}}\:\:+\:\:\sqrt[{\mathrm{4}}]{\mathrm{77}\:\:+\:\:\mathrm{x}}\:\:=\:\:\mathrm{8} \\ $$$$\mathrm{Find}:\:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$

Question Number 222197    Answers: 1   Comments: 0

question 211277

$${question}\:\mathrm{211277} \\ $$

Question Number 218129    Answers: 2   Comments: 0

how many different words can be formed from the word MATHEMATICS? note: here a word should have at least two letters, but mustn′t have a meaning.

$${how}\:{many}\:{different}\:{words}\:{can}\:{be} \\ $$$${formed}\:{from}\:{the}\:{word}\: \\ $$$$\boldsymbol{\mathrm{MATHEMATICS}}? \\ $$$${note}:\:\:{here}\:{a}\:{word}\:{should}\:{have}\:{at}\: \\ $$$${least}\:{two}\:{letters},\:{but}\:{mustn}'{t}\:{have}\:{a} \\ $$$${meaning}. \\ $$

Question Number 218128    Answers: 1   Comments: 0

determinant ((?,?,?,?))× determinant ((?))=8044 determinant ((?))

$$\begin{array}{|c|}{?}&\hline{?}&\hline{?}&\hline{?}\\\hline\end{array}×\begin{array}{|c|}{?}\\\hline\end{array}=\mathrm{8044}\begin{array}{|c|}{?}\\\hline\end{array} \\ $$

Question Number 218119    Answers: 2   Comments: 0

determinant ((ε,1,0,0,0,1),(1,ε,1,0,0,0),(0,1,ε,1,0,0),(0,0,1,ε,1,0),(0,0,0,1,ε,1),(1,0,0,0,1,ε))=?

$$\begin{vmatrix}{\varepsilon}&{\mathrm{1}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{1}}\\{\mathrm{1}}&{\varepsilon}&{\mathrm{1}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{1}}&{\varepsilon}&{\mathrm{1}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{1}}&{\varepsilon}&{\mathrm{1}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{1}}&{\varepsilon}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{1}}&{\varepsilon}\end{vmatrix}=? \\ $$$$ \\ $$

Question Number 218115    Answers: 1   Comments: 0

Question Number 218148    Answers: 2   Comments: 0

I=∫_0 ^( ∞) ((sin((√( x ))))/( (( e^x ))^(1/4) ))dx=?

$$ \\ $$$$\:\:\:\mathrm{I}=\int_{\mathrm{0}} ^{\:\infty} \:\frac{\mathrm{sin}\left(\sqrt{\:{x}\:}\right)}{\:\sqrt[{\mathrm{4}}]{\:{e}^{{x}} }}{dx}=? \\ $$$$ \\ $$

Question Number 218103    Answers: 2   Comments: 0

x+(1/x)=3 , x^5 +(1/x^5 )=?

$${x}+\frac{\mathrm{1}}{{x}}=\mathrm{3}\:,\:{x}^{\mathrm{5}} +\frac{\mathrm{1}}{{x}^{\mathrm{5}} }=? \\ $$

Question Number 218099    Answers: 5   Comments: 0

x^2 +x+1=0 , x^4 +x^2 +1=?

$${x}^{\mathrm{2}} +{x}+\mathrm{1}=\mathrm{0}\:,\:{x}^{\mathrm{4}} +{x}^{\mathrm{2}} +\mathrm{1}=? \\ $$

Question Number 218093    Answers: 2   Comments: 0

Solve for x (√(2x+3)) −(√(x−2)) =(√(x+2))

$${Solve}\:{for}\:{x} \\ $$$$\sqrt{\mathrm{2}{x}+\mathrm{3}}\:−\sqrt{{x}−\mathrm{2}}\:=\sqrt{{x}+\mathrm{2}}\: \\ $$

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