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Question Number 218025 Answers: 0 Comments: 0

I=∫_0 ^( ∞) te^(−t) J_(−(1/2)) (t ) dt =?

$$ \\ $$$$\:\:\:\mathrm{I}=\int_{\mathrm{0}} ^{\:\infty} {te}^{−{t}} {J}_{−\frac{\mathrm{1}}{\mathrm{2}}} \:\left({t}\:\right)\:{dt}\:=? \\ $$$$ \\ $$

Question Number 218021 Answers: 1 Comments: 0

Question Number 218019 Answers: 2 Comments: 0

x^2 +y^2 +x+y=18 xy+x+y=7 Solve.

$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{x}+{y}=\mathrm{18} \\ $$$${xy}+{x}+{y}=\mathrm{7} \\ $$$${Solve}. \\ $$

Question Number 218013 Answers: 1 Comments: 0

Question Number 218005 Answers: 0 Comments: 2

if x^2 +y^2 +z^2 =1, maximum value xy+2yz = ...

$$\: \\ $$$$\: \\ $$$$\:\boldsymbol{\mathrm{if}}\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{y}}^{\mathrm{2}} +\boldsymbol{\mathrm{z}}^{\mathrm{2}} =\mathrm{1},\: \\ $$$$\:\boldsymbol{\mathrm{maximum}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{x}}\mathrm{y}+\mathrm{2yz}\:=\:... \\ $$

Question Number 218003 Answers: 0 Comments: 6

1. ∫ ((x dx)/((x + 2)∙(x + 4))) 2. ∫ ((x + 2)/(x^3 − 2x^2 )) dx 3. ∫ ((2x + 7)/(x^2 − 4x + 3)) dx

$$\mathrm{1}.\:\:\:\int\:\:\frac{\mathrm{x}\:\mathrm{dx}}{\left(\mathrm{x}\:+\:\mathrm{2}\right)\centerdot\left(\mathrm{x}\:+\:\mathrm{4}\right)} \\ $$$$\mathrm{2}.\:\:\:\int\:\:\frac{\mathrm{x}\:+\:\mathrm{2}}{\mathrm{x}^{\mathrm{3}} \:−\:\mathrm{2x}^{\mathrm{2}} }\:\mathrm{dx} \\ $$$$\mathrm{3}.\:\:\:\int\:\:\frac{\mathrm{2x}\:+\:\mathrm{7}}{\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{4x}\:+\:\mathrm{3}}\:\mathrm{dx} \\ $$

Question Number 217992 Answers: 0 Comments: 0

Question Number 217991 Answers: 1 Comments: 0

x^2 +3=0 x^2 +5=3

$${x}^{\mathrm{2}} +\mathrm{3}=\mathrm{0} \\ $$$${x}^{\mathrm{2}} +\mathrm{5}=\mathrm{3} \\ $$

Question Number 217985 Answers: 0 Comments: 4

x^3 − 3x + 1 = 0 The roots of the equation → a , b , c Find → (a)^(1/3) + (b)^(1/3) + (c)^(1/3) = ?

$$\mathrm{x}^{\mathrm{3}} \:−\:\mathrm{3x}\:+\:\mathrm{1}\:=\:\mathrm{0} \\ $$$$\mathrm{The}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\:\rightarrow\:\mathrm{a}\:,\:\mathrm{b}\:,\:\mathrm{c} \\ $$$$\mathrm{Find}\:\rightarrow\:\sqrt[{\mathrm{3}}]{\mathrm{a}}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{b}}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{c}}\:=\:? \\ $$

Question Number 217982 Answers: 0 Comments: 2

Solve If 4^2^(2y−1 ) = 16^4^(y+1) and 8^3^(2x−1) = 2^9^(2−x) what is 2x + y?

$${Solve} \\ $$$${If}\:\mathrm{4}^{\mathrm{2}^{\mathrm{2}{y}−\mathrm{1}\:} } =\:\mathrm{16}^{\mathrm{4}^{{y}+\mathrm{1}} } \:{and}\:\mathrm{8}^{\mathrm{3}^{\mathrm{2}{x}−\mathrm{1}} } =\:\mathrm{2}^{\mathrm{9}^{\mathrm{2}−{x}} } \\ $$$${what}\:{is}\:\mathrm{2}{x}\:+\:{y}? \\ $$

Question Number 217964 Answers: 0 Comments: 0

Question Number 217958 Answers: 2 Comments: 2

a,b,c∈Z^+ and a^2 +b^2 +c^2 +ab+bc+ca=2025 find out all triplets (a,b,c).

$${a},{b},{c}\in\mathbb{Z}^{+} {and} \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} +{ab}+{bc}+{ca}=\mathrm{2025} \\ $$$${find}\:{out}\:{all}\:{triplets}\:\left({a},{b},{c}\right). \\ $$

Question Number 217952 Answers: 2 Comments: 0

If x∈Z ∧y non-negative integer such that x^2 +10x+23=2^y find out x,y

$${If}\:{x}\in\mathbb{Z}\:\wedge{y}\:{non}-{negative}\:{integer} \\ $$$${such}\:{that} \\ $$$${x}^{\mathrm{2}} +\mathrm{10}{x}+\mathrm{23}=\mathrm{2}^{{y}} \\ $$$${find}\:{out}\:{x},{y} \\ $$

Question Number 217949 Answers: 1 Comments: 1

Question Number 217940 Answers: 3 Comments: 0

Solve (√(2x+7)) −(√(x−1)) =2

$${Solve} \\ $$$$\sqrt{\mathrm{2}{x}+\mathrm{7}}\:\:−\sqrt{{x}−\mathrm{1}}\:=\mathrm{2}\:\:\:\:\:\:\:\:\:\:\: \\ $$

Question Number 217937 Answers: 0 Comments: 5

Question Number 217931 Answers: 2 Comments: 1

Given a regular triangle ABC. AG=2GC. CK=2KB. AK∩BG=M. Prove that CM⊥AK.

$$\mathrm{Given}\:\mathrm{a}\:\mathrm{regular}\:\mathrm{triangle}\:{ABC}. \\ $$$${AG}=\mathrm{2}{GC}.\:{CK}=\mathrm{2}{KB}.\:{AK}\cap{BG}={M}. \\ $$$$\mathrm{Prove}\:\mathrm{that}\:{CM}\bot{AK}. \\ $$

Question Number 217930 Answers: 0 Comments: 0

Question Number 217921 Answers: 1 Comments: 0

solve it: 2+(3/(2+(3/(2+(3/(2+...))))))

$${solve}\:{it}: \\ $$$$\mathrm{2}+\frac{\mathrm{3}}{\mathrm{2}+\frac{\mathrm{3}}{\mathrm{2}+\frac{\mathrm{3}}{\mathrm{2}+...}}} \\ $$

Question Number 217912 Answers: 0 Comments: 2

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Question Number 217911 Answers: 2 Comments: 0

Solve ((x/(x−1)))^2 +((x/(x+1)))^2 =6

$${Solve} \\ $$$$\left(\frac{{x}}{{x}−\mathrm{1}}\right)^{\mathrm{2}} +\left(\frac{{x}}{{x}+\mathrm{1}}\right)^{\mathrm{2}} =\mathrm{6} \\ $$

Question Number 217909 Answers: 0 Comments: 15

If two fair dice is thrown twice, what is the probability of obtaining an even number

Question Number 217897 Answers: 1 Comments: 7

Question Number 217895 Answers: 1 Comments: 6

Question Number 217894 Answers: 0 Comments: 0

In △ABC holds: Σ ((cot A)/( (√(cot B + 3 cot C)))) ≥ (1/2) ((27))^(1/4)

$$\mathrm{In}\:\:\bigtriangleup\mathrm{ABC}\:\:\mathrm{holds}: \\ $$$$\Sigma\:\frac{\mathrm{cot}\:\mathrm{A}}{\:\sqrt{\mathrm{cot}\:\mathrm{B}\:\:+\:\:\mathrm{3}\:\mathrm{cot}\:\mathrm{C}}}\:\:\geqslant\:\:\frac{\mathrm{1}}{\mathrm{2}}\:\:\sqrt[{\mathrm{4}}]{\mathrm{27}}\: \\ $$

Question Number 217888 Answers: 3 Comments: 0

Solve: ((x^2 −3x+2)/(x^2 −8x+15))=((x^2 −5x+6)/(x^2 −10x+24))

$${Solve}: \\ $$$$\frac{{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}}{{x}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{15}}=\frac{{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{6}}{{x}^{\mathrm{2}} −\mathrm{10}{x}+\mathrm{24}} \\ $$

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