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2 years ago

Answer this question please and thank you

Mathematics

2 answers:

sladkih [1.3K]2 years ago

6 0

Answer:

1x12

3x4

2x6

........................

Neporo4naja [7]2 years ago

3 0

Answer:

2, 6, 4, 3, 12, 1

Step-by-step explanation:

The dimensions are the length and width

Length(s): 2, 4, 12

Width(s): 6, 3, 1

Dimension(s): 2x6, 4x3, 12x1

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Let φ(x, y) = arctan (y/x) .

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Answer:

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b) $\large \mathbb{R}^2-\{(0,0)\}$

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Step-by-step explanation:

If φ(x, y) = arctan (y/x), the vector field F = ∇φ would be

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On one hand we have,

$\large \frac{\partial \phi}{\partial x}=\frac{\partial arctan(y/x)}{\partial x}=\frac{-y/x^2}{1+(y/x)^2}=-\frac{y/x^2}{1+y^2/x^2}=\\\\=-\frac{y/x^2}{(x^2+y^2)/x^2}=-\frac{y}{x^2+y^2}$

On the other hand,

$\large \frac{\partial \phi}{\partial y}=\frac{\partial arctan(y/x)}{\partial y}=\frac{1/x}{1+(y/x)^2}=\frac{1/x}{1+y^2/x^2}=\\\\=\frac{1/x}{(x^2+y^2)/x^2}=\frac{x}{x^2+y^2}$

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$\large \mathbb{R}^2-\{(0,0)\}$

i.e., all the plane X-Y except the (0,0)

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$\large (-\frac{y}{x^2+y^2},\frac{x}{x^2+y^2})=(k,k)$

where k is a real number other than 0.

But this means

$\large -\frac{y}{x^2+y^2}=\frac{x}{x^2+y^2}\Rightarrow y=-x$

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