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2 years ago

Figure 1 is dilated to get Figure 2.

Mathematics

2 answers:

liq [111]2 years ago

8 0

I'm pretty sure it's 5 over 10! Hope I helped =)

maks197457 [2]2 years ago

3 0

Given two diamonds with same shape but different sizes.

The side given of one diamond = 10 units.

And the corresponding side of the other diamond = 24 units.

To find the scale factor of them, we need to find the ratio of the sides.

So here scale factor = $10:24$ = $\frac{10}{24}$

Now we have to simplify the fraction. We can simplify it by dividing the numerator and denominator by a common factor of it.

The common factor of 10 and 24 is 2. If we divide 10 by 2, we will get 5 and if we divide 24 by 2, we will get 12.

So we will get,

$\frac{10}{24} = \frac{5}{12}$

We have got the required answer.

The scale factor is $\frac{5}{12}$ .

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2 years ago

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2 years ago

Let φ(x, y) = arctan (y/x) .

Alexandra [31]

Answer:

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

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

c) the points of the form (x, -x) for x≠0

Step-by-step explanation:

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

$\large F(x,y)=(\frac{\partial \phi}{\partial x},\frac{\partial \phi}{\partial y})$

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,

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