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2 years ago

If two right triangles have the same ratios of legs, what can you conclude about the triangles?

Mathematics

2 answers:

MrRissso [65]2 years ago

4 0

The answer is B. You are welcome.

marin [14]2 years ago

3 0

The answer would be B

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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,

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

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

The domain of definition of F is

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

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

Here we want to find all the points such that

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

where k is a real number other than 0.

But this means

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

So, all the points in the line y = -x except (0,0) are parallel to the vector field F, that is, the points (x, -x) with x≠ 0

8 0

3 years ago

Passes through (3, 4) and (5, -4) how do I solve

nikitadnepr [17]

Answer:

y = - 4x + 16

Step-by-step explanation:

Assuming you require the equation of the line passing through the points.

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (3, 4) and (x₂, y₂ ) = (5, - 4)

m = $\frac{-4-4}{5-3}$ = $\frac{-8}{2}$ = - 4, thus

y = - 4x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (3, 4), then

4 = - 12 + c ⇒ c = 4 + 12 = 16

y = - 4x + 16 ← equation of line

8 0

3 years ago

Does a sheet of paper accurately represent a plane?

LiRa [457]

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3 years ago

Please help a picture of the problem is attached plz no trolls

Dmitry [639]

3r+1w=5
5r+1w=80

System of equations :)

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2 years ago

SOMEBODY PLEASE HELP ME! ILL CASHAPP YOU!

lutik1710 [3]

I believe it is 55 days

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3 years ago