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balandron [24]
3 years ago
10

Marking as brainliest!!!!

Mathematics
1 answer:
7nadin3 [17]3 years ago
5 0

Answer:

The answer to your question is: Letter A

Step-by-step explanation:

Data

M (-6, 7)

E (4, 11)

r = 1 / 3

Formula

x = \frac{x1 + rx2}{1 + r}

y = \frac{y1 + ry2}{1 + r}

x = \frac{-6 + (1/3)(11)}{(4/3)} = \frac{-6 + (4/3)}{(4/3)}  = \frac{-18 + 4}{4} = \frac{-14}{4}  = \frac{-7}{2}

y = \frac{7 + (1/3)(11)}{4/3} = \frac{7 + (11/3)}{(4/3)} = \frac{21+ 11}{4}  = \frac{32}{4} = 8

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Line CD passes through points C(3, -5) And D(6, 0). What is the equation of line CD in standard form?
Fynjy0 [20]
Y = mx + b
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0 = 5/3(6) + b
b = -10
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3y = 5x - 30
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8 0
3 years ago
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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:

a)

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}

So

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

b)

The domain of definition of F is  

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

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

c)

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
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Answer:

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Here, we want to know the number of children at the party

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Answer:

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Step-by-step explanation:

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