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aev [14]
3 years ago
15

How to prove that IC is parallel with AB?

Mathematics
1 answer:
Karo-lina-s [1.5K]3 years ago
7 0
There is something wrong with drawing. IC intercepts with AB at A.
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Kinda need help fast.
Ivan

Answer:

the amswer is c

Step-by-step explanation:

3 0
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:

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
3 years ago
5x + 3x - 2 = 22<br><br> Number only please.
sattari [20]

x=3

5x+3x-2=22

8x-2=22

8x=24

x=3

7 0
2 years ago
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A cone is placed inside a cylinder. The cone has half the radius of the cylinder, but the height of each figure is the same. The
Yuliya22 [10]
Here is the answer: 3/4 (pi r^2 h)
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If y= (2x^2+x)^3 +(x-1) /(1-x). find dy dx​
Mrrafil [7]

Answer:

Step-by-step explanation:

y=(2x²+x)³+(x-1)/(1-x)

=(2x²+x)³+(x-1)/-(x-1)

=(2x²+x)³-1

dy/dx=3(2x²+x)(4x+1)-0

=3x(2x+1)(4x+1)

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