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goldfiish [28.3K]

2 years ago

10

HELP!!!

2 answers:

anygoal [31]2 years ago

4 0

Answer:

-2 > -5

Step-by-step explanation:

think about which of the two numbers is nearest to 0

Dmitrij [34]2 years ago

3 0

Answer:

-2 Celsius >-5 Celsius is the answer.

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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

2 years ago

Solve for x using

vlada-n [284]

Answer:

11

Step-by-step explanation:

cross multiply - 2(2x-4) = 3(x=1)

4x - 8 = 3x + 3

4x - 3x = 3 + 8

x = 11

4 0

2 years ago

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Need help i don't understand

BabaBlast [244]

Answer:

Commutative property of multiplication

Step-by-step explanation:

This property states that numbers can be switched around when multiplying and the answer still remains the same

3 0

2 years ago

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find the area of this circle. Use 3.14 as (pie symbol) click the photo to see the circle ! Please help <3 if you can’t see, t

igor_vitrenko [27]

Answer:

$\displaystyle 4536,4597918...\:cm.^2 = A$

Step-by-step explanation:

Split the diametre in half before proceeding:

$\displaystyle \pi{r}^2 = A \\ \\ 38^2\pi = A \hookrightarrow 1444\pi = A \\ \\ \boxed{4536,4597918... = A}$

I am joyous to assist you at any time.

8 0

2 years ago

A Arrange the following integers in ascending order<br>1) 37, 41, 76, -2.25 -25<br>Answer:

madreJ [45]

ASCENDING ORDER

76,41,36,25,-2,-25

7 0

2 years ago

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