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2 years ago

14

Use the rule y= -x + 7 to fill in the blank.if (1,y) is on the graph then y =

1 answer:

fomenos2 years ago

7 0

Answer:

Then y = 6

Step-by-step explanation:

y = -x + 7

x = 1

y = -1 + 7

= 6

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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

Emily and her family are planning to fly to Italy over the summer. If they fly out from LAX, the distance of the trip will be 6,

Iteru [2.4K]

The speed is the ratio between the distance and the time:

$s=\frac{d}{t}$

Data:

d=6343miles

t=9h

$s=\frac{6343\text{miles}}{9h}=704.77\frac{miles}{h}$ Then, the plane traveled at a speed of 704.77 miles per hour.

8 0

8 months ago

Polynomial add or subtract (-2x^2-4x+13)+(12x^2+2x-25)

BigorU [14]

1.Simplify.

-2{x}^{2}-4x+13+12{x}^{2}+2x-25−2x2−4x+13+12x2+2x−25

2.Collect like terms.

(-2{x}^{2}+12{x}^{2})+(-4x+2x)+(13-25)(−2x2+12x2)+(−4x+2x)+(13−25)

3.Simplify.

10{x}^{2}-2x-1210x2−2x−12

6 0

2 years ago

PLEASE HELP FAST ILL GOVE YOU AS MUCH POINTS AS YOU NEED! PLEASE ANDWER ONLY IF YOU KNOW! I REALLY NEED THIS!!

Aliun [14]

Answer: It has to be b if not sorry

6 0

2 years ago

Read 2 more answers

What is the value of the function at x = −3?

zlopas [31]

Answer:

the answer is D

Step-by-step explanation:

(0, -3) , (1, -3) , (2, -3)

Hope this helps! :)

~Zane

4 0

3 years ago

Read 2 more answers