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3 years ago

5(2-y)+y=-6 Please the yr is almost over

Mathematics

2 answers:

KATRIN_1 [288]3 years ago

8 0

Answer:

Step-by-step explanation:

5(2-y)+y=-6
10-5y+y= -6
10-4y= -6
4y=10+6
4y=16
y=16/4
y=4

lana [24]3 years ago

3 0

Answer: 4

Step-by-step explanation:

16 - 4y =-4 • (y - 4)

-4 • (y - 4) = 0

y-4 = 0

y = 4

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sp2606 [1]

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3 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:

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

The table lists several points that form a line on a coordinate plane.

omeli [17]

Answer:

Slope is 1/4 (0.25) while y-intercept is 5

Step-by-step explanation:

Here, we are interested in getting the y intercept and slope of the line joining the given points.

We can get the slope by using any two points

Let’s say (4,6) and (12,8)

Mathematically; slope

= (y2-y1)/(x2-x1) = (8-6)/(12-4) = 2/8 = 1/4 = 0.25

To get the y-intercept, we proceed

kindly recall that the equation of a straight line is;

y = mx + c

where m is the slope and c is the y-intercept

Let’s take any of the points (28,12)

Thus:

12 = 0.25(28) + c

12 = 7 + c

c = 12-7

c = 5

6 0

3 years ago

Simplify: 10 - 2(3+4)*

melomori [17]

Answer: -4

Step-by-step explanation:

8 0

3 years ago

If 4.5 pounds of chocolate cost $10, how

allsm [11]

I think 5.4

4.5÷10= 0.45

0.45x12=5.4

3 0

3 years ago