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Aliun [14]
3 years ago
8

On a number line 8.63 would be located where

Mathematics
1 answer:
Oksanka [162]3 years ago
4 0

Answer:

It would be slightly higher than 8.5 and lower than 9.

Step-by-step explanation:

8.6 is bigger than 8.5, but it's smaller than 9, so you would place it in between the two but closer to the 8.5 mark.

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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
3 years ago
ASAP HELP! BRAINLIEST! can someone help me with this? i need work shown. will mark brainliest!
ki77a [65]

Answer:

  4x^2 +12x +44 remainder 161x +84

Step-by-step explanation:

At each step, the quotient term is the ratio of the leading dividend term to the leading divisor term. The first quotient term, for example, is ...

  (4x^4)/(x^2) = 4x^2

The quotient term found this way is multiplied by the divisor and subtracted from the dividend. The difference is the new dividend and the process repeats.

You're done when the degree of the dividend is less than the degree of the divisor. This remainder can be expressed as a fraction with the divisor as the denominator.

  \dfrac{4x^4+5x-4}{x^2-3x-2}=4x^2+12x+44+\dfrac{161x+84}{x^2-3x-2}

5 0
2 years ago
Let x represent the number of television show episodes that are taped in a season. Enter an expression for the number of episode
Vinil7 [7]

Answer:

x=8 ???

Step-by-step explanation:

??? not 100% sure but im pretty sure ;w;

8 0
2 years ago
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Need help with numbers 8 and 9
ikadub [295]

Answer:

did not understand ur q.a

3 0
3 years ago
Russ' checking account charges an $11.25 monthly service fee and a $0.22 per-check fee. If Russ writes 14 checks per month, shou
masya89 [10]
Yes,because that is $3.03 higher than what he is receving right now so that will be an accelent option:)
3 0
3 years ago
Read 2 more answers
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