3 years ago

Please help with 13-16. All help appreciated.

Mathematics

1 answer:

ivolga24 [154]3 years ago

6 0

The answer is negative three

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Consider the vector field f(x,y,z)=(2z+3y)i+(3z+3x)j+(3y+2x)kf(x,y,z)=(2z+3y)i+(3z+3x)j+(3y+2x)k.

natima [27]

$\dfrac{\partial f}{\partial x}=2z+3y\implies f(x,y,z)=2xz+3xy+g(y,z)$

$\dfrac{\partial f}{\partial y}=3x+\dfrac{\partial g}{\partial y}=3z+3x$
$\dfrac{\partial g}{\partial y}=3z\implies g(y,z)=3yz+h(z)$
$\implies f(x,y,z)=3xz+3xy+3yz+h(z)$

$\dfrac{\partial f}{\partial z}=3x+3y+\dfrac{\mathrm dh}{\mathrm dz}=3y+2x$
$\dfrac{\mathrm dh}{\mathrm dz}=-x$

But we assume $h$ is a function of $z$ alone, so there is no solution for $h$ and hence no scalar function $f$ such that $\nabla f=\mathbf f$ .

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3 years ago

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Answer:

25?

Step-by-step explanation:

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Point M is located at (-2,7). If point N is 10 units away from point M, how many possible cordinate pairs

natulia [17]

Answer:

2 possible coordinate pairs

N (8, 17) OR (-12, -3)

Step-by-step explanation:

The rule:

(x, y) => (x + 10, y + 10) OR (x - 10, y -10)

(-2 + 10, 7 + 10) OR (-2 - 10, 7 -10)

(8, 17) OR (-12, -3)

Hope this helps!

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Step-by-step explanation:

It's simple. Look at the problem ;)

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sertanlavr [38]

Answer:

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Step-by-step explanation:

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3 years ago

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