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2 years ago

Simplify.

Mathematics

1 answer:

Dominik [7]2 years ago

6 0

Simplify: [{y^(2/7)}/{y^(1/2)}]

Since, [{a^(p/q)}/{a^(r/s)}] = a^{(p/q)-(r/s)}

Where,

a = p
p/q = 2/7 and
r/s = 1/2

so,

= y^{(2/7)-(1/2)}

Take the LCM of denominator i.e.,2 & 7 is 14.

= y^{(2*2 - 1*7)/14}

= y^{(4-7)/14}

= y^(-3/14) Ans.

read more similar questions: Which equation can be simplified to find the inverse of y = x2 – 7? a: x=y ^ 2 - 1/7 b: 1/x = y^2 - 7 c: x = y^2 – 7 d: –x = y^2 – 7..

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Answer:

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2 years ago

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3 years ago

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Free_Kalibri [48]

Answer:

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3 years ago

For each of the following vector fields F , decide whether it is conservative or not by computing curl F . Type in a potential f

Phantasy [73]

The key idea is that, if a vector field is conservative, then it has curl 0. Equivalently, if the curl is not 0, then the field is not conservative. But if we find that the curl is 0, that on its own doesn't mean the field is conservative.

$\mathrm{curl}\vec F=\dfrac{\partial(5x+10y)}{\partial x}-\dfrac{\partial(-6x+5y)}{\partial y}=5-5=0$

We want to find $f$ such that $\nabla f=\vec F$ . This means

$\dfrac{\partial f}{\partial x}=-6x+5y\implies f(x,y)=-3x^2+5xy+g(y)$

$\dfrac{\partial f}{\partial y}=5x+10y=5x+\dfrac{\mathrm dg}{\mathrm dy}\implies\dfrac{\mathrm dg}{\mathrm dy}=10y\implies g(y)=5y^2+C$

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so $\vec F$ is conservative.

$\mathrm{curl}\vec F=\left(\dfrac{\partial(-2y)}{\partial z}-\dfrac{\partial(1)}{\partial y}\right)\vec\imath+\left(\dfrac{\partial(-3x)}{\partial z}-\dfrac{\partial(1)}{\partial z}\right)\vec\jmath+\left(\dfrac{\partial(-2y)}{\partial x}-\dfrac{\partial(-3x)}{\partial y}\right)\vec k=\vec0$

Then

$\dfrac{\partial f}{\partial x}=-3x\implies f(x,y,z)=-\dfrac32x^2+g(y,z)$

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so $\vec F$ is conservative.

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so $\vec F$ is not conservative.

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