3 years ago

Pls help I’ll brainlest

Mathematics

1 answer:

Natali [406]3 years ago

8 0

Answer:

C. 5.8 × $10^{-5}$

Step-by-step explanation:

0.000058

4 zeros

4 + 1 = 5

5.8 × 10⁻5

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n200080 [17]

$\vec F(x,y,z)=y\,\vec\imath+x\,\vec\jmath+3\,\vec k$

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$\dfrac{\partial f}{\partial x}=y$

$\dfrac{\partial f}{\partial y}=x$

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(or perhaps the last partial derivative should be 4 to match up with the integral?)

From these equations we find

$f(x,y,z)=xy+g(y,z)$

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$f(x,y,z)=xy+3z+C$

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$\displaystyle\int_{(1,2,3)}^{(5,7,-2)}y\,\mathrm dx+x\,\mathrm dy+3\,\mathrm dz=\int_{(1,2,3)}^{(5,7,-2)}\nabla f(x,y,z)\cdot\mathrm d\vec r$

$=f(5,7,-2)-f(1,2,3)=\boxed{18}$

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3 years ago