Determine whether or not F is a conservative vector field. If it is, find a function f such that F = ∇f. F(x, y) = (2x − 7y)i + (−7x + 8y − 6)j

f = x^2-7yx+4y^2-6y

Step-by-step explanation:

A vector field is conservative if the work done by that vector field around any loop is 0 or the end points only matter when calculating the work done, not the path in between (think of gravity). The curl(F) must equal 0.

curl(F) = ∇ x F =0

= det( ) (***partial derv)

-7 - (-7) = 0

Yes, it is conservative, which means we can find the potentional energy function by turning the vector field into the gradient of scalar function.

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step-by-step explanation:

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step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2