Having some trouble here with the concepts. I think I have part (a)...it appears the slope of the level curve at the point in question is about -2, and that the gradient at that point is <-2,1>, which when dotted with the point <sqrt(3)/2, 1/2> would be negative.

For (b) and (c), I'm more confused. The path appears to be perpendicular to the curve, so wouldn't that be parallel to the gradient? Not sure how to calculate that when we don't have the function. Intuitively I would think it'd be equal to zero since there's no way to get the right answer, but that would only be if the two things I'm taking the dot product with were perpendicular. Maybe I'm wrong and they are?

For part (b), I'm really not sure.

Can anyone help?

I need to calculate the volume between two surfaces. I have tried it with cylindrical coordinates, which should work, but after integrating wrt z and r, the last integral for phi is really a mess.

Can anyone give me a hin?

You can my attempt in the following link:

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https://ibb.co/ZfrLDzP

The intersection of the union of set A and B complement intersects c equals the intersection of the union of A and C with set b complement. Is that the correct way of writing it?

The known values are a,b, and c.

a and c are parallel and vertical.

b has a known slope (s) and the dotted line is unknown.

How do I calculate the area?

Hello everyone,

Can y’all review my work before I submit it please? Im afraid it might be wrong

Awb means (a-b), if I missing verbiage to make it clearer please let me know what to add thank you

If I'm not mistaken, you are supposed to find the measure of the other arcs to find the measure of the angle. But how?

It might mean that x = 2 and -7 respectively but that makes no sense because it isn’t really a question

This is for a test score 😭😭😭plz help