Use stokes' theorem to evaluate c f · dr where c is oriented counterclockwise as viewed from above. f(x, y, z) = xyi + 5zj + 7yk, c is the curve of intersection of the plane x + z = 1 and the cylinder x2 + y2 = 81.

Step-by-step explanation:

The given curve is .

Let us parameterize C to obtain a vector equation for C.

We have ,   .

This is the equation of a circle( a cylinder in space) with radius, r=9 units.

The parametric equation of a circle is given by:

and

This implies that:

and

From, , we obtain, ,

A vector equation for C is;

for

Also, we have;

Since C is oriented counterclockwise as viewed from above, we can apply the Stokes' Theorem.

Thus, by Stokes' Theorem;

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step-by-step explanation:

fa tha first one you gonna add y to both sides

it look like this

x-y+y=6+y

x=y+6

therefore your answer is

x =y+6

fa tha second one

you gonna flip tha equation

it gonna look like x-4y=y

then add 4 to both sides

it gonna look like tha

x-4 +4 =y +4

so therefore tha answer is x=y+4

step-by-step explanation: