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;

sorry can't

step-by-step explanation:

i googled though and something came up but it was in science langueage not common english sooo

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."