Find the potential of the vector field f~ (x, y, z) = e xy/z (1 + xy z )~i + x 2 z ~j − x 2y z 2 ~k , and use the fundamental theorem for line integrals to evaluate z c f~ · d~r, where c is the straight line segment from (1, 1, 1) to (2, 2, 1). can one choose an arbitrary piece-wise smooth curve c with initial point (1, 1, 1) and terminal point (2, 2, 1) instead of the straight line segment?

hi there! my name is zalgo and i am here to you out today. the answer is pretty simple (in a way). this equation equals to 25.2!

i hope this answer !

"stay and stay proud! " - zalgo

i think asking google will you get the answer to that question

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).