Find the potential of the function V = 60cos θ/r at the point P(3, 60, 25).

The potential of a function ( V = frac{60cos(theta)}{r} ) at a point ( P(r, theta, z) ) is calculated directly by plugging the coordinates of the point into the function. Given the point ( P(3, 60, 25) ), the values of ( r ) and ( theta ) are provided in the coordinates of the point, where ( r = 3 ) and ( theta = 60 ) degrees.

First, we need to convert the angle ( theta ) from degrees to radians because trigonometric functions in calculus are typically evaluated in radians. ( theta = 60^circ = frac{pi}{3} ) radians.

Then, we can substitute ( r ) and ( theta ) into the formula:

[ V = frac{60cos(theta)}{r} = frac{60cos(frac{pi}{3})}{3} ]

Knowing that ( cos(frac{pi}{3}) = frac{1}{2} ), we get:

[ V = frac{60 times frac{1}{2}}{3} = frac{30}{3} = 10 ]

So, the potential ( V ) of the function at the point ( P(3, 60, 25) ) is ( 10