Evaluate the line integral along the curve C.ds, C is the curve r(t) = (6 sin 2t)i + (6 cos 2t)j + 5tk, 2 ≤ t ≤ 4

Find the requested partial derivative of the given function. f(x, y) = x ln (y – x) Find

Using Green’s Theorem, compute for the given path C. Assume C is closed and positive orientated. F = (4x + 9y)i + (2x – 9y)j; C is the region bounded above by y = -2×2 + 54 and below by in the first quadrant

Using Green’s Theorem, compute for the given path C. Assume C is closed and positive orientated. F = (4x + 9y)i + (2x – 9y)j; C is the region bounded above by y = -2×2 + 54 and below by in the first quadrant

Give a geometric description of the set of points whose coordinates satisfy the given conditions. x2 + y2 + z2 ≤ 64

Solve the problem. Unless stated otherwise, assume that the projectile flight is ideal, that the launch angle is measured from the horizontal, and that the projectile is launched from the origin over a horizontal surfaceA projectile is fired at a speed of 1160 m/sec at an angle of 36°. How long will it take to get 29 km downrange? Round your answer to the nearest whole number.

Find the angle between the given vectors. Round to the nearest tenth of a degree.u = i – j, v = 3i + 5j

Using Green’s Theorem, compute for the given path C. Assume C is closed and positive orientated. F = (9x + 2y)i + (8x – 6y)j; C is the region bounded above by y = -3×2 + 96 and below by in the first quadrant

Find the angle between the given vectors. Round to the nearest tenth of a degree.u = i – j, v = 5i + 6j

Find the length of the curve with the given vector equation.r(t) = 3ti + j + k; 2≤ t ≤ 7