# Calculus

2) Maple syrup is being pumped into a cone-shaped vat in a factory at a rate of six cubic feet per minute. The cone has a radius of 20 feet and a height of 30 feet. How fast is the maple syrup level increasing when the syrup is 5 feet deep?

(4) Let d(x) = sin(e). Determine d'(x).

13. The terminal point of vector DE-[-4, 2, 6] of the is E(3, 3, 1). Determine the coordinates initial point, D.

Find the centroid (x, y) of the region bounded by: y=e²x, y=0, x=0, and x = = 3. 18 IN y || ||

(5) Let T(x) = (cos(2t³ - 4t+6))7. Determine T'(x).

14. Write an ordered triple for each vector. a) AB with A(0, -3, 2) and B(0, 4,-4) b) CD with C(4, 5, 0) and D(-3, -3, 5)

11. Determine the exact magnitude of each vector in question 10.

(2) Let g(x) = ex-5. Determine g'(x). Page 1 of 4

The masses m, are located at the points P¿. Find the moments Mr and My and center of mass of the system. 1, m2 = 2, m3 = 9. P₁ = (-2,0), P₂ = (6,4), P3 = (2,8). m1 Mx My x = y = = =

(6) Olivia is vacationing in a cabin along a river. The path of the river near Olivia's cabin can be modeled by the function y = r². Olivia's cabin is located at the point (0,3) on the diagram. He noticed that a boat is floating at the point (3,2.25) on the river. River 2 Cabin (a) What is the distance of the boat from Olivia's cabin? (3.2.25) (b) What is the minimum distance from Olivia's cabin to the river? (c) What are the location(s) on the river that are closest to Olivia's Cabin? Page 3 of 4