Consider f and c below. f(x, y, z) = yzexzi + exzj + xyexzk,

c. r(t) = (t2 + 5)i + (t2 − 3)j + (t2 − 5t)k, 0 ≤ t ≤ 5 (a) find a function f such that f = ∇f. f(x, y, z) = (b) use part (a) to evaluate c f · dr along the given curve

c.

Find the area and perimeter of each composite figure. use 3.14 for π. round your answer to the nearest tenth. a square and a right triangle share a common side. image long description a 3-meter by 0.5-meter rectangle has triangles attached like wings to the 3-meter sides. the other two sides of both triangles measure 2.5 meters. the height of each triangle is 2 meters. a 6-inch by 4-inch rectangle has 2 half-circles attached like wings to the 6-inch sides. the radius of each half-circle is 3 inches. find the surface area and volume of each figure. use 3.14 for π. round your answer to the nearest tenth. a right circular cylinder has a base radius of 6 yards and a height of 20 yards. a rectangular prism has a base that is 9 centimeters long and 7 centimeters wide. the height is 2 centimeters. a rectangular prism has a base that measures 11 millimeters by 11 millimeters. the height is 11 millimeters.

There are 15 plates and each plate is either 7 or 12 inches diameter. which systems of equations do you use to find the number of 7 inch plates, x and 12 inch plates, y

Janet drove 300 miles in 4.5 hours. write an equation to find the rate at which she was traveling