Calculus 3 :

Section 10.2: Problem 11 (1 point) A horizontal clothesline is tied between 2 poles, 18 meters apart. When a mass of 5 kilograms is tied to the middle of the clothesline, it sags a distance of 3 meters. What is the magnitude of the tension on the ends of the clothesline? NOTE: Use g = 9.8m/s' for the gravitational acceleration. Tension = NSection 10.2: Problem 12 (1 point) The nine Ring Wraiths want to fly from Barad-Dur to Rivendell. Rivendell is directly north of Barad-Dur. The Dark Tower reports that the wind is coming from the west at 65 miles per hour. In order to travel in a straight line, the Ring Wraiths decide to head northwest. At what speed should they fly (omit units)?Section 10.2: Problem 13 (1 point) The figure shows a rectangular box in three-dimensional space that contains several vectors. (The vector c is in the xz-plane, and the vector e is in the xy-plane.) b Are the following statements true or false? ? 1. a = -b ? v 2. C = f F v 3. e = a-b v 4. a = d v 5. g =f + a (Click on graph to enlarge) v 6.d =g-c ? True No False earn 50% partial credit for 3 - 5 correct answers.Section 10.2: Problem 14 {1 point] Leta = {4,3} and b = {1, 3}_ Show that there are scalars a: and t 50 that 53+ tb = {5, 15} You might want to sketch the venture to get some intuition. :8 Section 10.2: Problem 15 {1 point] In the gure below the yaxis points north, the :r-axis points east, and the Iy-plane corresponds to the surface of the water. Suppose a boat is at point E, a submarine is 9 units below point 3, and a helicopter is 15 units above point H. 1. Find the displacement vector and the distance from the submarine to the boat. Displacement C] Distance: E] 2. Find the displacement vector and distance from the helicopter to the boat. Displacement; C] Distance: E] 3. Find the displacement vector and distance from the submarine to the helicopter. Displacement E] Distance: C] Section 10.2: Problem 16 [1 point] Find the following expressions using the graph below of vectors u, v, and w. H3 ..... ll v t I I _1 1 . -1. . Section 10.2: Problem 17 (1 point) Find vectors that satisfy the given conditions: 1. The vector in the opposite direction to u = (-4, 2) and of half its length is 2. The vector of length 7 and in the same direction as v = (-1, 3, 3) isSection 10.2: Problem 18 (1 point) Let u = (2, 4), v = (1, 0), and w = (-3,3). Find the vector I that satisfies 9u -U+1 = 91 + W. In this case, ISection 10.2: Problem 19 (1 point) Suppose u = (-3, -3) and v = (-3, 15) are two vectors that form the sides of a parallelogram. Then the lengths of the two diagonals of the parallelogram are Separate answers with a comma