SECTION 6.7

13. Given v = 6i - 2j and w = -i -j, a. Find projwV. b. Decompose v into two vectors v, and v2, where v, is parallel to w and v2 is orthogonal to w. a. projw V = (Type your answer in terms of i and j.) b . V1 = Type your answer in terms of i and j.) V2 = (Type your answer in terms of i and j.) 14. If v= 4i + 5j and w= - 2i + 7j, find projwv . Then decompose v into two vectors v, and v2, where v, is parallel to w and v2 is orthogonal to w. projwv = (Simplify your answer. Use integers or fractions for any numbers in the expression. Type your answer in terms of i and j.) V 1 = (Simplify your answer. Use integers or fractions for any numbers in the expression. Type your answer in terms of i and j.) V 2 = (Simplify your answer. Use integers or fractions for any numbers in the expression. Type your answer in terms of i and j.) 15. If v = 3i + 5j and w = 6i + 10j, find projwv . Then decompose v into two vectors v, and v2, where v, is parallel to w and v2 is orthogonal to W . projwv = (Simplify your answer. Use integers or fractions for any numbers in the expression. Type your answer in terms of i and j.) V 1 = L (Simplify your answer. Use integers or fractions for any numbers in the expression. Type your answer in terms of i and j.) V2 = (Simplify your answer. Use integers or fractions for any numbers in the expression. Type your answer in terms of i and j.)'16. Letu=i+j. v=3i2j. and w: 4j. Find 4u -(3v2w}. 4u - (3v 2w) 2 1:1 (Simplify.r your answer.) '17. Given u: i+j, v=8i6j. and w: 8j. find projuiv+w]. DFOJu(V + W) = :1 (Type your answer in terms ofi and j.) '18. Determine whether v and w are parallel, orthogonal. or neither. v=3i5j. w=6i10j Choose the correct answer below. 0 parallel O orthogonal O neither 19. Find the work done in pushing a car along a level road from pointA to point B, 85 feet from A, while exerting a constant force of 92 pounds. Round to the nearest footpound. The work done is 1:1 footpounds. 20. Aforce is given by the vector F 2 3i + 7]. The force moves an object along a straight line from the point {4.5} to the point {3020). Find the work done if the distance is measured in feet and the force is measured in pounds. The work done is [1} {Simplify your answer.) (1) 0 feet. 0 footpounds. 0 feet perpound. 0 pounds. 0 pounds perfoot. 6. Find h to the nearest tenth. 450 76 A BA D - 287 -1 The length of h is approximately (Round the final answer to the nearest tenth as needed. Round all intermediate values to the nearest tenth as needed.) 7. Find a to the nearest tenth. 190 320 294 The length of a is approximately (Round the final answer to the nearest tenth as needed. Round all intermediate values to the nearest tenth as needed.) B. Find x. 19 20 140 The value of x is (Do not round until the final answer. Then round to the nearest tenth as needed.)9. Use the given measurements to solve the triangle. Round lengths C of sides to the nearest tenth and angle measures to the nearest degree. h a = 900, b = 600 28 A B C The measure of angle B is approximately (Round to the nearest degree.) The measure of angle A is approximately (Round to the nearest degree.) The measure of angle C is approximately (Round to the nearest degree.) The length of c is approximately (Round to the nearest tenth.)10. The figure shows a 1300-yard-long sand beach and an oil platform in the ocean. The angle made with the platform from one end of the beach is 85" and from the other end is 76". Find the distance of the oil platform, to the nearest tenth of a yard, from each end of the beach. 769 1300 yards The platform is about yards from one end of the beach and yards from the other. (Use descending order. Round to the nearest tenth as needed.) 11. A pine tree growing on a hillside makes a 73" angle with the hill. From a point 80 feet up the hill, the angle of elevation to the top of the tree is 65" and the angle of depression to the bottom is 18". Find, to the nearest tenth of a foot, the height of the tree. 730 650 The height of the tree is about feet. (Round to the nearest tenth as needed.) 12. A pier forms an 82" angle with a straight shore. At a distance of 105 feet from the pier, the line of sight to the tip forms a 35" angle. Find the length of the pier to the nearest tenth of a foot. 105 ft The length of the pier is about feet. (Round to the nearest tenth as needed.)13. Trees in a local park are hundreds of feet tall. The height of one of C these trees is represented by h in the figure shown. 25 B 15 A | $50 feet a. Use the measurements shown to find a, to the nearest tenth of a foot, in oblique triangle ABC. The length of a is approximately feet. (Do not round until the final answer. Then round to the nearest tenth as needed.) b. Use the right triangle shown to find the height, to the nearest tenth of a foot, of the tree in the park. The height of the tree, h, is approximately feet. (Do not round until the final answer. Then round to the nearest tenth as needed.)14. Select the correct choice that completes the sentence below. A triangle that is not a right triangle is an (1). triangle. (1) O oblique O obtuse O acute 15. Two buildings of equal height are 750 feet apart. An observer on the street between the buildings measures the angles of elevation to the tops of the buildings as 29" and 41". How high, to the nearest foot, are the buildings? The buildings are about feet high. (Round to the nearest foot as needed.) 16. Two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results. a= 10, b=9, A=70' Selected the correct choice below and, if necessary, fill in the answer boxes to complete your choice. (Round side lengths to the nearest tenth and angle measurements to the nearest degree as needed.) A. There is only one possible solution for the triangle. The measurements for the remaining side c and angles B and C are as follows. O B. There are two possible solutions for the triangle. The measurements for the solution with the the smaller angle B are as follows. The measurements for the solution with the the larger angle B are as follows. B2 = C2 = G2 = O C. There are no possible solutions for this triangle.17. Two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results. a = 14, b = 17.5, A=439 Selected the correct choice below and, if necessary, fill in the answer boxes to complete your choice. (Round side lengths to the nearest tenth and angle measurements to the nearest degree as needed.) O A. There is only one possible solution for the triangle. The measurements for the remaining side c and angles B and C are as follows. CA O B. There are two possible solutions for the triangle. The measurements for the solution with the the smaller angle B are as follows. The measurements for the solution with the the larger angle B are as follows. B, # O C. There are no possible solutions for this triangle