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- A pirate has buried his treasure on an island with five trees located at the points (30.0 m, 20.0 m), (60.0 m, 80.0 m), (10.0 m, 10.0 m), (40.0 m, 30.0 m), and (70.0 m, 60.0 m), all measured relative to some origin, as shown in Figure P1.69. His ships log instructs you to start at tree A and move toward tree B, but to cover only one-half the distance between A and B. Then move toward tree C, covering one-third the distance between your current location and C. Next move toward tree D, covering one-fourth the distance between where you are and D. Finally move toward tree E, covering one-fifth the distance between you and E, stop, and dig. (a) Assume you have correctly determined the order in which the pirate labeled the trees as A, B, C, D, and E as shown in the figure. What are the coordinates of the point where his treasure is buried? (b) What If? What if you do not really know the way the pirate labeled the trees? What would happen to the answer if you rearranged the order of the trees, for instance, to B (30 m, 20 m), A (60 m, 80 m), E (10 m, 10 m), C (40 m, 30 m), and D (70 m, 60 m)? State reasoning to show that the answer does not depend on the order in which the trees are labeled. Figure 1.69arrow_forwardPerform the following arithmetic operations, keeping the correct number of significant figures in your answer. a. The product 56.2 0.154 b. The sum 9.8 + 43.4 + 124 c. The quotient 81.340/arrow_forwardIf A = 2i − j − k, B = 2i − 3j + k, C = j + k, find (A · B)C, A(B · C), (A × B) · C,A · (B × C), (A × B) × C, A × (B × C).arrow_forward
- Replace the polar equation r= 8 cos 0 + 4 sin 0 with an equivalent Cartesian equation. Then identify the graph. The equivalent Cartesian equation is (Type an equation using x and y as the variables.)arrow_forwardEvaluate the commutator[L, L,·Ly]. (a) ħ²Lx (b) 0 (c) ħ²L, (d) ħ²L₂arrow_forwardLet 5 = (-1m)î + (2m)ĵ – (3m)k and T = (4m)î – (6m)k. The angle between these two vectors is given by: Select one: cos 1(14/15) O b. cos 1(14/27) O a. cannot be found since S and T do not lie in the same plane O d. cos (11/15) cos '(104/225) Oe.arrow_forward
- The spherical coordinates of a point (x, y, z) are unique. O True O Falsearrow_forwardLet vectors A→ =(2,−4) and B→=(−3,1).Calculate the following: (A) A→ * B→ (B) what is the magnitude of A→ (C) what is the magnitude of B→ (D) what is the angle θAB between A→ and B→arrow_forward- D1.2. A vector field S is expressed in rectangular coordinates as S = {125/ [(x - 1)²+(y-2)² + (z+1)²]}{(x − 1)ax +(y− 2)ay+(z+1)a₂}. (a) Evaluate S at P(2, 4, 3). (b) Determine a unit vector that gives the direction of S at P. (c) Specify the surface f(x, y, z) on which |S| = 1. Ans. 5.95ax +11.90ay +23.8az; 0.218ax +0.436ay +0.873az; √(x − 1)² + (y-2)² + (z + 1)² = 125arrow_forward
- Using the method of separation of variables, find the solution of the following equation Pu Pu = 0 dy? for 0 < r < 3 and 0 < y < 3, which satisfies the following conditions: a) u(0, y) = 0 for 0arrow_forwardEvaluate the volume between the surface z = 3 + 2x + xy, and the rectangle in the xy plane given by 0 < x < 2, 1 < y< 3: Select one: O 12 O 27/2 о 45/2 O 28arrow_forwardLet F(x,y) = 24x -y. If (x , y) changes from ( 7 , 3 ) to ( 5 , 4) , find A F and dF. Enter A F in Blank # 1 and enter dF in Blank # 2. Enter an integer or a fully reduced fraction such as -2 , 0, 15 , 3/4 , -7/9 , etc. No Spaces Please. Blank # 1 Blank # 2arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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