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i have the cartesian coordinates x=4, y=3, and z=4. I'm trying to figure out thespherical coordinates. I haven't done these 3-d stuff in a long time please help
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- Suppose i = 31 + 8j – 18k and u = 3i + 3j + k. Compute the following: %3D The cosine of the angle between v and u is The scalar component of u in the direction of v is proj, i =Answer 5 6 7 8 9 10The Kentucky Derby is a 2 km race. Assume the track is circular and horses run counterclockwise around the track starting due east of center. Let theta be the angle (in radians) the horse has swept out counterclockwise since starting the race. 1)How many kilometers has the horse traveled if the angle swept out by the horse is pi radians? 90 degrees? Determine which is longer and explain your answers. 2)Suppose the horse travels at a constant speed of 55 km per hour. How long does it take the horse to run once around the track? Justify and include units.
- Hi! I already have answers for parts A-C in this problem, but I'm having trouble with the last part (D.). Attached is the guide to answer it. My answers for part C are: A = 0 B = (V_o cos theta)/omega C = -(mg)/k D = (V_o sin theta)/omega E = mg/k I tried substituting these coefficients to the x(t) and y(t) formulas, but I still can't reduce them to the usual projectile kinematic equations. Also, what does it mean to do a small angle approximation? I hope you can help, thank you in advanced!The surface integral of V = x + yŷ + (z - 3)2 over the sphere of unit radius centred at the origin is Select one: ○ a. 4π ○ b. O ○ c. 4π/3 ○ d. πProblem 1. Evaluate the expression (-2 + 3i)(-3 - 9i) and write the result in the form a + bi. The product is
- Figure 10: River B VB VR A boat crosses a river of width 23.4 meters. The boat was traveling with a speed of 5.2 meters per second relative to the water. The river was moving to the right with a speed of vr = 3.5 m/s relative to the shore. The boat was traveling at an angle of theta = 0 = 56.5 degrees relative to the water away from the near shore. In other words, theta e is the angle between the velocity of the boat relative to the water and the velocity of the water relative to the shore. The situation is shown in figure 2, above. The boat left the near shore at point A and reached the opposite shore at point B (both indicated in the diagram above). Assume the shores of the river are parallel and straight, and all velocities are constant. Point B is a distance d downstream (to the right) from Point A. Calculate the distance d in meters.Evaluate the expression A Xn-1 Xn-2 X₁ n!ſdxn-1 § dxn-z [ dx-... dx₂ § dx, § dx¸ n-3.... 0 0 0 0 0 07
- part 2 of 3 In 3d, we may extend this idea to cylindrical coordinates (r, o, z), which you may think of as a plane polar coordinate system with the z-dimension tacked on. (r, 6,2) y This coordinate system is useful when deal- ing with problems that have radial symmetry about some central axis. Question: You are given a hollow cylinder of radius R whose central axis is the z-axis and whose base rests on the xy-plane. What are the Cartesian coordinates of an arbitrary point on the surface of the cylinder in terms of cylindrical quantities? 1. (x² + y², tan¯ Y ¹(²-).. Т 2. (R cos o, R sin o, z) ○ 3. (x, y, z) ○ 4. (R, o, z) 5. (x cos o, y sin o, z) O 6. (R sin o, R cos , z)Match the vector to its description. The vectors are given by their components in 3D space, that is by (x,y,z) In the x,y plane, 45° to the x- and y-axes A vector pointing straight up, in the z direction. A vector of length √5 A vector making an angle of 45° to all three axes A. (10,10,10) B. (1,1,0) C. (0,0,99) D. (0,1,2)B3