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Fun with logarithms.
(a) Simplify the expression
(b) Assuming that
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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_forwardA pirate has buried his treasure on an island with five trees located at the points (30.0m,220.0m),(60.0m,80.0m),(210.0m,210.0m),(40.0m,230.0m), and (270.0m,60.0m), all measured relative to some origin, as shown in above figure. 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,…arrow_forwardI have written down a y(x,t) for the given values, but I think that I am not supposed to solve for the problem and then sketch. Am I supposed to solve the y(x,t) for the problem? Before I sketch? The problem is #7.1arrow_forward
- A farmer wants to fence off his four-sided plot of flat land. He measures three sides, shown as A, B, and D in the Figure, and then correctly calculates the length and orientation of the third side C. The length of A, B, and D are all 7.06 km. Their angles theta1, theta2, and theta3 are all 2.16 degrees. What did he find as the magnitude of C (in unit of km)?arrow_forwardA circular area S is concentric with the origin, has radius a, and lies in the yz-plane. Calculate ∫??⃗·?ˆ??∫SE→·n^dA for ?⃗=3?2?ˆ.E→=3z2i^.arrow_forwardCan you further explain the step 2 (the quadratic equation) and please show the setp-by-step solution? thank youarrow_forward
- Imagine a 3-dimensional world with coordinates that are labeled with x, y, and z, as if you are in a large room with walls, a high ceiling and a floor. The edges are x, y and z with z up toward the ceiling, the flat plane floor is x-y. Starting at the origin, go along "x" 2 meters. Then go parallel to "y" 4 meters. Then go up parallel to "z" 3 meters. This point is somewhere in the room above the floor. What is the vector from the origin to the point? What is the magnitude of that vector? That is, what is its length? What angle does it make to the floor? This would be 90°-θ where θ is the angle down from the z azis. (Hint: Use the arctangent knowing z and the length of the vector.) If you dropped from that point directly down to the floor, how far would you fall? How long would it take, given that falling objects accelerate at 10 m/s every second (10 m/s2)?arrow_forwardcan you please solve this problem, explaining step by step in a piece of paper please.arrow_forwardA certain corner of a room is selected as the origin of a rectangular coordinate system. If a fly is crawling on an adjacent wall at a point having coordinates (2.7, 1.8), where the units are meters, what is the location of the fly in polar coordinates?arrow_forward
- According to the Theory of Relativity, the length of an object depends on its velocity v with respect to an observer. For an object whose length at rest is 10 m, its observed length L satisfies the equation c2L2 + 100v2 = 100c2 where c is 300,000 km/s, the speed of light. (Round your answers to four decimal places.) (a) Express L as a function of v and c.L = 10√(c+v)(c−v)c (b) What is the observed length L of a meteor that is 10 m long at rest and that is traveling past the earth at 20,000 km/s?(c) What is the observed length L of a satellite that is 10 m long at rest and that is traveling at 15,000 km/s?(d) What is the net change in the observed length L of an object whose velocity changes from 15,000 km/s to 20,000 km/s?arrow_forwardA certain corner of a room is selected as the origin of a rectangular coordinate system. A fly is crawling on an adjacent wall at a point having coordinates (2.9, 2.7), where the units are meters. Express the location of the fly in polar coordinates. Looking for; radius in meters and theta is equal to what degree?arrow_forwardAt one point in space, the direction of the electric field vector Is given In the Cartesian system by the unit vector . If the magnitude of the electric field vector is E=400.0V/m , what are the scalar components , and of the electric field vector at this point? What is the direction angle of the electric field vector at this point?arrow_forward
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