Numerade

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8.17 The next five problems are based on the Messenger spacecraft launched from Earth on August 3, 2002. After gravity-assist maneuvers around the earth, Venus, and Mercury, Messenger is scheduled (at the time of this writing) to go into orbit around Mercury on March 18, 2011. The radius and mass of Mercury are 2,440 km and $3.3 \times 10^{23}$ kg, respectively. The orbit is designed to be highly elliptical, with the altitude of closest approach (periapsis) of 200 km, and the altitude of farthest distance (apoapsis) of 15,193 km. (Note: These are altitudes above the surface of Mercury, not the distances from the center of the planet.) Calculate the period of the Messenger orbit. Ignore the influence of the gravitational attraction of the sun on the spacecraft orbit. 8.18 For the Messenger spacecraft in orbit about Mercury (see Prob. 8.17), calculate the spacecraft's velocity at periapsis and at apoapsis. 8.19 For the Messenger spacecraft in orbit about Mercury (see Probs. 8.17 and 8.18), calculate its angular momentum per unit mass. 8.20 What is the eccentricity of the Messenger's orbit about Mercury? 8.21 From the characteristics and properties of the orbit, some of which are given in Prob. 8.17, it is not possible to extract the mass of the Messenger spacecraft. Why?

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Without the aid of a calculator, convert 3.5 x 106 to standard form and clearly explain your process. Zero marks without an explanation.

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Internal controls are designed to provide reasonable assurance that: Multiple Choice management's plans have not been circumvented by worker collusion. the internal auditing department's guidance and oversight of management's performance is accomplished effectively and efficiently. management's planning, organizing, and directing processes are properly evaluated. material errors or fraud would be prevented or detected and corrected within a timely period by employees in the course of performing their assigned duties.

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Required 2

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How much of society do you think uses budgets regularly? Explain.

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10. Determine the partial fraction expansion for V(s) and compute the inverse Laplace transform. The transfer function V(s) is $V(s) = \frac{400}{s^2 + 8s + 400}$

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Find the perimeter of the right triangle. If necessary, round to the nearest tenth. a. 27.6 cm b. 190 cm c. 66.6 cm d. 39 cm Please select the best answer from the choices provided.

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Problem 1 - The EV charging station at Shelby Hall delivers 3.5 kW of power for 4 hr. to the vehicle that is plugged in. a) If the voltage used is 350 V, what is the current in the circuit while charging? b) How many Joules of energy have been stored in the battery during charging? c) If the cost of electricity is $0.075/kWh, how much did this cost the user?

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7) The kinetics of the reaction A + 3B ? C + 2D were studied and the following results obtained, where the rate law is: \frac{\Delta[A]}{\Delta t} = k[A]^n[B]^m For a run where $[A]_0 = 1.0 \times 10^{-3}$ M and $[B]_0 = 5.0$ M, a plot of ln $[A]$ versus $t$ was found to give a straight line with slope = $-5.0 \times 10^{-2}$ s$^{-1}$. For a run where $[A]_0 = 1.0 \times 10^{-3}$ M and $[B]_0 = 10.0$ M, a plot of ln $[A]$ versus $t$ was found to give a straight line with slope = $-7.1 \times 10^{-2}$ s$^{-1}$. What is the value of n? a. 0 b. 0.5 c. 1 d. 1.5 e. 2

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Please Help with questions 1 and 2 please. Our entire activity will be about the following system.Let denote the position of a particle p, of unit mass on the horizontal axis, where two other particles lying on the vertical axis act on it. The motion of p is restricted to the -axis. The first acting particle, Pi initially lies d units above the -axis, acts with an repulsive force on p,and may oscillate up and down on the vertical axis with time so its height above the -axis is given by d+Acos(t where A< d.The other acting particle, p2, stays stationary on the vertical axis, acts with an attractive on p, and stays a fixed distance d below the -axis. Assume that the magnitude of the force of each acting particle is inversely proportional to the square of the distance between the particle doing the acting and p,with constants of proportionality k and k2respectively.We will always assume k > k Also assume the motion of p is damped with a force proportional to its velocity, with constant of proportionality b. 1.15 points Sketch a diagram of the mechanical system and carefully erplain why it leads to the second order differential equation k2x 2.For this question assume that there is no damping b=0 and that pi is stationary A=0 Moreover,assumed=d=d. a5 points Under the hypotheses of this question, transform the differential equation describing the motion of p into a system of differential equations using = v. Find the equilibrium of this system (this part should be easy). b 5 points Explain why near the equilibrium you found the system behaves like k-k2 d3 Then classify the equilibrium and justify your result with a graph (turn in the graph too. c5 pointsAssuming 0=0,use pplane to decide how large must the initial velocity be to prevent (t from being periodic. Be sure to include the values of the other parameters you used.

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jonathan p.