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Find a basis for the solution space of the homogeneous linear system and find the dimension of that space. The most complete answer will receive best, please SHOW ALL work thank you!
A twisted line which may be approximated by a two-wire line is very useful in the telephone industry. Consider a line comprised of two copper wires of diameter 0.12 cm that have a 0.32- cm center-to-center spacing. If the wires are separated by a dielectric material with ε = 3.5ε0, find L, C, and Zo.
For the following system, try to determine the value of k such that the damping ratio zeta = 0.5. Moreover, calculate the rising time tr, peak time tp, maximum overshoot Mp, and settling time ts in the unit-step response.
Suppose a ship departs from a port on Monday at 10 am and it travels at a constant speed of A km/h. Two hours later, a second ship departs from the same port heading in the same direction with a speed of 60 km/h. Choose any positive integer value for A of either 50, 51, 53 or 54. Using the information given with your chosen value for A, determine the day and time on the clock at which the ships are both at the same distance from the port. a. Solve by using algebra. (10 marks] b. Solve by using geometric series. [15 marks]
1 1 Use mathematical induction to prove that for all integers n > 2, 1 1 + + + <1 4 9 Clearly state the base case, inductive step and inductive hypothesis. n2 n
Task 1: The figure below represents part of the performance data of a car owned by a physics student, suppose you are asked to analyse this performance and to write a report includes the following: position (m) 8 E H G 40 44 -- 5 11 20 30 2 с D time (sec) an A B Figure (1) A. Calculate the total displacement travelled between positions A and G (between t=0 and t=44s)? B. What is the average velocity of the car between positions A and G (between t=0 and t=44s)? C. During which time interval(s) the car was at rest? Explain your answer. D. In which time interval the car was traveling with its greatest speed? Explain your answer. E. During which time intervals the car was traveling in negative direction? Explain your answer. F. Draw a graph of its velocity versus time between A and G (between t = 0 and t = 44s)?
21"- A particle moves in the xy plane starting from time = 0 second and position (Im,2m) with a velocity of = 4. Find A. The vector position of the particle at any time t. B. The acceleration of the particle at any time t.
Task III Figure 2 shows a graph of v, versust for the motion of a car as the driver starts from vx = 4.5 m/s and moves along the road. ,(m/s) 6.0 4.0 2.0 0.0 (s) 10 20 30 10 50 -2.0 -6,0 Figure 2 (a) Find the average breaking acceleration in the time interval t=0 to 5.00 . (b) During which time interval/intervals the car is accelerating. Explain
Task TV Osama was testing his new car by racing with his fiend Adam, Osama was driving at 54.0 mile/hr, enters a one-way narrow subway. Osama then observed a Truck 100 m ahead traveling at a low constant speed 3.00 m/s. Osama used his brakes but can accelerate only at -2.00 m/s because the road was wet. Will there be an accident? Explain. If yes, HTU. Page 5 of 8 جامعة الحسين التقنية Al Hussein Technical University at what time the accident occurs and how far into the subway. If no, determine the distance of closest approach between Osama's car and the Truck. (I mile=1609m).
