Question Solved1 Answer The figure(Figure 1) shows a thin rod of length L with total charge Q. Figure 1 of 1 L P . Find an expression for the electric field E at distance x from the end of the rod. Give your answer in component form. Express your answer in terms of the variables Q. L, x, unit vectors i, j, and appropriate constants. ΟΙ ΑΣφ ? kQ L2 72 4

The figure below shows a pendulum with length L and the angle from the vertical to the pendulum. It can be shown that, as a function of time, satisfies the following nonlinear differential equation de 9 dra sin = 0 where g denotes the acceleration due to gravity. For small values of we can assume esine such that the differential equation can be considered to be linear. (a) Find the equation of motion of the pendulum with length 750 cm if 15 and its initial angular velocity is is initially (b) - 1 rad/s. What is the maximum angle from the vertical? What is the period of the pendulum (the time to complete one back-and-forth swing)? When is the duration for the pendulum to be vertical, that is, 8 = 0? What is the angular velocity when the pendulum is vertical? Describe how the pendulum concept is used in the pendulum clock.

[-/3 Points] DETAILS MENDSTATC4 4.E.073. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER If an experiment is conducted, one and only one of three mutually exclusive events S, Sy, and Szcan occur, with these probabilities. P(S) = 0.1 P(S) = 0.5 P(Sz) = 0.4 The probabilities of a fourth event A occurring, given that event S, Szor Szoccurs, are the following. P(AIS) = 0.1 P(AIS) = 0.2 P(AS) = 0.4 If event A is observed, find P(S,A), P(S2/A), and P(Sz|A). (Round your answers to four decimal places.) P(SIA) = P(S21A) = P(S31A) = Need Help? Read It (-/1 Points] DETAILS MENDSTATC4 4.E.076. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A worker-operated machine produces a defective item with probability 0.07 if the worker follows the machine's operating instructions exactly, and with probability 0.09 if he does not. If the worker follows the instructions 90% of the time, what proportion of all items produced by the machine will be defective? Need Help? Read It

help asap Check my war Two wooden members are joined by plywood splice plates that are fully glued on the contact surfaces Knowing that the clearance between the ends of the members is 6 mm and that the ultimate shearing stress in the glued joint is 2.5 MPa, determine the length L for which the factor of safety is 2.75 for the loading shown. Take P=15 kN. P The length mm

Sex Race Age 2 2 1 NNN 25 78 70 33 60 78 72 Region Ancestors astrosci educ 2 3 1 1 1 1 1 1 2 3 4 1 3 3 1 2 1 2 2 2 1 3 4 2 3 1 4 2 1 2 1 2 2 3 1 3 2 2 2 3 3 3 1 3 1 3 3 2 2 3 3 1 4 3 Income 16 34.57 15 78.65 17 56.73 18 23.46 13 54.53 13 44.23 16 66.54 16 67.85 25.67 27.87 17 55.61 16 26.54 18 76.54 16 33.46 16 23.47 NN 2 3 2 1 2 1 1 1 1 2 37 44 50 Sex= Sex of the Respondent 1=Male 2=Femal Age Age of the Respondent Race=Race of the Respondent 1= White 2=Black 3-Other Region= Region of Respondent 1= Mid West 2=Mid Atlantic 3= New England Ancestor=Do you believe that your deceased ancestors have supernatural powers? 1= Yes, Definiity; 2= Yes, Probably 3=No, Probably not; 4=no definitely not Astrosci= Is Astrology Scientific; 1=Very Scientific 2=Sort of Scientific 3= Not Scientific at all Educ=Highest Year of School completed Income=Income in 1000s of Dollars For the nominal variables race and region provide the mode and index of qualitative variation (IQV). Which variable has more variation? 2. For ordinal variables ancestor and astrosci provide the mode and median. Describe what each statistic tells you about the data. 3. For interval level variables age, education and income, provide the range, inter-quartile range, mean, median, variance, and standard deviation. Interpret each statistic. Answer the following questions: 4. Briefly explain the difference between measures of central tendency and measures of variability. Why do we need both? Can you think of a situation where central tendency might be misleading if you did not know the variability? 5. Why don't we use means for nominal level variables?

1) a) i) Define what is a vector space. ii) The 2-D Laplace equation: av av + - 0 ax? Əy? ay with appropriate boundary conditions, has a general solution of the type v(x, t) = G(x + iy) + H(x – iy) iii) Let F be a real field. Show that the general solution in part 1) a) ii) forms a vector space over F. (8 + 4 + 4 marks) = ii) The 2-D Laplace equation: a2v av + = 0 Əx2y2 with appropriate boundary conditions, has a general solution of the type v(x, t)=G(x + iy) + H(x – iy) iii) Let F be a real field. Show that the general solution in part 1) a) а ii) forms a vector space over F.

Fať 7 -6+ 62 – 4ac x = xo + vot+ v = vo + at , v2 = võ + 2aAx ,t= 2a Problem 1: A ball is thrown straight up from the ground. The ball reaches a maximum height of 5 m. For simplicity, for this problem, use g 10 m/sec. (a) Calculate the initial speed of the ball. Answer: 10 m/sec. (b) Calculate the time it takes the ball to reach the maximum height of 5 m. Answer: 1 sec. (c) Calculate the time it takes the ball to hit the ground. Answer: 2 sec. (d) Make a sketch of the position vs. time graph for this problem, y(t) vs. t. (e) Calculate the time(s) when the ball is at a height of 3 m above the ground. Answer: t = 0.37 sec and t = 1.63 sec. (f) Calculate the velocity of the ball when the ball is at a height of 3 m above the ground. Answer: v= : +6.3 m/sec for t = 0.37 sec and v -6.3 m/sec for t = 1.63 sec. =