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A: d) Note that {3, 1, 9, 0, -1} = {-1, 0, 1, 3, 9}So {-1, 0, 1, 3, 9}⊆{3, 1, 9, 0, -1} The given…
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A: We know that De Moivre’s Formula (cos x + i sin x)n = cos(nx) + i sin(nx)
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- Find parametric equations for a normal line to the level curve of the function f (x, y) = −3x(x − 2) − y(y −1) at the point P(3,3).The line tangent to a curve at a point (x1, y1) is y = 2x – 2. The normal to that curve at the same point passes through (11, -5). Taylor sits at the point (x1, y1).An investor has his savings invested in various investments. The amount at the end of each month, in the first semester, is shown in the table. a. Assuming that the rate of change of the amount can be represented by: y ′ (x) = (0.06y (x)) / x, obtain an approximation for the amount in the month of August, using the Improved Euler method, using h = 1 and initial condition given by the data for the month of June.b. What is the relative percentage error knowing that the particular solution of the PVI is y (x) = e ^ (0.06 lnx + 4.46).
- Suppose an experiment were conducted on the stretching of a spring as a function of the force applied to the spring yielding the data in the following table Time (s) Position (m) 0.0 0.0 2.0 1.4 4.0 2.8 6.0 4.2 8.0 5.6 10.0 7.0 12.0 8.4 plot a graph of Position vs. Time, then draw the theoretical curve, Draw the best straight line you can through the origin and the plotted points. Try to leave about as many points above and below the line. This is the line of best fit. Find the slope of the best fit line on your graph. Calculate the uncertainty of your line of best fit. Statistically, it is accepted to subtract the slope of the MAX line and the slope of the MIN line and divide by 2. This will give the uncertainty of the slope of the line of best fit.One can fit a curve y=f(x) to data points(x1,y1), (x2,y2),.....,(xN,yN) by minimizing the sum of the squared errors:Find the normal lines to the curve xy + 2x - y = 0 that are parallel to the line 2x + y = 0.
- find the average rate of change of the function over the given interval y= 3/x-2 , [4,7]A contractor is planning to bid for a job of filling potholes on a given stretch of a high way. Before approaching for the bid, he decided to have an idea about the road from government agencies. Three departments public works (PW), transport (T) and traffic (Tf),as usual reported, three different average number of potholes in a one KM stretch of the high way. The constant rate of number of potholes per one KM stretch of the high way are 30, 35 and 40 respectively from PW, T and Tf. The contractor believes information from Transport department is more reliable than the other two. The chance that PW will be considered is 1/4, T will be considered is 1/2 and Tf will be considered is 1/4, by the contractor for drawing conclusion. What is the probability of finding exactly three potholes in a randomly selected 100 meter stretch?The equation of line normal to f(x) = (x +4)1/2 at Q (0,3) is?
- Let C denote the curve x2/3 +y2/3 = 1. Let P denote a point on the curve C in the first quadrant. Let L denote the normal line to the curve C at the point P. If L passes through the point (1/2,0) find the gradient of the line L. Give your answer correct to two decimal places.A chemical production plant makes a particular chemical that is produced by mixing equal amounts of three liquids at an average flow rate of 20 litre/min. The first and second liquids are added at a rate of 14 litre/min and 15 litre/min respectively. a. At what rate does the third liquid need to be added to ensure the target average flow rate? b. After the mixture is ready, the final product is poured into industrial containers at a flow rate of 5 litre/min. What is the average rate of flow for the entire process of mixing the liquids and packaging the final product?Suppose ƒ is differentiable on (- ∞, ∞), ƒ(1) = 2, and ƒ'(1) = 3.Find the linear approximation to ƒ at x = 1 and use it to approximate ƒ(1.1).