Verify that if each x; is multiplied by a positive constant c and each y, is...
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right strophold has equation y--x2, with c a positive constant. strophoid with c 4 is graphed to the right. Use polar coordinates to show that the area of the loop is 2 -2 Parametrize the strophoid, letting t be the slope of the line segment connecting a given point on the curve and the origin. In other words, let y -tx, substitute into the equation of the strophoid, and write x and...
9. Consider the utility maximization problem max x + y s.t. px + y =m, where the constants p, 9, and m are positive, and the constant a € (0,1). (a) Find the demand functions, x* (p, m) and y* (p, m). (b) Find the partial derivatives of the demand functions w.r.t. p and m, and check their signs. (c) How does the optimal expenditure on the x good vary with p?8 (d) Put a = 1/2. What are the...
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(a) If a constant c is added to each x, in a sample, yielding y, -x+c, how does the sample mean of the ys relate to the mean of the x,s? lf a constant c is added to each Х, in a sample, yielding y'-x,+c,how does the medan creers relate to the median of terp ian of(C the median of xnc (b) reach x, is multiplied by a constant c, yielding y-cz, how does...
Find fY(y) from the domain:
Consider the domain D={(x,y): 0 < x < 1,-x < y < x} and let fix, y)=cx,where c is a constant. 1.1 (4.6 marks) To start with, we wish you to determine c such that f(x, y) a joint density of random vector (X, Y) that takes values on D. order to do that, you must first calculate fix, y) dA where dA is an area element of D, and then deduce c Hence you...
First, verify that y(x) satisfies the given differential equation. Then, determine a value of the constant C so that y(x) satisfies the given initial condition. Use a computer or graphing calculator to sketch several typical solutions of the given differential equation, and highlight the one that satisfies the given initial condition. y' =y+3; y(x) = CeX-3; y(0) = 8 What step should you take to verify that the function is a solution to the given differential equation? O A. Differentiate...
Two positive charges each of charge q are fixed on the y-axis, one at y = d and the other at y = -d as in the figure shown below. A third positive charge 27 located on the x-axis at x = 2d is released from rest. 9 + 29 d 24 +-* (a) Find a symbolic expression for the total electric potential due to the first two charges at the location of the charge 2q. (Use any variable or...
By 5. (a) Verify that y = {24 sin x is a solution to the differential equation dx2 dy + 5y = 0. dc [10 marks) (b) Differentiate the following functions with respect to c: (i) In(1 + sin? 2) (ii) * 2x3 - 4 - 8 dc. (c) Evaluate the integral / 272 * +432 – 4.7" [15 marks] [25 marks] 6. (a) let f: R+R be a function defined by f(x) 3 + 4 if : 51 ax+b...
random vibrations
Problem 1 Two random variables x and y have the joint probability density function where c is a constant. Verify that x and y are statistically independent and find the value of c for plx, y) to be correctly normalized. Check that Elx) Elyl-0 and that Elx2] and Ely') are both infinite Problem 2. Each sample function x(t) of a random process x(t) is given by: where a, a2, wh, and w are constants but 61 and 62,...
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a) Verify that the function y = ?? + is a solution of the differential equation zy' +2y 4x? (x > 0). b) Find the value ofe for which the solution satisfies the initial condition (2) - 5. = Submit Question a) Verify that the function y=x? + с 2 is a solution of the differential equation ry' + 2y = 4x², (x > 0). b) Find the value of c for which the solution satisfies the initial...
4) Given the equation: y = 1.55 x +7 a) Find the slope of the line. b) Find the y-intercept. c) Find two points on the line where x = 3 and y = -7 5) Given the equation y = - 4x, +0.75x + 2 a) Find y on the line where xy = 9 and again where x2 = -6 b) Find the new value of y when x1 = 4 while X2 is held constant at -7....