4. Consider the following curves: (i) y2 r-7x + 3 (ii) y2 7ax +9 (ii) y23-7a...
Q1. Consider the curve y2 = x3 + 3x + 5 mod 17. (i) (ii) (iii) (iv) (v) (vi) Confirm that it is an elliptic curve. Determine three points on the curve over real numbers Determine three points on the curve over integer numbers For one of the points P in (iii), find 2P (or double) For two of the points P and Q in (iii), find P+Q Find the bound for the number of points on this curve using...
PLEASE ANSWER ALL NUMBER 3 (Parts A-F) Consider the following list of properties 3. f(x)oo x-+1 ii) lim()2 iv) f(1)-3 v) lim f(x)-n x+1 For each of the following, decide if it is possible for a function to have the given set of properties. If so, sketch and label a possible graph for the function on the axis provided. If no such function is possible, explain why not. a) (i) and (i) b) (), (ii), and (iv) c) (i), (iii),...
Consider the following potential function and the graph of its equipotential curves to the right. Then answer parts a through d. phiφ(x,y)equals=2 e Superscript x minus y Consider the following potential function and the graph of its equipotential curves to the right. Then answer parts a through d. 4(x.y)=2*-y a. Find the associated gradient field F = V p. F=CD b. Show that the vector field is orthogonal to the curve at the point (1,1). What is the first step?...
1. Use the method of cylindrical shells to find the volume of the following solids rotation (i) Spin the region bound by y -Vx,y 0, x-1 around the y-axis; (ii) Twist the area bound by x -1+(y-2)2 andx- 2 about the x-axis; (iii) Rotate the region between y - x2 and y -6x-2x2 around the y-axis; (iv) Twirl the space between y V and x 2y about the line x 5 2. Use both methods discussed in class to compute...
just make circle questions which 2,(b) and 3,(i) thank you 2. (Polar Coordinates: Polar Plots). (a) Consider the curve given in polar coordinates (i) Use a scientific calculator to fill in the following table with the (approximations of) values of the function r(0) on π, π r(e) (the approximations of the values r(e) must be good to at least two decimal places). (i) Use the graph paper for the polar coordinate system (attached to the assignment sheet) to plot the...
3) Consider the region R bounded by y 9-x2,y = 0, and x 0 (in the first quadrant) (Note: you may use MATH 9 and your answers should be correct to 4 decimal places) c) Sketch the graph and find the volume of the solid obtained by rotating Rabout the line y = - 1 Vertical or Horizontal slicing? 1=S4y) dy ? V Slice is a Disk or a Washer? A or Arca of a slice A = Volume V...
Exercise 4. Density Curves a. In each row of this table, assume the distribution is normal. Knowing any two of the mean, standard deviation, Q1 or Q3 is enough to determine the other two. Complete the table by filling in numbers for 0-(V). (You may use pnorm and qnorm in Rand also use R as a calculator.) Mean Q. Q SD 5 10 (0) (ii) (1) (iv) 20 80 b. A study conducted by the Kaiser Foundation compared blood pressures...
Questions. Please show all work. 1. Consider the vector field F(x, y, z) (-y, x-z, 3x + z)and the surface S, which is the part of the sphere x2 + y2 + z2 = 25 above the plane z = 3. Let C be the boundary of S with counterclockwise orientation when looking down from the z-axis. Verify Stokes' Theorem as follows. (a) (i) Sketch the surface S and the curve C. Indicate the orientation of C (ii) Use the...
For Questions 1, consider the following classifications: Feasible Region I- Finite Line Segment II -Non-existent III - Polygon IV-Single Point V - Unbounded Optimal Solution A -Alternate Optima B-No feasible solution C- Unbounded D-Unique 1. Suppose an LP with 5 regular constraints (other than the non-negativity constraints) has "lr as its feasible region. If a new constraint is added, which of the following CANNOT be the type of the new optimal solution? a, A b. В с. С d. De,...
0 1 (c) Consider the matrix0 2 -2 k 3 i. Compute the determinant. ii. For what value(s) of k does A exist? iii. For what value(s) of k does the linear system A7 = 7 have nontrivial solutions? iv. For what value(s) of k does A have zero as an eigenvalue? v. For any vector be R*, find the value(s) of k for which the linear system A7 = b has a unique solution.