Consider the line x (1,3,2) + t(-1,5,-2) Decide which of the following points lie on the...
2. Consider the line (t) = (4t + 1,3,2-t) and the ellipsoid + + z2 = 1. What is the distance from the point (-3,3,3) on the line to the point where the line intersects the ellipsoid? a) 8/5 b) (2+ 89)/10 c) (2 - 89)/10 d) 62/V10 e) It makes no sense, the line does not intersect the ellipsoid. 3. Suppose f(x,y) is a function such that f.(0,1) = -3 and f(0, 1) = 8. What is the rate...
Question 8: [20pt total] Consider the line (1, -3, -1) + t(1,3,2). Q8)a) [12pt] Complete the table below by calculating the relevant points on the line and their central projections onto the plane x = 2 (the first one is done for you). t Point on line Central projection onto r = 2 t=0 (1, -3, -1) +0(1,3,2) = (1, -3, -1) (2, -6, -2) t=1 t = 10 t = 100 Q8)b) (5pt] Determine vanishing point of the line...
Which one of the following is the vector from the point with coordinates (1,5, 2, 3) to the point with coordinates (4,1,0, 3)? 0 (-3,4,2,0) O (3,-4, -2,0) (3, 4,2,0) O (5,6,2,6)
Determine whether or not the d and select the reason why or why not. x 3 57 Answer 2 Points First, decide whether the distribution is a discrete probability distribution, then select the reason for Decide Nex Prev O Yes No Reason Since the probabilities lie inclusively between 0 and I and the sum of the probabilities is equal to 1 Since at least one of the probability values is greater than I or less than 0. Since the sum...
4. [3/8 Points) DETAILS PREVIOUS ANSWERS SCALCCC4 9.5.013. Consider the line that passes through the point and is parallel to the given vector. (4, -3,6) < 1, 2, -3> (a) Find symmetric equations for the line. 2-6 -(x-4)= 2 3 y +3 (b) Find the points in which the line intersects the coordinate planes. (5 X IX 0) (0,9 X -6 (4 x 0, 4 X) 1 Consider the line that passes through the point and is perpendicular to the...
y(m) 1. (10 points) The temperature of a plate in the ry-plane is given by 3 48 2 T(x, y) x2 2y2 2 1 T is in degrees Celsius (°C) and x, y are in meters (m). A contour plot of T(x, y) is shown at right. -3 -2 4 3 4 (a) At the point (-2,1) draw and label a vector in the direction 6 of VT(-2, 1 8 4 (b) At (-2, 1) draw and label both vectors...
help a31. 5 marks Consider the following data: x0.45 0.68 1.04 1.21 1.52 y0.12 0.64 3.51 6.43 16.00 The points on the plot of log,o(x) against logo(y) lie on a straight line (you may graph is not required). Express y as a function of x. a31. 5 marks Consider the following data: x0.45 0.68 1.04 1.21 1.52 y0.12 0.64 3.51 6.43 16.00 The points on the plot of log,o(x) against logo(y) lie on a straight line (you may graph is...
Question 3: [10pt total] Consider the line in 3D space that goes through the points (2,5,-4) and (2,8,0). Q3)a) [5pt] Calculate a parametrization of the line. Parametrization of the line: Q3)b) (5pt] This line lies on a plane which is perpendicular to a coordinate axis: what equation describes that plane? Equation of the plane:
(2 points) Find the least-squares regression line y = bo +b x through the points (-2,0), (2,9), (6, 13), (8, 20), (10,27). For what value of x is 9 = 0?
Additional Problems: (HINT: It suffices to consider Just what happens (DX c A. Show by example that (a x b xc* a with i, j and k:) B. Find a vector which is perpendicular to every vector parallel to the plane z+y 0. C. Find the line which is the intersection of the planes x + y 0 and 3y-z = 0. D. Explain why the vectors in the following form describe a plane (where both t and s are...