2. [8 points] a) What is the smallest degree of a polynomial that passes through all 5 of the poi...
4. Find the degree 3 polynomial y = ax + bx2 +er+d which passes through the following four points. (0.1), (1.-1). (2.-1). (3.7)
1. Determine the polynomial function whose graph passes through the points (0, 10), (1, 7), (3, -11), and (4, -14). Be sure to include a sketch of the polynomial functions, showing the points. Solve using the Gauss-Jordan method or Gaussian elimination with back substitution. Show the matrix and rovw operation used for each step. 2. The figure below shows the flow of traffic (in vehicles per hour) through a network of streets. 300 200 100 500 YA Y 600 400...
7. Find the polynomial of degree 4 through the points (1, 2), (-1,0), (2, 15), (0,1) and (-2, 11), and check that it works.
(5) Let Ф, : Z5[x] Zg denote the evaluation homomorphism at r Zg Find a nonzero polynomial of smallest degree which in kernel of all φ-for r 0,1,2,3,4 (5) Let Ф, : Z5[x] Zg denote the evaluation homomorphism at r Zg Find a nonzero polynomial of smallest degree which in kernel of all φ-for r 0,1,2,3,4
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...
(3 points) Find a formula for the polynomial of least degree through the points shown in the graph. f(x) = help (formulas) - - -2
(a) Find symmetric equations for the line that passes through the point (2, -2, 8) and is parallel to the vector (-1, 3,-4). -(x + 2) = 3(y-2) = -4(2 + 8). Ox+2-472.28 2-8 -4 -(x - 2) = 3(y + 2) = -4(2-8). *+2.1;2-28 (b) Find the points in which the required line in part (a) intersects the coordinate planes. point of intersection with xy-plane point of intersection with yz-plane point of intersection with xz plane
Problem 4: (a) (5 points) Find the equation for the line that passes through the points (-4,-2) and (8, 1). Write your equation in se form, slope-intercept form, or point- slope form. (Extra Credit: Write the equation for the line in all three forms) (b) (5 points) Graph the line. Problem 5: (10 points) Find the equation for the line passing through the point (3.2) and perpendicular to the line y = ',x + 7. The the line Problem 6:...
12. Given the data set: We want to find the interpolating polynomial of degree 2 through these points. a) Write the interpolating polynomial in Lagrange form b) Write the interpolating polynomial in Newton form.
Find the polynomial of degree 4 whose graph goes through the points (-3,-194), (-2,-36), (0, 10), (2, 16), and (3, -56) f(x) +10