In Problems 20 to 31, evaluate each
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- 5. Prove that the equation has no solution in an ordered integral domain.arrow_forward1. The components of V are given by the expressions u = x² + y²; U = -2ry Find the integral along the path s between the points (0, 0) and (1, 2) of Vds for the following three cases: (a) s is a straight line. (b) s is a parabola with its vertex at the origin and opening to the right. (c) s is a portion of the x axis and a straight line perpendicular to it.arrow_forwardC. Reduction OF Order and Variation oF Parame ters (o* +4) y- 1. tan 2xarrow_forward
- 4. Consider a square service region of unit area in which travel is right angle and directions of travel are parallel to the sides of the square. Let (X, Y₁) be the location of a mobile unit and (X₂, Y₂) the location of a demand for service. The travel distance is D =Dx + Dy where Dx = |X₁ - X₂ and Dy = |Y₁ — Y2\. Assume that the two locations are independent and uniformly distributed over the square. a. Show that the joint pdf for Dx and Dy is (4(1-x)(1-y), fpx.D¸y (x, y) = {4(1 – b. Define Ryx = D/Dr. Show that the pdf of Ryx is 2 3 fryx (r) = . 2 3r² 1 r, 3 1 3r3' 0, 0≤x≤ 1,0 ≤ y ≤ 1 otherwise 0 ≤r≤1 1 ≤r <∞0arrow_forward3. [2sec (w) - 8csc(w)cot(w) dw from w = л/6 to w = л/3arrow_forward3.Find [, L (3x² + y)dydxarrow_forward
- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,