2. Locate the centroid (x, y)of the following areas: b) %D For Problem 2b
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- Compute by hand the natural cubic spline for the data points (2,0), (1, 1), (0, 0).Evaluate Ic1² (2x - y) dx + (x + 7y) dy. C: x-axis from (0, 0) to (0, -7) and (0, -7) to (3, -7)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 <∞0
- 5. The coordinate of the point of the corners of a geometric figure are (4,0), (4,4), (10,8), (12,4) and (12,0). Locate the distance of the centroid from the origin with respect to y-axis.Find the centroid of the triangle with vertices (−2, −2), (4, 1) and (4, 4).Match the graph of the function z = 2- (** +y*) (x +y) to the system of the level curves. Which of the following level curves matches the given surface qraph? O A. OB. OC.
- 6. A flying robot is programed to follow the following three-dimensional position function while navigating an open space with no wind. The displacements in x, y, and z are measured in meters and t in seconds. x(t) = 0.0560t* – 1.200t² + 2.300t + 0.3400 y(t) = 0.6700t3 – 1.570t² z(t) = 0.2200t³ (a) At t = 1.44 s, what angle does the robot's velocity vector, v, make with its acceleration vector, å? Os1.1 Determine the y coordinate of centroid of the line in the shape of parabola as shown. 1.2 Determine the x coordinate of centroid of the line in the shape of parabola as shown.8. Find the points on the surface z² = xy+1 that are closest to the origin using LaGrange multipliers5. The equation of the circle whose center is the centroid of the triangle with venices (-72 (4,-3) and (6, -5) and passes through (4,2) is ....4 VectorProduct 10.4: Problem 7 Find the volume of the parallelopiped with adjacent edges PQ, PR, PS where P(-2, -1, -3), Q(0, 2, 0), R(-3, -2, -4), S(4, -3, -1).15. Integrate G(x, y, z) = z – x over the portion of the graph of z = x + y² above the triangle in the xy-plane having vertices (0, 0, 0), (1, 1, 0), and (0, 1, 0). (See accompanying figure.) (1, 1, 2) z = x + y? (0, 1, 1) (0, 0, 0), (0, 1, 0) х (1, 1, 0)SEE MORE QUESTIONS