Please help!! Need solutions to calculus problems. Thank you.

LAB #6 I. Partial Fractions, Determinants, Cramer's Rule: (sections 7.4, 8.4, 8.5) 4383: 3816 1. Decom pose into partial fractions: 2. Determinants. Systems 12.r + 7 y = 29 a). Employ an appropriate cofactor expansion 1;), Solve to evaluate the determinant of matrix A 3): + 145' = '13 below: I 3 1 1 0 71 7 by Cramer's Flule. A: LuvD Lo-IUIN UNA-D II. 3D Rectangular Coordinate System: (section 11.1) 3. Piot the point (2. 3. 4) in the rectangular coordinate system with perspective box . 4. Find the center and radius of the sphere 4x2 + 45:2 + 422 4x 32y + 82 + 33 = 0: III. 2-D Vectors: (sections 6.3, 6.4) 5. At what acute angle from the horizontal did a boy pull a dog in a wagon if he expended 2650 ft-lbs of energy exerting a constant force of 38.5 lbs on the wagon throughout the entire distance of 118 ft? 6. The tension force F on a chain necessary to keep a 4650-lb truck from rolling down the incline is 1845 lbs. What is a). the angle of elevation of the ramp (i.e.. nd 9 in degrees). and what is b). the normal force of the truck on the ramp? N IV. 3-D Vectors: (section 11.2) 7. The lights in an auditorium are 24-lb discs of diameter 32 inches. Each disc is supported by three equally-spaced cables that are 40 inches long. Use vectors to calculate the tension T in each cable. T V. Vector Cross Product: (section 11.3) 8. Use vectors to calculate the area of the triangle with designated vertices. (0.10.6) (-1.8,21 (8.11.4) 9. The wrench and the applied force are in the same plane. 2 Find: a). the torque vector and b). the magnitude of the 4 torque on the bolt by the wrench if the origin is set at the center of the bolt as in the gure; also, c). describe the \\ . 23 lb direction of motion of the bolt relative to the page. VI. Lines and Planes: (section 11.4) 10. Find parametric equations for the line passing through the point (4.7,6) and orthogonal to the plane 2x 3y + z = 5 . 11. Determine the general equation of the plane with integer coefficients defined by the two intersectinglines L1: x=t.y=2t.z=3+2t and L2: x=43s,y=-1+25,z=2+35