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- The diagram shows a small block B, of mass 0.2kg, and a particle P, of mass 0.5kg, which are attached to the ends of a light inextensible string. The string is taut and passes over a small smooth pulley fixed at the intersection of a horizontal surface and an inclined plane.The block can move on the horizontal surface, which is rough. The particle can move on the inclined plane, which is smooth and which makes an angle of θ with the horizontal where tanθ = 3/4The system is released from rest. In the first 0.4 seconds of the motion P moves 0.3m downthe plane and B does not reach the pulley.(a) Find the tension in the string during the first 0.4 seconds of the motion.(b) Calculate the coefficient of friction between B and the horizontal surface.1)Let F be the vector 1/yi +1/xj let C be the curve xy=4 from P=(1,4) to Q=(4,1) 2) Evaluate integral_c Xdx _x^2dy from (-1,0) to (1,0) when C is A) The line segment a long the x-axis from (-1,0) to (1,0) B)The semidried y= srtroot 1-x^2 from (-1,0) to (1,0) C) The broken line from (-1,0)to (0,1) to (1,1) to (1,0)Compute the intersections of the curve xy = 1 and the lines x +y = 5/2, x+y = 2, x+y = 0, x=0 , x=1 in the affine space and then in the projective space by using homogeneous coordinates. Complex solutions are valid. Please show your steps for both affine space and in project space. Box your final answer.
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- Suppose R3 has the Euclidean inner product. Apply the Cauchy Schwarz inequality to the vectors u = (a, b) and v = (cos θ, sin θ) to show that | a cos θ + b sin θ |2 ≤a2 + b2. Note: Do not skip any step to arrive at the result, apply the Cauchy Schwarz inequality to arrive at the result (In the image the enunicoado is better seen)Represent the line segment from P(−2, −3, 8), Q(5, 1, −2) by a vector-valued function and by a set of parametric equations.A plane π is said to be tangent to a spherical surface with center C and radius r if the distance from C to π is equal to r and, where P is the point of tangency, the vector CP is a vector normal to π. Check the alternative that contains the equation of the spherical surface with center C(2,4,5) and tangent to the plane π:x+2y−2z−2=0. Choose the correct alternative: a. x2−36x+y2−72y+z2−90z+72=0 b.9x2−36x+9y2−72y+9z2−90z+401=0 c.x2−36x+y2−72y+z2−90z+397=0 d.9x2−36x+9y2−72y+9z2−90z+72=0 e.9x2−36x+9y2−72y+9z2−90z+397=0
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