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- : A parametric cubic curve passes through the points (0,1), (2.5), (3,5) (5,-3) which are parameterized at t=0.1, 0.3, 0.6 and 0.9 , respectively. Determine the geometric coefficient matrix and the slope of the curve when t-0.5.The image of (-2 , 5) under reflection y = -x followed by translation with translation vector (-3 , 1) is?What kind of transformation results in applying the rule (x, y) → (x + 5, y)?
- The points on the surface x2−2y2−3z2 = 33 at which the tangent plane is parallel to the 8x+4y+6z=5 plane are:a. (1,0,1) y (2,3,1)b. (-4√3, √3, -√3) and (-4√3, -√3, √3) c. (4√3, -√3, -√3) and (-4√3, √3, √3) d. (-4√3, -√3, -√3) and (-4√3, -√3, √3)Find the distance between u = (-1,2,5) and v = (3,0,1)A point moves so that sum of the squares of its distances from the vertices of a triangle is always constant. Prove that the locus of the moving point is a circle whose centre is the centroid of the given triangle.
- 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.Find parametric equations of the line through the point (5, 0,−2) that is parallel to the planes x −4y + 2z = 0and 2x + 3y −z +1 = 0.Find the equation of the plane in xyz-space through the point P=(3,3,2) and perpendicular to the vector n=(−2,1,5).