Masses of 3 kg, 7 kg and 1 kg are located at points with co-ordinates (3,10), (6,6) and (6,4) respectively Find the co-ordinates of their Centre of Mass,(,y), correct to one decimal place.

Q: A force F = -3i +j+6k acts through the point (5,-2,-1). Find its moment about the point (3,0,2).

A: Moment of force about the point is given by cross product of position vector r about a point and…

Q: Find an equation of the tangent plane to the surface at the given point. 4x2 + 2y? + 4z2 22, P = (2,…

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Q: 2. Find the coordinate of the points on the cardioid r=1- cose at which there is a horizontal…

A: We are given the polar curve: r = 1- cosθ use formula:         x=r cosθy=r sinθ then,  dxdθ=-sinθ+2…

Q: A bridge is built in the shape of a semielliptical arch. The bridge has a span of 140 feet and a…

A: equation of the ellipse is x2/a2 + y2/b2 = 1

Q: Masses of 3 kg, 1 kg and 5 kg are located at points with co-ordinates (1,2). respectively.

A: Please refer to the image below

Q: Decompose v into its vertical and horizontal components.

A: Decompose vector v in vertical and horizontal components.

Q: Find all points of intersection of the graphs of the two equations   y = 1 − x2, y = x2 − 1 , (a)…

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Q: 1. A line, passing through point (6, 3, 2) and is perpendicular to the yz-plane. Find a point on th

A: We have to find point.

Q: 11) Find the distance between point A(-3, 1,1) and the line of symmetric equations x = -y = -z.

A: This question is related to coordinate geometry, We will solve it using given information.

Q: (A) Find plane equation that passes through the point (7,3,-5) and contains unit tangent vectors of…

A: To find the equation of a plane containing two lines and passing through a point (a, b, c) is given…

Q: Determine the location of a point (x, y, z) that satisfies the condition y < 0

A: With the given condition there are 4 scenarios 1) x>0,y<0,z>0 2) x<0,y<0,z<0 3)…

Q: A robot begins moving on a linear path at (2, 1). When it reaches (5, 2) , the robot turns 90°…

A: The robot begins moving at (2,1) and reaches at (5, 2) taking a linear path. So, the equation of a…

Q: The plane through the point (3,-1,2) can perpendicular to the a) x-axis b) y-axis c) z-axis d) non d…

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Q: Find an equation of the tangent plane to the surface at the given point. 6x² + 2y² + 4z² = 30, P=…

A: NOTE: Refresh your page if you can't see any equations. . the function f is

Q: Jategrate h (x.y) = (x+y)i+(-x)j over the closed curve that begins at (-1, 0), goes along the x-axis…

A: we will use green theorem here to solve this question

Q: Find a parametrization of the curve. The vertical line passing through the point (3, 2, 0)

A: Consider the given point  3 , 2 , 0

Q: Find the shortest distance from the point (1, 5, -5) to the plane 2x + 9y - 3z = 6, using two…

A: Given point is 1,5,-5 and plane is 2x+9y-3z=6

Q: PCt) =<5-t, 4t -3,3t7 uking are length Reparami tize parameter from the point (4,113).

A:

Q: Find parametric equations for the tangent line to the curve of intersection of the cylinders x = 74…

A: given curves x2+z2=74 , y2+z2=74 , point 5,-5,7  to find parametric equations for the tangent line…

Q: 3. Calculate the centroid of the given illustration below. y-axis 7.5ft- 4ft 2ft 5ft- х-ахis 2ft

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Q: A robot begins moving on a linear path at (2,1). When it reaches (5,2), the robot turns 90°…

A: Linear equation

Q: find the centroid of the thin plate bounded by thegraphs of the given functions. Use Equations (6)…

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Q: Find Vector, Parametric and Scalar equations for the line that passes through t -2,11) and (6,1).

A: Given: - The line that passes through the points -2,11and 6,1. To find: - The parametric equations…

Q: Determine the center and the radius: X2 + Y2 + 2X +10Y + 1 = 0 O (-1,-5) Radius 5 O (1,5) Radius 5 O…

A: Topic-circle

Q: Find the orthogonal trajectories of the family of ellipses with centers at (0, 0) and two vertices…

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Q: A robot begins moving on a linear path at (2,1). When it reaches (5,2), the robot turns 90°…

A: This is a problem related to linear coordinates. based on the diagram shown in solution we will…

Q: Derive the orthogonal trajectories of the family of hyperbolas ??=?.

A:

Q: . The distance of a point in the 3-D system from the origin a. is defined by the absolute value of…

A: Note: We will answer the first question only as the exact one is not specified. Please resubmit the…

Q: 1)If the 15 kilogram object is resting on a table tilted at 40 °. indicate the decomposition of the…

A: Consider the provided question,

Q: Find the equation of the plane tangent to the following surface at the given points (7,5, ln 36) and…

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Q: Li Syaoran is riding an airplane which departs from an airport located at (360, 0) miles in the…

A: The westward speed of the airplane = 480 miles/ hour The northward speed of the airplane = 120…

Q: A point moves so that sum of the squares of its distances from the vertices of a triangle is always…

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Q: Find the unit vectors that are parallel to the tangent line to the parabola y = x² at the point (5,…

A: Given: y=x2 at the point (5,25)

Q: Find the distance between the points (−2, 2), (4, −6) using (a) the Distance Formula and (b)…

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Q: Find the tangent plane to the equation z 2y cos(3r - 6y) at the point (6,3,6) %3D

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Q: 5. What are the coordinates of the centroid of triangle FGH: F(6,-1), G(12,4), H(15,-2)?

A: follow next step

Q: A quadrivector AH has components (1, 1, 1, 0, 1)' in the system S. Calculate the T components of AH…

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Q: Exer. 35-36: Find equations of the tangent line and normal line to the hyperbola at the point P. 3…

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Q: Find the point(s) of intersection of the curves r = 1 and r = 2 sin 0. ^(1.5)(1.플) 1, 27 3 В. 1, 1,…

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Q: Line t contains the points (1,1) and (-5,3). Plot a point other than point P with integral…

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Q: Find the centroid (, ) of the triangle with vertices at (0, 0), (10, 0), and (0, 2). 19 120 y=

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Q: Find an equation of the tangent plane to the surface at the given point. 4x2 + 2y? + 4z? = 22, P =…

A:

Q: Q2 / A man moved from the point (2, -2, 1) to the point (8, 3, 4). Express the displacement moved by…

A: The given point is                    P1 (2, -2, 1)  and  P2 (8, 3, 4) To find displacement in terms…

Q: Charlie and Alexandra are running around a circular track with radius 60 meters. Charlie started at…

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Q: Find the shortest distance from the point (2,0,–3) to the plane x + y + z = 1. . Use Lagrange…

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Q: of the solid in revolution as it axis and the function 2 – x) 0<x< 2

A: The given function is fx=x2-x,    0≤x≤2. Find the volume of the solid in revolution as it rotates…

Q: 3. Parametrize the circle of radius 5 having centre (8, –3) and hence find a tangent vector and the…

A: We have to find parametric equation, tangent vector and tangent line for the given circle.

Q: BThe distance from the point (-1, -2, 3) to the plane 2z = - 4x + 5 is [b] (input exact value in…

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Q: What coordinate system is suggested if the integrand of a tripleintegral involves x2 + y2?

A: Given: The integrand of a triple integral involves x2 + y2

Q: Find the centroid (ã, g) of the triangle with vertices at (0, 0), (5, 0), and (0, 9). y=

A: In the question it is asked to find centroid of the triangle with coordinates (0,0), (5,0) and…