Find the centroid (ĩ, g) of the triangle with vertices at (0, 0), (10, 0), and (0, 9).

Q: Compute the new position of the square [A(19,19), B(29,19), C(29,29), D(19,29)] after its rotation…

A: ABCD is a square , we need to rotate it clockwise along with centroid.

Q: Find an equation of the plane. The plane through the point (1, 7, 2) and with normal vector 4i + j –…

A: Given:   Point : ( 1 , 7 , 2)  Normal vector : 4i + j - k

Q: Find the centroid of the “triangular” region bounded by the lines x = 2, y = 2 and the hyperbola xy…

A:

Q: Find the scalar equation of the plane that contains (1,1,1), (3,-1,5), and (4,2,-2). -2x1 + 9x2 + x3…

A: Equation of the plane, passing through three points

Q: write the equation of the plane with normal vector n passing through the given point in the scalar…

A: We have, Equation of plane through P0 =(x0, y0, z0) with normal vector n = <a, b, c> Vector…

Q: Explain how the Symmetry Principle is used to conclude that the centroid of a rectangle is the…

A: We already know that a rectangle has two lines of symmetry in which one line of symmetry is parallel…

Q: Find the coordinates of the centroid of APQR with vertices P(-2,5) , Q(4,1) , and R(-2,- 3). The…

A: Explanation of the answer is as follows

Q: Determine the x-component (m) of the centroid of the given figure if the cut portion is a semicircle…

A: Given, a=39 m, b=16 m and c=2 m To find the x-component of the centroid of the given figure.

Q: y=x¯, y= 2x

A: We can find the centroid using the required formula as below

Q: Find the centroid (x¯,y¯) of the triangle with vertices at (0,0), (6,0), and (0,1).

A:

Q: 2(a) Explain centroid of a triangle and rectangle with sketch.

A:

Q: Find the centroid (x, y) of the triangle with vertices at (0, 0), (10, 0), and (0, 2). 18 15 X=

A: Consider a triangle with vertices at (0,0),(10,0) and (0,2)

Q: Find a vector function that represents the curve of intersection between the paraboloid 2 z = 4x² +…

A:

Q: Find the centroid of the shape with endpoints (0,0),(0,4),(-2,4).(-2,6),(2,6),(2,3),(4,3) and (4,0)…

A:

Q: Use Exercise 22 to find the centroid of the triangle with vertices (0,0), (a, 0) and (a, b) where…

A: To find the centroid we add the x coordinates and the y coordinates respectively and then divide by…

Q: Find the centroid

A: Given,            The vertices of the triangle are 0,0,1,0 and 0,7.To find : The centroid x¯,y¯ of…

Q: Z is the centroid of AUVW. What is UY if UZ = 8? O A. 4 о с. 6

A:

Q: Find an equation of the plane. The plane through the point (2, 3, 6) and with normal vector 8i + j…

A: We will solve the problem.

Q: 3

A:

Q: Find an equation of the plane. The plane through the point (2, 9, 6) and with normal vector 7i + j –…

A: Find an equation of the plane

Q: Find the centroid of the region in the polar coordinate plane defined by the inequalities 0<=…

A:

Q: 6. For a plane with a normal of ñ = [1,2,-9] and containing a point P (3,-4, 0), write the scalar…

A: Given: Normal of the plane π is given by, n→=i→ + 2j→-9k→ Point P on the plane is P3,-4,0 To find…

Q: Find the centroid of a thin, flat plate covering the region enclosed by the parabola y2 = x and the…

A: Given information:

Q: 1 2.5" y 3" 6 -Х

A: Given data:-

Q: The vertices of AJKL are J(-3, 4), K(3, 0), and L(-5, -4). The equation of the median JLis y = 0.…

A:

Q: Find an scalar equation of the plane containing the line x = 2 – 4t, y = 4 – 5t and z = 5+t and the…

A:

Q: Find an equation of the plane. The plane through the point (6, 1, 5) and with normal vector 5i + j -…

A:

Q: ch is the centroid of the section reckoned lower left hand corner. 100 100 600 100 -500- Dim

A:

Q: Determine the scalar equation of the plane containing the point (-2, 9, 7) and 9. perpendicular to…

A:

Q: Write the scalar equation of the plane with normal vector = [1, 2, 1)] and passing through the point…

A: here normal vector is  and the given point is

Q: Find the centroid of the surface cut from the cylinder y2 + z2 = 9, z>= 0, by the planes x = 0…

A:

Q: Determine the centroid of the following Fig from X and Y axes. Y, 30 centT1 2 CentQ1 -4 -3 -2 -1 1 2…

A:

Q: Find an equation of the plane. The plane through the point (9, 3, 4) and with normal vector 8i + j…

A: To find- equation of  the plane.

Q: Write the equation of the plane with normal vector n = 4k passing through the point (7, 2, 5) in the…

A: The equation of plane with normal vector (a,b,c) passing through the point p0 =(x0 ,y0 ,z0 ) is…

Q: Find the centroid (¯x,¯y) of the triangle with vertices at (0,0)(1,0) and (0,5) x¯=    y¯=

A: Answer is given in next step.

Q: Find the orthogonal trajectories of the conicoid (x + y)z = 1 of the conics in which it is cut by…

A: Given:The equation of conicoid is (x+y)z=1The system of the plane is x-y+z=K, where k is…

Q: Find the moments and center of mass of the system of objects thathave masses 3, 4, and 8 at the…

A: We use the following equations to find the moments of the system of the given objects: Here mi are…

Q: Find the centroid of the triangle formed by joining the points A (3, 2), B (-1, 4), and C (5, -3).…

A: Explained below

Q: Find the centroid of a thin, flat plate covering the “triangular” region in the first quadrant…

A: Consider the given curve.

Q: Determine the scalar equation of the plane that passes through (5, -5, 5) and is perpendicular to…

A: Here we will find the required equation of the plane,

Q: Find the centroid of a thin, flat plate covering the region enclosed by the x-axis, the lines x = 2…

A: Given information:

Q: Determine the coordinates of the centroid of the shaded area. y 25 E 50 60 25 60 70 50

A:

Q: The centroid of a triangle lies at the intersection of the triangle's medians, because it lies…

A:

Q: Write the equation of the plane with normal vector n = (1, 3, 4) passing through the point (3, -1,…

A:

Q: Find the scalar product of x and y x =(-1, 0, 2) and y =(-7, 7, 3)

A:

Q: Find the centroid (, j) of the triangle with vertices at (0, 0), (8, 0), and (0, 9). x=

A:

Q: perpendicular

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Q: 4. Find the centroid of a thin flat plate covering the region enclosed by the parabolas y = 2r and y…

A: The given problem is to find the centroid of the thin flat plate covering the region enclosed by…