A line intersects the xy plane at an x– intercept of N and a y intercept of F. Determine the volum of the solid formed by the line and coordinate axes if the axis of rotation is the x- axis.

Q: Find the plane tangent to the surface z=x x+ y° at the point (3,4,25). a. 6x+8y-z=25 O b. 6x-8y-z=25…

A: As we know that; The equation of the tangent plane: nxx-x0+nyy-y0+nzz-z0=0 And The normal vector at…

Q: find a parametrization of the surface. 1.The surface cut from the parabolic cylinder y = x2 by the…

A:

Q: Find the area of the surface 2x^(3/2) + 2y^(3/2) - 3z = 0 above the square R: 0<= x<= 1,…

A: find z.

Q: find a parametrization of the surface Parabolic cylinder between planes The surface cut from…

A: To find a parametrization of the surface: Given that, Between the planes z=0 & z=3 Thus, 0≤z≤3…

Q: Integrate G(x, y, z) = xyz over the surface of the cube cut from the first octant by the planes x =…

A: Here, the surface is in the first octant. Therefore, the integration is

Q: Find the highest and lowest point of the surface z2 = x2 + y2 ,on the plane 4x – 3y + 8z = 10 %3D…

A:

Q: The solid region bounded on the sides by the paraboloid z = 4-x-y, above by the plane z= 3, and…

A: The Equation of paraboloid: z = 4-x2-y2The equation of upper plane: z = 3The equation of lower…

Q: Find the average height of the hemispherical surface z = sqrt(a2 - x2 - y2 )above the disk x2 + y2…

A:

Q: Find the area of the surface. The part of the plane z = 9 + 2x + 5y that lies above the rectangle…

A: Given: The part of the plane z=9+2x+5y that lies above the rectangle0, 9×1, 6. To Find: Area of…

Q: find a parametrization of the surface. The paraboloid z = x2 + y2, z<=4 The paraboloid z = 9 - x2…

A:

Q: Find the area of the surface. The part of the plane  z = 3 + 2x + 5y  that lies above the rectangle…

A:

Q: Find an equation for the plane that is tangent to the surface z = In (x³ + y²) at the point…

A: Given:   A surface   z = ln x3 + y2   To Find :  An equation  for the plane that is tangent to the…

Q: Find the area of the surface. The part of the paraboloid z = 1 − x2 − y2 that lies above the plane…

A: Given that the part of the parabola z=1-x2 -y2 that lies above the plane z= -6 . Here we have to…

Q: Find an equation for the plane that is tangent to the surface z = In (x´ +y) at the point P(1,0,0).…

A:

Q: Find the area of the surface. The part of the hyperbolic paraboloid  z = y2 − x2  that lies between…

A: In the question we have to find the value of area enclosed by the function of given figures.

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

A: Given information:

Q: What is the center of gravity of the solid formed when the plane region bounded by y^2 = 4x in the…

A:

Q: Find an equation of the surface consisting of all points P(x, y, z) that are twice as far from the…

A: Let d1 be the distance from the point 0,0,1 to the point Px,y,z and d2 be the distance from the…

Q: state the type of the quadric surface and describe the trace obtained by intersecting with the given…

A: The given quadratic surface is  x2+y42+z2=1 , y=0

Q: Find an equation for the plane that is tangent to the surface z= In (x²+y^) at the point P(0,1,0).…

A:

Q: Sketch the curve of intersection of the surfaces. The paraboloids z = x² + y² and z = 25 – x – y².…

A: Given that: z=x2+y2      ......(1)z=25-x2-y2      ......(2)

Q: Find the centroid of a thin, flat plate covering the region enclosed by the parabolas y = 2x2 and y…

A:

Q: the trace of the surface in the plane x=1?

A:

Q: Find an equation for the plane that is tangent to the surface z= In (x* +y) at the point P(1,0,0).…

A: The solution for the above question is as shown below.

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

A:

Q: Find all points on the surface xy - z2 = 1 which are closest to that origin. Let x,y,z be the…

A:

Q: Find the area of the surface. The part of the paraboloid z = 1 – x2 - y? that lies above the plane z…

A:

Q: Find the area of the surface. The part of the plane z = 7 + 5x + 2y that lies above the rectangle…

A: The given equation is, z=7+5x+2y The partial derivatives are, fx=5fy=2

Q: Find the surface area of the portion of the cone x² + y² = z² above the region inside the…

A:

Q: Find the surface area of the ellipse that lies on the plane z=11-3x+2y and inside the cylinder…

A: The plane z=11-3x+2y and cylinder is x2+y2=9. Obtain the partial derivatives of z=11-3x+2y:…

Q: (b) Integrate (x, y,z)=(y+z)+1 the paraboloid 4x - y-z -0 by the plane x 1. over the surface cut…

A:

Q: Find the centroid of the polyhedron with four triangular faces in the first octant that is bounded…

A: The region is bounded by the three coordinate planes and the plane x+y+z=1. Thus, the region can be…

Q: Find %3D as if F(x, y, z) = 2xi+2yj+2zk and S is the part of the paraboloid z = 4-x-y lying above…

A:

Q: Find an equation for the plane that is tangent to the surface z = vy-x at the point (1, 2, 1).…

A: To find an equation for the plane that is tangent to the surface at the given point (1,2 1).

Q: Find the centroid of the lamina cut by the parabolas y2=x and y=x2.

A: For the clear understanding of curve we have the following graph which is shown below as:

Q: Find an equation for the plane that is tangent to the surface z = In (x² + y) at the point P(0,1,0).…

A:

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

A: Consider the given curve.

Q: Find the area of the surface. The part of the plane z = 4 + 3x + 2y that lies above the rectangle…

A:

Q: Find the area of the finite part of the paraboloid  y = x2 + z2 cut off by the plane y = 4.

A: To find the area of the finite paraboloid y=x2+z2 cutt off by 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: Find parametrizations The portion of the paraboloid y = 2(x2 + z2 ), y<=2, that lies above the…

A:

Q: Find the area of the surface. The part of the plane z = 7+ 2x + 3y that lies above the rectangle [0,…

A: We have to find the area of the surface of the given problem.

Q: y. y:3x- 31 to

A: Consider the figure, which is given below

Q: Find the plane tangent to the surface z=x+ y at the point (3,4,25). a. 6x+8y-z=25 b. 6x-8y-z=25 c.…

A: We have to find the plane tangent for the given surface

Q: The surface that is linear with the three variables, x, y, and z is called cylinder plane sphere O…

A:

Q: Find the surface area of the part of the plane z = 4 + 6x + 2y that lies above the rectangle [1, 4]…

A:

Q: Find the centroid when revolved in y-axis: y³ = x² ; y = 4.

A: As per the question we are given a solid of revolution obtained by rotating the area between y3 = x2…

Q: Integrate G(x, y, z) = x + y + z over the surface of the cube cut from the first octant by the…

A: Definition used:

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…

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.