Find the average distance of a point in a disk of radius a to a fixed point on the boundary of the disk.

Q: Find the change in the lateral surface area of a right circular cone, with radius of base fixed as…

A: There is a right circular cone with base radius r and altitude height h.

Q: A stream line is a line that is everywhere tangent to the velocity filed 0 صواب ihi O

A: False

Q: Find the area of the circular washer with outerradius 2 and inner radius 1, using Fubini’s Theorem

A: Given Circle with radius ‘2’  Circle with radius ‘1’

Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r = 30,0 < 0 <…

A: Given, r=3θ,  0≤θ≤5.4

Q: A disk of radius 4 cm has density 14 g/cm? at its center, density 0 at its edge, and its density is…

A:

Q: Sketch the region enclosed by the following curve and find its area. x = y^4, y =√2 − x, y = 0

A:

Q: Give a parametric description for a cone with radius a and heighth, including the intervals for the…

A: We can parameterise the same as following: Assume s &amp; t as two parameters radius = a and height…

Q: Find the dimensions of the right circular cone of minimum volume V that can be circumscribed about a…

A:

Q: Find the exact area of the surface generated by revolving the curve over the given interval about…

A: Given data: The given expression for the curve is y=(2x-x2)1/2. The given limits of x are [a,…

Q: What is the area of the curved surface of a right circular cone of radius 3 and height 4?

A:

Q: Find the change in the lateral surface area of a right circular cone, with radius of base fixed as…

A: The lateral Surface area of a right circular cone is given as A =πrh2+r2        A2 =π2r2(h2+r2)…

Q: Find the area of the surface generated by revolving the curve y = sqrt(x2 + 2), 0…

A: find dy/dx and solve for ds.

Q: find the centroid of volume if the volum is equal to 7/15 π

A:

Q: Use spherical coordinates to compute the surface area of a sphereof radius R.

A: given,         a sphere of radius R

Q: Find the exact area of the surface obtained by rotating the given curve about the y-axis.

A: Given that      x(t)=3t-t3y(t)=3t2 Since, we are rotating about y-axis, the formula is:…

Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r = 30, 0 < 0…

A: According to the given information, it is required to find the area enclosed by the given curve.

Q: Find the centroid of the region cut from the first quadrant by the circle x2 + y2 = a2.

A:

Q: Determine the area of the surface generated by rotating around the "y" axis, the curve described by:

A: Here, the given parametric curve is: x=t33, y=t+1; 1≤t≤2⇒x'(t)=t2, y'(1)=1 Now, the surface area…

Q: The change in the relative configuration of point within a solid is called strain

A: Strain is a description of deformation in terms of relative displacement of particles in the body.

Q: Find the area of the portion of the plane in the first octant passing through the points (0,0,6),…

A: This question can be solved using the area of triangle in three dimensional geometry.

Q: Find an arc length parameterization of the circle in the plane z = 9 with radius 4 and center (1, 4,…

A: The parametrization of the circle in the plane z=9 is:                                   r(t)=⟨1, 4,…

Q: Find the area of the resulting surface.

A: Given that: The equation of the curve is y = 14 x2 - 12 ln ( x)    , 4≤ x ≤5 .

Q: Give an example of a plate such that its center of mass does not occur at any point on the plate.

A:

Q: Find the exact area of the surface obtained by rotating the given curve about the x-axis.

A: To find the surface area of obtained by rotating the curve about x axis.   If the curve y=f(x),…

Q: Find the average Vvalue of flxiy) =xy over the part of the whit disk in the first quadrant.

A: Given problem is :

Q: Find the Area of the Surface obtained by rotating the curve about the x-axis y = cosh x, 0≤x≤1

A:

Q: Evaluate the surface integral

A: Given,                ∫∫S8z2dS Where S is the boundary of the cube C=-1, 1×-1, 1×-1, 1.

Q: Find the area of the surface generated by revolving the curve about each given axis. x = St, y= 9t,…

A: We have to find the surface area.

Q: Find the area of the surface obtained by rotating the region formed by 1 In x, 1<x < 2, - 2

A:

Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r = 10, 0 < 0…

A:

Q: Find the centroid of the region cut from the first quadrant by the circle x +y =

A: Given x2 + y2 = 81 y=81-x2 Area of Quadrant(A) = πr24                              A  = 81π4

Q: Find the centroid of the region cut from the first quadrant by the circle x +y = 1.

A:

Q: Find the area of the surface generated by revolving the curve about each given axis. x = 8t, y - 6t…

A: Given that, x = 8t y = 6t + 1 0≤t≤1 We have to find the area of surface generated by revolving the…

Q: Find the length of the subtangent and sub-normal at a point of the curve X y= bsin a

A:

Q: Find the average distance from a point inside a solid ball of radius R to the center of the ball.

A: The average value of a function fx,y,z is davg=1V∫∫∫f(x,y,z) dV. Here the function is the distance…

Q: A right cylinder of radius r is inscribed in a hollow sphere of fixed radius a. The

A: Given, a right cylinder of radius 'r', is inscribed in a hollow sphere of fixed radius 'a'. The…

Q: Calculate the area of the surface of rotation created by rotating the curved segment about the…

A:

Q: A disk of radius 3 cm has density 6 g/cm? at its center, density 0 at its edge, and its density is a…

A: Given radius of disc r = 3 cm Density at center ρc = 6 g/cm2 Density at edge ρe = 0 given density is…

Q: Find the linear velocity of a point rotating at 30 revolutions per second on a circle of radius 6 cm

A:

Q: Find the Center of Mass of Lamina bounded bythe graphs

A: We have to find out the center of mass of given lamina bounded by x=y2,x=1 and ρ(x,y)=y2+x+1.

Q: Find the average distance from a point in a ball of radius to its center.

A:

Q: Find the radius of the outer disk when the region bounded by y = x^2 and y = 1 + x − x^2 is revolved…

A: We will find out the required value.

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis.

A:

Q: Find the average value of r over the solid sphere ρ ≤ a (spherical coordinates).

A:

Q: Sketch the region bounded by the given curves, then find its area. 1. у%3D х*, у%3D2х

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Evaluate the surface integral.

A:

Q: Find the center of mass of a thin plate of constant density δ covering the given regions. The…

A:

Q: A stream line is a line that is everywhere tangent to the velocity filed ylgn ihi

A: The statement is TRUE

Q: Find the average distance from a point P(x, v) in the first two quadrants of the disk x2 + v s25 to…

A: We have a given point P(x, y) and a disc   x2+y2≤25 We need to calculate the average distance from…