wi the shope Find the mass of a spung of a conical helix řCt) = where ost 2T and s(xiy,2)= 2 gr/cm.

Q: Find the mass of a wire of density δ(x,y,z) = kz if it has the shape of the helix C parameterized by…

A:

Q: . Find the rate at which the volume increases when the radius is 30 cm. (Hint: Volume 4 of the…

A:

Q: Calculate the moments My and My and the center of mass of a lamina with the given density (p = 3)…

A:

Q: Calculate the moments M, and My and the center of mass (x, ỹ) of a lamina with the given density and…

A: The moments of the lamina can be calculated using the equation Mx=∬Ryρx,ydA and My=∬Rxρx,ydA. Now,…

Q: Find the center of mass of the lamina in the following figure if the circular portion of the lamina…

A: In the question it is asked to calculate the center of mass of the lamina given in question. Given:…

Q: Suppose that a curved lamina o with constant density 8(x, y, z) = 8o is the portion of the…

A: mass=∫∫∫δx,y,z dv

Q: Find the center of mass of the lamina that has the given shape and density. r = 3 + 3 cos(θ), y =…

A: First and second quadrants; means 0 to π Obtain the area: ∫0π3+cosθdθ=3θ+sinθ0π=3π Then, mass of the…

Q: B) Show that V=367 is the volume of a sphere of radius 3 by using spherical coordinates.

A:

Q: The composite body below is composed of several uniform, slender rods, as well as triangular and…

A: Consider the composite body whose areas is divided into 5 parts as below.

Q: Calculate the moments Mx and My and the center of mass of a lamina with the given density ane p = 7…

A:

Q: Verify the given moment(s) of inertia and find x and y. Assume that each lamina has a density of   =…

A:

Q: Find the centre of mass of the uniform lamina ABCDE shown below. E бст 30 A 10cm B The shape is…

A: Given that the shape is symmetric about the line though C. Thus, the center of mass lies on the line…

Q: rge grape is approximately cylindrical with a diameter of 2 centim ylindrical cork has a diameter of…

A: a) For grapes (Cylindrical) :-  diameter d=2cm radius r=d2=22=1 cm height h= 3cm mass of grapes = m=…

Q: What solid is formed when this net is folded? B D

A: there is no introduction for the above question.

Q: If R is revolved about the x-axis, find the center of mass of the solid generated. Please note that…

A:

Q: The surface area of a sphere increases at a rate of 64 m2/sec. Then the rate at which the radius…

A: Given rate of increase in the surface of sphere=64m2/sec And radius of sphere=3m Now we have to find…

Q: Find the mass of a thin wire in the shape of the quarter circle a² + y² = 9 in the first quadrant,…

A:

Q: The exterior of a cone consists of two parts: a circular base and a curved lateral surface. O True O…

A: Given:

Q: Find the mass of the sphere x2 + y2 + z2 = a2 where the density at any point is two times the…

A:

Q: Find the moment or center of mass of the wire, as indicated. 10) Find the moment about the x-axis of…

A:

Q: =) Given a lamina that occupies the region outside the circle r = 2 and inside the %3D cardioid r =…

A:

Q: V=$t re h for r (geometry, volume of a spherical tuumor).

A:

Q: Find the center of mass of a circular cone of regular steel of height (b)

A: It is given that a circular cone with height b and radius R

Q: Determine the coordinates of the mass center of the welded assembly of uniform slender rods made…

A: Given data, Let ρ = density per unit length

Q: a pluke is composed of hwo semi - cireles, y= = vi- x? and a y> Ju-x?. find the center of mass of…

A: Given the semicircles are  y=1-x2y=4-x2 For the first semicircle, y=1-x2y2=1-x2x2+y2=1 So the radius…

Q: A thin wire lies along the curve C:7(t) = vZti + v7tj + (4 – t²)k, 0 < t s 2. Find the wire's mass…

A: Given is c: r⇀(t)=2ti→+7tj→+(4-t2)k→…

Q: Calculate the moments Mx and  My and the center ofmass of a lamina with the given density and shape.

A: It is given that ρ=10

Q: Find the mass of the lamina in the shape of the portion of the plane with equation 4x + 8y + z = 8…

A: Surface integral

Q: The surface area of a sphere increases at a rate of 77 m2/sec. Then the rate at which the radius…

A:

Q: Calculate the moments Mx and My and the center of mass of a lamina with the given density and shape.…

A:

Q: Find the mass and center of mass of a wire in the shape of the helix x = t, y = 2 cos(t), z = 2…

A: Given :-  The mass and center of mass of a wire in the shape of helix x = t , y = 2 cos  t   ,  z =…

Q: Find the mass of a sheet whose shape is given by the portion of the plane 3x+2y+z=6 which is in the…

A: We will find out the required solution.

Q: Find ThE Mass and MOMENT about ThE X- axis. x+y=2, X=9 (EXPlain with DEtail )

A: If the surface density at any point Px,y is ρ.Then the mass of the plane lamina is bounded by two…

Q: Find the total mass of two turns of a spring with density p in the shape of the circular helix…

A:

Q: 4. Find the mass of the part of the unit sphere in the first octant with mass density u(x, y, z) =…

A: Consider the given density function. μx,y,z=x2+y2+z2 The unit circle is defined as. x2+y2+z2=1 The…

Q: culate the moments M, and M, a 1

A: We have to solve given problem:

Q: Find the center of mass for a quarter of a regular circular plate of radius (b) b

A:

Q: 4. Find the center of mass of the triangle below.

A: Given: The figure of a triangle, as follows:   To find: The center of mass of the given triangle.

Q: Calculate the moments My and My and the center of mass of a lamina with the given density (p = 3)…

A:

Q: Find the center of mass (in cm) of the particles with the given masses located at the given points…

A:

Q: Calculate the moments M, and M, and the center of mass of a lamina with the given density and shape.…

A: Here, we will first find moments Mx , My and then we will find the centre of mass of the given…

Q: Find the volume of the ellipsoidal solid given by 4x² +4y² +z? = 16

A:

Q: Q5: A- Find the mass of the region cut from the sphere++d by the cone z= density &?? +y² if the

A: Mass is given by M=∬∫V δ dv

Q: Find the total mass of two turns of a spring with density p in the shape of the circular helix…

A:

Q: Verify the given moment(s) of inertia and find x and y. Assume that each lamina has a density of p =…

A:

Q: Find the exact mass of a thin wire in the shape of the helix x = 2 sin(t), y = 2 cos(t), z = 3t, 0 <…

A:

Q: Find the center of mass of a thin wire lying along the curve r(t) = 5ti + tj + k, 0sts2 if the…

A: Mass and Center of Mass of a Wire:- Mass and center of mass of a wire: - The following formulas are…

Q: A. What is the total mass, the moment about the x-axis and moment about the y-axis? b. Where is the…

A:

Q: b) Write the mass in spherical coordinates of the solid bounded above by x+y+z² =1 and below by x+…

A: The given problem is to set an triple integral to evaluate the mass of solid over given region using…

Q: ind the center of mass of the point masses lying on the x-axis. m1=6, m2=2, m3=6 x1=−6, x2=0, x3=4…

A:

Q: The volume of the open cylindrical tank is

A: