Find the mass M and center of mass x of the linear wire covering the given interval and having the given density 8(x). -45x54, 8(x) = 4 + 3x? Set up the integral that gives the mass of the thin bar. dx (Type exact answers.)

Q: Evaluate the triple integral. 3x dV, where E = {(x, y, z) I 0 s y s 2, 0sxs V4- y², 0 s z s 2y}

A: Given region is E=x,y,z/0≤y≤2,0≤x≤4−y2,0≤z≤2y We have to evaluate the triple integral ∭E3xdV in…

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: Compute the center of mass on a rod of density p(x) = 3x° + xe' with a E (0, 2). 12.5939 Round to 4…

A: Explained below

Q: 3 Find the mass of a wire that lies along the curve r(t) = (P - 3) j+ 2tk, 0sts2, if the density is…

A: Use parametric to solve

Q: Calculate the total mass of a metal tube in the helical shaper(t) = (cost,sin t,t2) (distance in…

A: r(t)=cost,sint, t2 , 0≤t≤2πδx,y,z=z g/cm

Q: Find the mass of a thin wire lying along the curve r(t) = sqrt(2)t i + sqrt(2)t j + (4 - t2)k…

A:

Q: Find the mass and center of mass of the lamina bounded by the graphs of the equations for the given…

A:

Q: Find the moment of inertia with respect to x- axis of the area between y = sin x from x = 0 and x =…

A:

Q: Find the center of mass of the homogeneous lamina bounded by  x = pi/4,   x=3pi/4, y = 0,  f(x) =…

A: Centre of mass = x = My/A ,    y = Mx/A A= ∫ab[f(x)]-g(x)dx My =∫ab x[f(x)-g(x)]dx Mx = ∫ab1/2[f2(x)…

Q: Find the mass and center of gravity of the lamina bounded by the x-axis, the line x = 49, and the…

A: Given problem:- Find the mass and center of gravity of the lamina bounded by the x-axis, the line x…

Q: 4. Find the mass and center of mass of a wire in the shape of the helix x = t, y = cost, z = sint,…

A:

Q: change the cartesian integral in an equvalant polor integral then evalute 2x-x² 1 the polor integral…

A: To change cartesian equation into polar, we use following substitutions x=r cosθy=r sinθdydx=r dr dθ

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 center of mass and the moment of inertia about the​ y-axis for a thin rectangular plate cut…

A: Given that density = x + 2y + 4 and rectangular plate is bounded by the lines y =1 and x = 6

Q: A lamina occupies the part of the rectangle 0 <x < 7, 0 < y< 4 and the density at each point is…

A:

Q: Find the mass and center of mass of the lamina bounded by the graphs of the equations for the given…

A: The region is bounded by the graphs of the equation y=cosπx4, y=0, x=0 and x=2. The density is given…

Q: Find the moment of mass from the x-axis for y = x ln(x) − 3x and y = 1 bounded by x = 3 and x = 6.…

A: Given data:- Surface density is equal to 0.37 kg/unit2 y=xlnx-3xy=1 Bounded by, x=3 and x=6

Q: The double integral T f(x)g(y)dydx,where a,b.c, and d are constants, is equal to

A:

Q: Calculate the total mass of a metal tube in the helical shape r(t) = (cos(t), sin(t), t2) (distance…

A: We have given; The mass density and

Q: valuate the double integral. SL,(6x + 3y) dA, D is bounded by y = VT and y = r²

A:

Q: Find the moment of inertia with respect to the y-axis for the area bounded by y = cos²x³, x = 0.2…

A: To find the moment of inertia with respect to the y-axis for the area bounded by the below curves.…

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

A:

Q: Find the center of mass and the moment of inertia about the y-axis of a thin plate bounded by the…

A: Consider the provided question, We have to find the centre of mas and moment of inertia about the…

Q: Evaluate the integral by changing to cylindrical coordinates. 100 y2 13 10 xz dz dx dy Vx2 + y2 100…

A:

Q: 5. Find the mass of a ball B given by x2 + y? + 22 < a² if the density at any point is proportional…

A:

Q: Use cylindrical coordinates to evaluate the integral ([[, x*dV , where E is the solid that lies…

A: Given: x2+y2=1 z2=4x2+4y2

Q: Evaluate the triple integral. 8z dv, where E is bounded by the cylinder y2 + z2 = 9 and the planes x…

A: Please refer the attached image for complete solution.

Q: Find the moments of inertia of the rectangular box of constant density δ(x, y, z) = 1 shown here…

A:

Q: 3. Find the center of mass of the solid cube given by [0, a] × [0, a]x [0, a] with density function…

A:

Q: Evaluate the triple integral. III. 7z dv, where E is bounded by the cylinder y2 + z² = 9 and the…

A:

Q: Find the mass of a wire in the shape of helix r(t) = cos πt i+sin πt j+8tk 0≤t≤1, where the density…

A: syms x y z r t rho real x=cos(t*pi) y=sin(t*pi) z=8*t  r=[x,y,z] rho=x^2+y^2+z^2…

Q: Evaluate the following integral in cylindrical coordinates. 4 V16 - x2 3 1 -dz dy dx v2 1+x + -4 0 0

A:

Q: 3) Find the mass and center of mass of a wire in the shape of the helix: x = t, y = cos t ,z = sin t…

A:

Q: A solid E lies within the cylinder 64x² + 64y² = 9, below the plane z = 16 and above the paraboloid…

A:

Q: (3) Find the mass of the lamina described by the inequalities, given that its density is p(x, y) =…

A:

Q: valuate the following integral in cylindrical coordinates. 5 vz V4-x [ [ e-*- dy dx dz 0 0 x

A:

Q: When 20 N of force is applied to a spring of natural length 2 m, the resulting compression is 0.5 m.…

A: Natural length = 2 x1=2-1.5=0.5x2=2-1=1

Q: A solid E lies within the cylinder x2 + y2 = 1 below the plane z = 10, and above the paraboloid z =…

A:

Q: dV, where E is the region between two cylinders ²+², 5. Evaluate the integral and 2² +2²9 with 1 ≤ y…

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: 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: The center of mass of a thin rod oriented along the x-axis from x = a to x = b with linear density…

A:

Q: e mass of the solid bounded below by the c phere z = 6.52 – a? – y² if the density

A: The given equation of the circular cone z=x2+y2 and the hemisphere z=6.52-x2-y2 and the density…

Q: Evaluate the triple integral. {x, y, z) | 0 s y s 2, 0 sxs 4- y², 0 sz s Sy 6x dV, where E =

A: From the given problem:   ∫∫∫E6xdV   And region:   0≤y≤20≤x≤4-y20≤z≤5y   So, we can write as:…

Q: The double integral f(x)g(y)dydx ,where a,b.c, and C d are constants, is equal to

A:

Q: (3) Consider a wire in the shape of a semi circle of radius 2, given by x² + y² = 4 and y ≥ 0.…

A: Formula: The mass of the region R with density function ρx, y is: m=∫∫Rρx, y dA The center of mass…

Q: Evaluate the triple integral. 5z dv, where E is bounded by the cylinder y2 + z2 = 9 and the planes x…

A:

Q: Set up an integral in Cylindrical coordinates that represents the volume of the solid above the cone…

A:

Q: Compute the center of mass on a rod of density p(x) = 5x3 + xe 3D5r3 xe- with a E (0, 5).

A: Given: ρx=5x3+xe-x, x∈0,5 We know that center of mass is given by  x¯=∫abxρxdx∫abρxdx      1 , where…