5. Consider a hollow spherical bowl with radius r = 18 cm that is filled to the top with water. h(t) u(t)

Q: 4/ Find the area of the region enclosed between the curves y= cos 2x, y=0, x=TT/4, x= TT/2 ? ans/…

A:

Q: 10. (1 – y³) dx + (x³ + e*) dy, Č is the boundary of the region between the circles x² + y² = 4 and…

A:

Q: 46.) (a) Parameterize S the 1st octant portion of the cylinder y² + z² = 9, 0 <x<4 (b) Use above to…

A: y2+z2  0≤x≤4x=uy=3 cos vz=3 sin vparameterise the surface ass(u,v)=(u   3 cos v   3 sin v)0≤u≤4,…

Q: find the derivativa dy for the frurrtion y=x by using lagarithmic differatiation.

A: Given y=x5x Taking logarithmic both sides, lny=lnx5x implies lny=5xlnx

Q: Evaluate the integral (12x + 12y)dx + (9x - y)dy along the parabolic arc y = x from (0,0) to (1, 1).…

A:

Q: 3) Find The solution of the intigl uglue pablem ty =y+ 3 Vy?+ yl-e) = 2 %3D of the given answers…

A:

Q: Consider the following boundary value problem: d?u du +--u = 0, dx du(0) = 0, u(4) = 1 (Eq 1) dx2 dx…

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Q: 4. Which would not be sufficient to prove AWXZ AWYX? C ZWXZ = LY WZ А WX XW YW WZ D WX WX XY XZ WX…

A: To show that the given two triangles are similar we need to show that the sides of the two triangles…

Q: 1 Evaluate dV, where E lies between the spheres a? + y? + z? = 16 and x2 + y2 + z2 = 64 in the first…

A: The region E lies between the spheres: x2+y2+z2=16  and  x2+y2+z2=64  in first octant.

Q: 18. Ris the annulus in the first and second quadrants bounded by x +y² = 9 and x² + y = 36; 8(x, y)…

A:

Q: 3 The triple integral L (x + 2y – z)dxdydz is equal to

A:

Q: Question 3 Selve the linear Ruation: dy 3. Integral faualian.

A:

Q: a. Solve the boundary value problem d? y +7y = 0, with conditions y(0)=1 & y(37)=0. 2 dx?

A: first find its solution

Q: A// compute $(4+ e*) dx+ (siny + 3x*)dy Where c is closed bounded region lying in the first quarter…

A: See the attachment

Q: Compute the irertia móment by x ( Ix=Sy?JA) tor number off segment n=s hyte multple-trapezoidal…

A:

Q: 1 Evaluate dV, where E lies between the spheres x + y + z = 16 and + y? + z2 = 64 in the first…

A:

Q: 1 The volume of a right circular cone of radius a and height y is given by V = ²y. 3 when x = 6 and…

A:

Q: ve the given boundary-value problem. (If an answer does not exist, enter DNE.) y" + y = 0, y'(0) =…

A: Topic:- differential equations

Q: 3) Find The solution of the intigl uglue psblem ty =y+ 3 Vy?+E yl-e) =0

A: We have to solve the initial value problem

Q: Solve u +u =0 for the square mesh with boundary values as shown in Figure 11.14. Iterate till the…

A: Consider the given differential equation, uxx+uyy=0 Here we have to find the mess values which are…

Q: # 4. Evaluate the line integral | (x +2x²y) ds, where C is the upper half of the unit circle x2 + y2…

A:

Q: 1.13 Evaluate the line integral $ x*dx + xydx where C is the triangle with vertices at (0, 0), (0,…

A: The given function is x4dx+xydy By green's theorem, the integral becomes, ∫06∫06∂M∂y-∂N∂xdxdy where…

Q: 2 Evaluate the fullowng cartesianntegrat changing theminte equivalent Pelarintegrals: Fー dxdy 2-

A: We have to find the double integral using polar coordinates.

Q: Evaluate the integral (12x + 6y)dx + (9x – y)dy along the parabolic arc y = x² from (0,0) to (1, 1).…

A:

Q: 1 The volume of a right circular cone of radius x and height y is given by V = Txʻy. Suppose that…

A:

Q: 2.7 Describe cll soilutions of Asso where A is the Yow ta the matirix meg Vse Y S, and/or t as in…

A: Given  A=1-6-50-2-100100-200001-7000000 Here, we have to solve Ax=0

Q: 10- Evaluate JJI where E is the region that lies inside the cylinder Vx2 + y?dV E x? + y? = = 16 and…

A: Here we use polar coordinate and Jacobian .

Q: PROBLEM [ B2 ]: Find the volume of the solid of reolution bounded by the circle z +y = 16, and the…

A: We have to find  The volume of the Solid of revolution bounded by the Circle x2+y2=16 and the lines…

Q: 1. Evaluate ſf, y dS where S is the portion of the cylinder 4x² + 2y² = 16 that lies between z = 0…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Evaluate the integral (6x +12y)dx + (6æ — y)dy along the parabolic arc y = x² from (0,0) to (1,1).…

A: Let us evaluate the given integral in the next steps.

Q: 22. Evaluate xyz dV, where E lies between the spheres p - 2 and p- 4 and above the cone - 7/3.

A: Solution:-

Q: (3) Find The selution of the intigl ualue problem ts =y+ 3 Vy?+E, yle) =0 yl-e) 3,-2 %3D of the…

A:

Q: A string of length 1m attached with two points. The deflection in the string is given by y" + Ay =…

A:

Q: 16. Evaluate * :- S S $6(x² + y² + z? )dV В where B is the ball with center at the origin and radius…

A: (16).  We have to find the integral∫∫∫B 6x2+y2+z2 dV  ;      where B is the ball with center at…

Q: 20- What is the share of the formula that allows calculating the y coordinate of the center of…

A:

Q: Problem 10  The volume of the solid obtained by rotating the region enclosed by y=(x^2), y=2x, about…

A:

Q: 4. Find дw b. dz a. дх at the point (x, y, z) = (0, 1, T) if w = x² + y? + z? and y sin z + z sin x…

A:

Q: In his work Nova stereometria doliorum vinariorum (New Solid Geometry of a Wine Barrel), published…

A:

Q: A sphere of radius 2 cm contains a volume charge density Pv given by py = 4 cos“0 [C/m³]. Find the…

A: Given: Radius of the sphere=3 cm Charge density, ρv=4 cos2θ C/m3

Q: Evaluate the integral / (2x + 12y)dx + (24x – y)dy along the parabolic arc y = x² from (0,0) to…

A: For the arc y = x2 and the range of x from 0 to 1. So, dy = 2x dx. Now,…

Q: find the valume 9tntrat ed by y= X? on [0,31 rotating abaut thlina X-5.(shell melthod) rated

A:

Q: 1 9. Evaluate dV;where E is the solid between the spheres of radius 1 (x² + y² + z²)³/2 E and 2…

A:

Q: 1 The volume of a right circular cone of radius x and height y is given by V Tx y. Suppose that the…

A:

Q: 2. 7 3. Find the centroid of the region bounded by y 3, 3 to the nearest thousandth. nd Since you…

A: To find the centroid of the given region R by integration

Q: 1 The volume of a right circular cone of radius x and height y is given by V TXʻY. Suppose that the…

A: Given that:                        Volume of the cone, V=13πx2yV=204π cm3x=6y=17

Q: th 2 Evaluate khe fulawingcartesian integrat by changing theminte equiv alent Pelarintegrals: E 4-y…

A:

Q: By using homogeneous meth od , solve dy %3D

A:

Q: given FCX)= x° t use definatron Of desivative

A: Given: fx=x2+1x Definition of derivative: f'x=limh→0fx+h-fxh