8. The y coordinate of the centroid of the plate (uniform density) formed by the curve f(x) = e and the x-axis from x = 0 to x 2 is a. e-1 e-1 b. (e-1) C. none of the above

Q: (b) / = xyz dV if S is the region bounded by the cylinders x² + y² = 25, x² + z² = 25 and the first…

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Q: he characteristic curves for the IVP u+4 u,+2 u 0; (x, 0) = sin x; - 00 C are O a. T= X-t . T=X- 8…

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

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Q: 5. Suppose z=f (x,y), where x=g(s,t)and y=h(s,t). Show that Oz d'x, z 0y +. 生() az ôx ôy d:(dy +2-…

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Q: The velocity field in the region shown is given by V = ( aj + byk ) where a = 10 m/s and b = 5 s-1.…

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Q: 4. Evaluate S, cos dA where D is the region bounded by D = {(x, y)/ VL < x < v3Ln , 0 < y< x² }.

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Q: 20. Evaluate dædy by changing the limits of integration appropriately. e y/2

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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: 15 - The number Af(x,y) = f(x + dx, y+ dy) – f(x, y) is estimated by df below. Calculate df at P(3,…

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Q: A rod of length L coincides with the interval (0, L] on the r-axis. Set up the boundary-value…

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Q: 1. Under the paraboloid = 3z2 + y? and above the region bounded by y = x and r= y² – y

A: Find point of intersection of:  y=xx=y2-y y=y2-yy2-2y=0y=0,2

Q: 3

A: It is given that the variables X and Y are independent.

Q: 9) Consider the solid Q in the first octant, generated by the surfaces: x = (y-3)2+ 1, x + 2z = 8, x…

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Q: Volumes of solids Find the volume of the following solids.

A: The region is bounded by the curves, The region is shown in the graph given below,

Q: could i please get help with 9a?

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Q: 4.78 Compute P(u – 20 < X < µ + 20), where X has the density function f (x) = { 6x(1 – x), 0<x< 1,…

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Q: 1. If F= (y,z,x), the outward flux through a smooth closed surface (a) depends on the surface. (b)…

A: Given, F=y,z,x We know,  Flux by the Gauss divergence theorem. ∬F.ds=∬∫divF.dvF=yi+zj+xk If you…

Q: 9. Use Green's Theorem to evaluate (e* +y²) dx +(e" +x²) dy where C is the boundary of the region…

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Q: 14.w.3 Find Ihe arcan region for he fllowwiy Regian honded.by.y= X- y=D and S= 2

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

Q: Ive the following PDE with nonhomogeneous boundaries: PDE UttUxx = 0, BCs u(0, t) = sin(t), u(L, t)…

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Q: 10. The integrating factor of the FOLDE y'-2xy x is e^(-x^2) I am Sorry !!!!

A: The given differential equation can also be written as dydx-2xy=x Since it is a first-order linear…

Q: 9) Consider the solid Q in the first octant, generated by the surfaces: x = (y-3)²+ 1, x+ 2z = 8, x…

A: We need to use triple integral to find volume

Q: When the group of terms in a first-order DE contains y dx - x dy , the following integrating factors…

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Q: let z be the from a paint minimum distance on the gra ph of y= 5€3x/2) to the Origin which is at (0,…

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Q: 7.* Give the candidates to local extrema (maximum or minimum) of f(r, y, z) = 2z – y – r under the…

A: The solution to the given question is as follows.

Q: 2e* xy" - (2x + 1)y' + (* + 1)y %3D * ond ex ore linearly indenerndent

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Q: Suppose that a, b, c, and d are constants such that ad- be # 0, and let m and n be arbitrary real…

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Q: The temperature distribution u(x, t) of the one-dimensional gold rod is governed by the heat…

A: The given equation is ∂u∂t=0.25∂2u∂x2 Using the Taylor series expansion and discretization, we…

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: A string is stretched between points x=0 and x=5. At time t = 0, the elastic medium is at rest and…

A: Given that: A string is stretched between points x=0 and x=5. At a time t=0, the elastic medium is…

Q: 1. Evaluate the line integral of E = xax - y ay along the segment P₁ to P2 of the circular path as…

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Q: If f′(0)=f′(2), find the difference 2c-d for the following cubic spline S(x) with clamped boundary…

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Q: 3.5 Given that H = x'a, + ya,, evaluate H· dl, where L is along the curve y = x from %3D (0, 0) to…

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Q: The strength E of an electric field at a point (x, y, z) due to an infinitely long charged wire…

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Q: 3. If we have a box with sides of length x, y and z and we know that dx 5m/s, * = -1m/s and = 2m/s,…

A: given that a box has a sides of length of x=3m ,y=7m and z=1m. and also the rate of change of this…

Q: 1. Suppose that D is a region with area A, on the xy plane and that f (x, y) is a continuous…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: b) Find the maximum and minimum values of the function u(x, y) = e' cos x throughout the region {(x,…

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Q: 4. Evaluate x² dV G where G is a solid that lies in the first octant bounded by x2 + y? = 3z and z =…

A: We have solid G in the first quadrant bounded by x2+y2=3z and z=3 equating the above two equations…

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Q: A 3 cm length silver bar with a constant cross section area 1 cm (density 10 g/cm³, thermal…

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Q: b.) xyz dv if S is the region bounded by the cylinders x² + y² = 25, x² + z² = 25 and the first…

A:

Q: 3. Given the closed curve defined by y = vx in the first quarter up to 1000 = x (area production),…

A: FIND: a) how many unit squares it contains b) number of squares needed in the cover

Q: 4. Suppose a function y = f(x) is so be revolved at x = e from point (a,b) to (c, d), what is the…

A: If a function y=fx is rotating in the interval a, b about the x-axis. Then the formula of the…

Q: 17. 6xy dV, where E lies under the plane z = 1 + x + y and above the region in the xy-plane bounded…

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Q: 10. Find the minimum of the integral I[y] subject to the constraint TIy) = [, s° dx = 2 JL over all…

A: Consider the problem: Extremize I[y]=∫x1x2F(x, y, y') dx subject to J[y]=∫x1x2G(x, y, y') dx=L ,…

Q: If p(x, y) is the density of a wire (mass per unit length), then =1p(x, y)ds т — 1+ cos(t), y =…

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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: The volume of the solid generated by the curve y = e¬ª, between x = 3 and x = 7 about the |3| x –…

A:

Average

In mathematics, everyone must have heard the term average in one place or other. Almost all types of calculation require taking out an average. In everyday life, the term is used for denoting a certain amount that can be said to be a typical quantity for multiple people or objects. In other words, if a group of people possesses a certain object, then the average gives us an idea regarding the quantity of the object possessed by each person. However, this is solely based on mathematical calculation. It is important to note that most people will not strictly have the average value in a group.