Evaluate O F.dT where +(3y %3D y + 1 and C is the triangle with vertices: (0,0), (6,0), (3, 5).

Q: In AMNP, T is the centroid. If MR=30 find MT. N R T M S

A: We are given that T is the centroid and MR=30. We know that the centroid divides each median in a…

Q: Evaluate O xy?dx + a°dy, where C is the rectangle with vertices (0,0), (6,0), (6,3), and (0,3)

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Q: Suppose we are considering 2D points, so x (x, x). Define (x) (x, V2x1x2, x). Show that (x) p(z) =…

A: Given that, considering 2D points x=(x1, x2). Define                 ϕ(x)=x12, 2x1x2, x22. We shall…

Q: Is the map T: R² → R² given by T(x, y) = (x,y + 1) linear?

A: T: V-> W  mapping from V to W is a linear map if and only if  ->(u+v)=T(u)+T(v) ->T(au) =…

Q: 4. C is the centroid of ADEF. Find CX if FX = 10. E Y X C F D

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Q: (b) If z r+ry- y7, 1= u+ and y = 2uv, find: in terms of du %3D u and v.

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Q: x y 11. Use Green's theorem to evaluate O In(1+ y) dx –- dy , where C is the triangle with vertices…

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Q: 35. f(x, y) = x² + 2y² – x; R is the disk x? + y? < 4.

A: fx,y=x2+2y2-x which is bounded by R, R:x2+y2≤4, where R is a disk Partially differentiating fx,y…

Q: y"(t) – 4y'(t) + 5y(t) = e"U (t – 2), %3D

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Q: Q3:- Find fx, fy if f(x, y) = y+cosx 2y %3D dw

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Q: Find the average value of f(x, y) over the plane region R.

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Q: Exercise 15.2.8 Y 1₁² Find ► Hint dA where D = {(x, y) : x ≥ 0, y ≥ 0, x² + y² ≤ 1}.

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Q: Use Green's Theorem to evaluate (y? tan- a?) dx + (3.xy+ 4x – In(y² + 4)) dy, where C is the…

A: We need to evaluate integral.

Q: Demonstrate that the functions Y1 = a", y2 = sin(x), Y3 = xe* are linearly independent on R. 9.

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Q: Suppose that VX=14.4, VW= 36, and VZ= 12. Find XY. %3D W XY = %3D

A: From the given figure

Q: I need help finding the absolute maximum and minimum values of f on the set D.

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Q: Suppose b, c E R. Define T: R³ → R² by T(x, y, z) = (2x − 4y + 3z + b, 6x + cxyz). Show that T is…

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Q: Show that fdx + gdy = S 36x°y?dx + 18yx*dy is independent of path: (3,6) (-2,4) (3,6) 2,4) C(3,6)…

A: The vector field is conservative if the components satisfy the test ∂P∂x=∂Q∂x. If the field is…

Q: Find the path of a heat-seeking particle placed at point P on a metal plate whose temperature at (x,…

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Q: Find the linearization z = = L(x, y) of the function z = f(x, y) = 3.x2 – y² + 5y at the point (xo,…

A: z=fx, y=3x2-y2+5y and the point is x0, y0=2, 1. Now, f2, 1=322-12+51=12-1+5=16 Now partially…

Q: du If u = x²y + y²z + z?x then at (1,1,0) is ax %3D -

A: Given that u=x2y+y2z+z2xTo find :∂u∂x  at 1,1,0Solution :u=x2y+y2z+z2x∂u∂x=2xy+0+z2∂u∂x=2xy+z2

Q: 26. If RX = 6z+2, XS 18, and RS = 14z, find z. j %3D %3D

A: Recall: If XY is line given such that XZ=a ; ZY=b and XY=c then  XY=XZ+ZY   ⇒a+b=c   Note :…

Q: 35. f(x, y) = x+2y2 -x; R is the disk x2+ y? < 4.

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Q: find the linearization L(x, y) of the function ateach point. ƒ(x, y) = x3y4 at a. (1, 1), b. (0, 0)

A: Consider the function: fx,y=x3y4 To calculate the derivatives of the given function with respect to…

Q: Find a parametrization c(t) of the line y = 5 − 2x such thatc(0) = (2, 1).

A: This question comes under the category of calculus and from the parametrization of the line here we…

Q: Evaluate p xy*dx + a*dy, where C is the rectangle with vertices (0,0), (2,0), (2,3), and (0,3)

A: *Concept:- Use Green's theorem.

Q: (b) ſf f(x,y) dA if f(x, y) = y², where R is the triangular region with vertices (0, 1), (1, 2) and…

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Q: a A = and if xy = 1, then det ( AAT ) is equal %3D to y a

A: Given:A=axyaif xy=1 then detAAT=?

Q: f (lnx + y) dx − a² dy, where & is the rectangle with vertices (1, 1), 1. Use Green's Theorem to…

A: Let I =∮(ln x+y)dx-x2 dy, where the region is C which is a rectangle with vertices…

Q: Evaluate x*dx C + xy dy, where C is the triangular curve consisting of the line segments from (0, 0)…

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Q: Differentiate the follo ear and non-linear. w +z =2 1. x +y- z= G X +v-

A: (i) First we differentiate the given equation with respect to x: xy+z=2⇒ddxxy+z=ddx2⇒y+xdydx+dzdx=0…

Q: Find Vq if (a) =In (r) %3D (b) p= In (-) %3D We know r= /x² + y² + z2

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Q: f(x, y) = xy over the triangular region with vertices (0, 0), (8, 0), and (0, 6) O 12 2 96 O 16

A: Solve

Q: Draw direction field of the DEQ below, by hand, and sketch an approximate solution curve that passes…

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Q: 2. Ostain the geweval folu fion a. my = nxydx b. (@ x*+y') = {ry y' c. xy = Y(x* + sy) y' %3D

A: Given differential equation is as  my2=nxydx/dy  Note : without introduction of dy whcih cant…

Q: Evaluate p xy da + a dy, where C is the rectangle with vertices (0,0), (3,0), (3,6), and (0,6).

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Q: Show that the function u = p(ry) + JFÿ¢(y/x) provides the quation „Pu = 0. dy

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Q: Compute the Vf = (x, y) for f(x,y) = 5y – x³y2 %3D %3D

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Q: T (x, y) (2x,y) is an is %3D

A: T(x,y)=(2x,12y) The transformation of any figure changes the size, shape and the position to create…

Q: Find the Jacobian d(x, y) / d(u, v) for the indicated change of variables. u- v), y =u + v) X = -

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Q: can u help me with pullbacks and integration plz

A: Given that the integral,

Q: PART C dy 12. Show that dx 2 for the relation %3D V%3D10, x, y X. # 0. y

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Q: Fx, y, z) = (10y – az – 5x)i + (3by – x + 8z)k + (z – 5y + 2cx)j %3D a

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Q: 4y" + 16у' + 17у %3D 0, when y %3D 1, х %3D 0;B у 3D 0, х %3Dт

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Q: Find r(t) u(t). r(t) = (5t – 4)i +j - +2k 2. %3D u(E) = i - 4j - ēk %3D | r(t) u(t) -

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Q: Is F(x,y)= (2²y,5– zy²) source free?

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Q: Let f(x, y, z) = 3x?y+ yz3, where x = 3 – t2, y = 2t + t3, and z = V1+ 3t. Calculate when t = 1.

A: NOTE: Refresh your page if you can't see any equations. . here we have . the given function is…

Q: Is AX'Y'Z' a reflection of AXYZ across line g? g X. Z' Y X'

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Q: Show that under the substitution u(x, y) = w(x, y)e¬(bx+ay) the equation ди +а—+b—+ си %3D 0 ду ди…

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