Find the Jacobian X = 8uv, a(x, y) = a(u, v) of the transformation. y = 3u/v

Q: Let y F = r2 + x + be the vortex field. Determine F - dr for each of the paths. (A) (B) (D) (E) (Use…

A: A simple closed curve is a closed curve with no self-intersection. For a simple closed curve C and F…

Q: Find the Jacobian of the transformation. x = 5es + t, y = 8es - t -40e²s a(x, y) a(s, t) = X

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Q: Consider F and C below. F(x, y) = x² i + y² j C is the arc of the parabola y = (a) Find a function f…

A: Consider F and C Fx,y=x2 i+y2 j C is the arc of the parabola y2=4x from -1,4 to 1,4

Q: Consider F and C below. F(x, y) = 1 + x² 49π 4 i + 2y arctan(x) j C: r(t) = t² i +7tj, 0 ≤t≤ 1 (a)…

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Q: Can movie rental revenue be predicted? A movie studio wishes to determine the relationship between…

A: a) In this case, the independent variable is theater revenue (x) and the dependent variable is…

Q: Find a parametric representation for the surface. The part of the plane z = x + 2 that lies inside…

A: Given: The part of the plane  z = x + 2  That lies inside the cylinder,  x2 + y2 = 9.

Q: F. dS =

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Q: Find the Jacobian of the transformation. x = 2es+t, y = 6es - t a(x, y) a(s, t)

A: The Jacobian transformation

Q: Eva te the st face integral. 16205 ² z dS S is the surface x = y + 2z², 0 ≤ y ≤ 1,0 ≤ z ≤ 3

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Q: (a) P(Z 1.45)= (d) P(Z > 2.15)=

A: Hi! Thank you for the question, As per the honour code, we are allowed to answer three sub-parts at…

Q: Compute F - dS for F = (4e*, 2z, 2x), S being a surface with parametrization (r, s) = (rs, r + 4s,…

A: Given F=4ez,2z,2x, S being a surface with parametrization φ(r,s)=rs,r+4s,r, 0≤r≤1, 0≤s≤3, oriented…

Q: Find the Jacobian of the a(x, y) a(u, v) transformation. x = 5u + 8v, y = 4u + 7v =

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Q: Use the given transformation to evaluate the integral. √√₂ 3(x + y) ex²_ 3(x + y) ex² - y² da, where…

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Q: Evaluate the line integral, where C is the given curve. Sext xªy√z dz, C: x = 5, y = t₁ z = t², 0 ≤…

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Q: 16.3 #8

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Q: Show that any integer of the form 6k + 5 is also of the form 3j + 2, but not conversely.

A: 2. We can write 6k+5 = 6k+3+2=3(2k+1)+2 lets write 2k+1=j hence 6k+5=3j+2

Q: Let F = (z,0. y) and let S be the oriented surface parametrized by (u, v) = (u² – v, u, v²) for 0 <…

A: (a) First, find the tangent vectors: Tu=∂ϕ∂u=2u,1,0Tv=∂ϕ∂v=−1,0,2v The vector N is the cross product…

Q: Evaluate the iterated integral. 1-z² 4 [²6² 0 0 28zey dx dz dy √₁-₂² (14e²-14) 2 V1- Z ×

A: In triple integrals if the limit of the integral are not related then we treat all else variables as…