Let I be the tetrahedron with vertices (2, 0, 0), (0, 5, 0), (0, 0, 3) and the origin. Write f(x, y, z) dV in the form: .5 v(y,z) L³ [*(*) *(*.³) 0 u(y) = v(y, z)= f(x, y, z) dx dz dy

Q: 3.Find [, (3x² + y)dydx -2

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Q: Show that the points A = (1, 2), B = (1,0), and C = collinear and express P = (-7,0) in barycentric…

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Q: Let P = (0,0, 0), Q = (1, –1, –2), R = (2,1, 1). Find the area of the triangle PQR. area = Let T =…

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Q: Let C = (-2, -1) be the center of dilation. Let X = (1, 1), Y = (3, 0) and Z = (2,5). Our dilation…

A: Center of dilation=-2, -1X=1, 1, Y=3, 0, Z=2, 5Dilation factor, k=3

Q: S SR (4x + 8y)dA, where R is the parallelogram region with vertices (-1,3), (1, −3), (3, −1) and…

A: To Evaluate: Where, is the parallelogram with vertices . Transfomations: ,

Q: Evaluate (2x - y) dx + (x + 8y) dy. C: x-axis from x = 0 to x = 3

A: To solve the line integral ∫(2x - y)dx + (x + 8y)dy over the curve C, which is the x-axis segment…

Q: b) Evaluate the value of I = S(e³y – 3x)dx + (6xey + y)dy, where C' is the parabola - C (0, 0) to…

A: One has to solve it by Green's Theorem.

Q: 6 (A) 2x-yS6 (B) 2+y<6 (C) 2-y26 (D) +2y26

A: The solution are next step

Q: Evalwate f, the inaicated point. (Y.y) and Fy y,y) CY.y) at 3. at (l,3)

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Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

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Q: Find the shortest distance from the point (2,0, –3) to the plane x + y + z = 1.

A: This is a problem related to geometry part. Based on the concept of plane and point we will find the…

Q: 3) 2 y dx + (x - x³y²³) dy

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Q: dx dy, where D is the disk x2 + y² < 9. (x² + y?)3/2 Evaluate

A: The given integral is,

Q: 3.Find [, L (3x² + y)dydx

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Q: where Dx = X₁-X₂ and Dy = |Y₁ — Y2]. Assume that the two locations are independent and uniformly…

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Q: $ x4* dx + 2x*y dy where C is the triangle wl vertices (0,0), (3=), and (2, 4) i ?

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Q: b) Evaluate the value of I = S(eºy − 3x) dx + (6xey + y)dy, where C' is the parabola y = C (0, 0) to…

A: The integrand is given here as         (e6y - 3x)dx + (6xe6y + y)dy        = (e6ydx + 6xe6ydy) -…

Q: dw Find ду dw at the point (w, x, y, z) = (3, - 1, - 1, - 1) if w = x3y? + yz-z° and x2 + y? +z? =…

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Q: Use Green's Theorem to calculate 4. [(x² – xy) dx + (y² - 2xy) dy] where C is a square with vertices…

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Q: ScF· dĩ, where F(x,y) = (6x - 2y)7+x²7, and C is the line segment Evaluate from (6, -3) to (0, 0).

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