What are the new coordinates of the point (18, 8) under the dilation (x, y) → (1.5x, 1.5y)? O (32, 12) O (27, 12) O (27, 16) O (18, 12)

Q: 1. = (xy, y,z²+y) , f(x,y,z) = xy . Find Curl(F) 2. Div curl(F) 3,. Div (fF) 4. Divgrad(f)

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Q: An object moves along the a-axis, its position at each time t > 0 is given by æ(t) = t" 3 4 +t.…

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Q: Find (url and dive rgence the of F(xy2)=Xy2 i+ 2x Y j t z(os xyk.

A: Given: F(x, y, z) = xyz i + 2xy j + 2cosxy k To find: Curl and divergence of the given function.

Q: Find a parameterization for a line passing through the points (1,1) and (5, 13) O x = t, y = 3t-2 O…

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Q: SF. dr, where F (x, y) = (6x − 2y)i +x²7, Evaluate from (6,-3) to (0, 0). and C is the line segment

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Q: Translate Q (0, -8) using (x, y) → (x - 3, y+ 2). Your answer: O Q'(-2, 5) Q' (3, - 10) O Q'(-3, -6)…

A: The transformation is, (x,y) ------> (x-3, y+2) So, (0, -8) ------> (0-3, -8+2)

Q: Evaluate y ds, C: x = t², y = t, - 1<t < 9 |3D (325)-(5)를 1 12

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Q: Evaluate e [ f(x, y, z) ds, where f(x, y, z) = 2 + 2y + (z + x) and C is the line segment from (2,…

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Q: Let C1 be the line segment from (1,0,1) to (0,3,6). Evaluate dx + dy + dz.

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Q: Use Linear Approximation to estimate the change, Az, in z = 8x2 + y? as (x, y) changes from (2, 3)…

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Q: What is the midpoint between z1 = 9i and z2 = 4? (2, 4.5) (-4,-9) (-2,-4.5) (4, 9)

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