Find the center of mass of a lamina as pictured below, with inner radius 1 and outer radius 5, with density function (z,y) 2²+372

Q: 1 [[ ] ₂²² + 3² +2² dV, where E lies between the spheres x² + y² + 2² = 25 and E = 36 in the first…

A: We have to evaluate: ∭E1x2+y2+z2dV. Here E lies between the spheres x2+y2+z2=25 and x2+y2+z2=36.

Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

A: The given acceleration a→t=5t, 5sin t, cos2t and the initial velocity and position vectors are…

Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = tan(4x + 5y+z) . F(x, y, z) =

A: given  f(x,y,z)=tan(4x+5y+z)we know that formula of gradient field is→gradient…

Q: • J / S₁ (²²+ // Let E be the solid below z = 72-x² - y² and above the square [-6, 6] x [-6, 6]…

A: Let E be the solid below z=72-x2-y2 and above the square [-6,6] x [-6,6]. And density is ρ=5. To…

Q: Evaluate /// 2xz dV where E = {(x, y, z) | 2 ≤ x ≤ 4, x ≤ y ≤ 2x,0 ≤ z ≤ x+2y} E

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Q: Multiple Choice The number 1 has this property, since the only positive integer not exceeding 1 is 1…

A: Given that there is a positive integer that equals the sum of the positive integers not exceeding…

Q: Convert the point (r, 0, z): (x, y, z) = (5, 7, -5) to Cartesian coordinates.

A: Given: r,θ,z=5,π4,-5 We are required to find: x,y,z

Q: Electric charge is distributed over the triangular region D shown below so that the charge density…

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Q: Find the surface area of the portion of the bowl z=8-2²-² that lies above the plane z = 4. When…

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Q: Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be…

A: Negation of and is or   Negation of or is and

Q: The curves 7₁(t) = (4t, t², 5t6) and F₂(t) = (sin(—t), sin(4t), t — π) intersect at the origin. ㅠ…

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Q: Find the mass of the solid bounded below by the circular paraboloid z = x² + y² and above by the…

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Q: Evaluate ³da-a³dy, where C' is the boundary of the region between the circles z² + y² = 9 and dx x²…

A: We have to evaluate the integral. We will use Green's theorem to evaluate the integral.

Q: Find the mass of the solid bounded below by the circular paraboloid z=²+² and above by the circular…

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Q: Let 3x² - 7xy + 2y²+x-12y-14=0. Use partial derivatives to calculate dy dz (-2,1) TE at the point…

A: First of all, we will differentiate then we will put the values of x and y

Q: Let p, q, r be the propositions: p: The user enters a valid password. q. Access is granted. r. The…

A: Given: p: The user enters a valid password.            q: Access is granted.            r: The user…

Q: Translate these statements into English, where C(x) is "x is a comedian," F(x) is "x is funny," and…

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Q: NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to…

A: Given that  p: swimming at the New Jersey Shore is allowed. q: sharks have been spotted near the…

Q: Find the gradient vector field of f(x, y, z) = √√√4x² + 5y² + 2z²

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Q: The compound propositions (p→→q) →r and p→ (q→) are not logically equivalent because Multiple Choice…

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Q: Find the center of mass of the solid S bounded by the paraboloid z = z = 9. Assume the density is…

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Q: Evaluate the integral [[(x + y). e²²-1²dA, where R is defined by x +y = 3, x+y = 7, R x² - y² = -1,…

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Q: Let w(1, y, z) = -zy arcsin(z) where z=t", y=t, z = 7t. dz dw dt dz dy dt' dt & and using the chain…

A: Given: wx,y,z=-xyarcsin(z)where x=t4,  y=t3, z=7t To find: dwdt

Q: Find of S. (5.2. (5x + 4y)dA where D = {(x, y) | x² + y² ≤ 9, x ≥ 0}

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Q: You need to guide a robot from the red dot on the left to the green dot on the right, avoiding the…

A: We will use the concept of Trigonometry to solve this question. Consider that,

Q: The statement is related to inhabitants of the island of knights and knaves created by Smullyan,…

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