Set up a triple integral in spherical coordinates for the volume inside the cone z = x² + y² + z² = 64 with x ≥ 0 and y ≥ 0. Do not evaluate the integral. Provide your answer below: x² + y² and the sphere

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A: According to guideline we need to solve only one question, rest of the question should be reposted

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Q: Relation Between Gamma and Beta Function : B (p, q) = r(p)r(q) r(p+q)

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Q: Use the Euclidean algorithm to find the gcd of 161 and 119. Show your work.

A: Euclidean algorithm: Let and b are two numbers then there exists q and r such that  a=bq+r, 0≤r<q

Q: The set B = {2 + 2x², 4 − 3x + 4x², 19 − 9x + 18x²} is a basis for P₂. Find the coordinates of p(x)…

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Q: Solve the following Differential equations: (y3-2yx²) dx + (2xy² - x³)dy = 0

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Q: 4. Let T: R4 → R³ with T 0-1 = a. What is the domain of T'? C. b. What is the codomain of T'? x + 2y…

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Q: If f(x) = 7x-2 and g(x) = 4x - x2, determine the following: a. f(x) o g(x) Answer (a):

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Q: # 3 Rigid Motions for Congruence: Translations, Reflections, and Rotations y₁ -6- 5- -4 ·3· N 1 -6…

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Q: - Determine whether the series is convergent or divergent. (-2)" nn 8 n=1

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Q: Classify the following sequences: (i)     6.5, 9.75, 13, 16.35,…….. (ii)    4, 8, 16, 33,………

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Q: Find the centroid of the region W lying above the sphere x² + y² + z² = 30 and below the paraboloid…

A: Given the sphere x2+y2+z2=30 and below the paraboloid z=18-x2-y2. And the density of δx, y, z=1.