Let G be the solid in the first octant bounded by the sphere 2x? + 2y? + 2z? and the coordinate planes. Evaluate fSfc(x² + y? + z?)dV (a) using rectangular coordinates (b) using cylindrical coordinates (c) using spherical coordinates. 32

Q: O Write the parametric equations x = 2t – °, y = 9 – 4t iven Cartesian form.

A: We have to write the given parametric equations into cartesian form

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Q: 16-y Convert (z² + y² + z²)dzdrdy into spherical coordinates.

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Q: osen y

A: Is it sen y =x

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Q: A sphere, Si is given by the equation: r? + y² + 22 – 2x – 4y + 8z + 17 = 0 (a) Write the equation…

A: (a) Consider the given information. x2+y2+z2-2x-4y+8z+17=0 Now, write the equation in the standard…

Q: the center and radius for each. z' + y? = 49 +y? = 324 2² + (y + 2)° = 64 (x+ 2) + y? 64 (z – 5) +…

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Q: Find the point on the sphere x +y +z = 4 farthest from the point (1, – 1,1). The point is ( ID:…

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Q: 91 a) Find an equation of the sphere with center (1,-3,-5) and tangent to xz-plane.

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Q: 5 25- y² 50-g² –y² Convert (x² + y² + z²)dzdædy into spherical coordinates. ²+y² 5/2 pª cos ødpdød0…

A: Answer:We have to convert∫50∫25-y20∫50-x2-y2x2+y2x2+y2+z2 dzdxdy into sphercal coordinates∵0≤y≤5…

Q: Evaluate by changing to spherical coordinates: /2–x²-y² xydzdydx x²+y2

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Q: a) Find an equation of the sphere with center (1.-3,-5) and tangent to xz-plane.

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Q: (b) Let w = 1+ j. Determine w giving your answer in rectangular form.

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Q: c. Find the distance from Po = (3,9, 6) to the plane 3.x + 4y – 5 = 0.

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Q: Which of the following point is the farthest point on the sphere z? + y² + z² = 4 from the point…

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Q: Find the area of the triangle formed by the points A = (3, –1, 2), B = (1, 1, 0), and C = (1,2,–1).

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Q: Find an equation of the line, and write it in (a) slope-intercept form if possible and (b) standard…

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