9- The circle a² + (y-2a)²-4a² is rotated about the line y--1 where a > 0. A torus is obtained from this rotation. Determine a if the surface area of the obtained torus is 24m2. (Use Pappus Theorem). a)a= 2 b)a=1 c)a=3 d)a <=4 e) None

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Q: find the center and the radius of the circle  a)x^2 +(y+2)^2 =16   b) 2x^2+2y^2-4x+8y-14=0

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A: We will find the value of a.

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A: Claim: for 0≤x≤1, f(x) = x⁴+(1-x)⁴ is minimum when x = 1/2  Proof: f(x) = x⁴+(1-x)⁴  So, f'(x) = 4x³…

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A: To draw an example of two lines that illustrates the Spherical Geometry Parallel Postulate.

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A: We have to solve given Questions.

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A: Given,  Let origine is at point O Coordinate of vertex A is ( 0 , 5 )  So,  OA = 5

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A: NOTE: Since we can solve only three subparts of a question, we have solved the first three question.…

Q: The sphere x² + 10x + y² + 8y + z² - 2z = 34 is centered at the point (a, b, c). Find abc, the…

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A: Volume of the sphere x2+y2+z2=16 or x2+y2=16-z2 is: V=∫z=12∬x2+y2≤16-z2dxdydz   =∫z=12π16-z2dz…