Question: why are they randomly adding 1/4 d. To identify this surface, convert the equation from spherical to rectangular coordinates, using equations y = p sin

why are they randomly adding 1/4

d. To identify this surface, convert the equation from spherical to rectangular coordinates, using equations y = p sin w sin 0 and p2 = x2 + y2 + 22: p = sin 9 sin (p p2 = p sin 9 sin (p Multiply both sides of the equation by p. x2 + y2 + 22 = 3/ Substitute rectangular variables using the equatio x2 + y2 y + z2 = O Subtract y from both sides of the equation. x2 + y2 y + i + 22 = % Complete the square. x2 + (y i) 2 + 22 = % Rewrite the middle terms as a perfect square. The equation describes a sphere centered at point (0, %, 0) with radius %
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