IDZ Ryabushko 4.2 Variant 6
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№1 Build surfaces and determine their type a) z = 8 - x2 - 4y2; b) 4x2 + 9y2 + 36z2 = 72.
№2 Write down the equation and determine the type of surface obtained by rotating this line around the specified coordinate axis, make a picture: a) 2x2 - 6y2 = 12; Ox; b) y2 = 4z; Oz.
№3 Build a body bounded by the indicated surfaces: a) y = x; y = 0; x is 1; z is x2 + 5y2; z = 0.
b) x2 + y2 + z2 = 9; x2 + y2 ≤ 1; x ≥ 0.
№2 Write down the equation and determine the type of surface obtained by rotating this line around the specified coordinate axis, make a picture: a) 2x2 - 6y2 = 12; Ox; b) y2 = 4z; Oz.
№3 Build a body bounded by the indicated surfaces: a) y = x; y = 0; x is 1; z is x2 + 5y2; z = 0.
b) x2 + y2 + z2 = 9; x2 + y2 ≤ 1; x ≥ 0.
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