IDZ Ryabushko 4.2 Variant 21
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№1 Build surfaces and determine their type a) 9x2 - 6y2 - 6z2 + 1 = 0; b) 15y = 10y2 + 6y2.
№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) 15x2 - 3y2 = 1; Ox; b) x = 3; y = 4; Oz.
№3 Build a body bounded by the indicated surfaces: a) y = 3x; y = 0; x = 3; z is xy; z = 0.
b) 4 · (x2 + y2) = z2; 4 · (x2 + y2) = 1; y ≥ 0; z ≥ 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) 15x2 - 3y2 = 1; Ox; b) x = 3; y = 4; Oz.
№3 Build a body bounded by the indicated surfaces: a) y = 3x; y = 0; x = 3; z is xy; z = 0.
b) 4 · (x2 + y2) = z2; 4 · (x2 + y2) = 1; y ≥ 0; z ≥ 0.
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