IDZ Ryabushko 4.2 Variant 4
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№1 Build surfaces and determine their type a) 4 x2 - 8y2 + z2 + 24 = 0; b) x2 - y = - 9z2.
№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) 3y2 - 4z2 = 12; Oz b) y = 4; z is 2; Ox.
№3 Build a body bounded by the indicated surfaces: a) z = 5y; x2 + y2 = 16; z = 0.
b) x + y + z = 5; 3x + y = 5; 2x + y = 5; 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) 3y2 - 4z2 = 12; Oz b) y = 4; z is 2; Ox.
№3 Build a body bounded by the indicated surfaces: a) z = 5y; x2 + y2 = 16; z = 0.
b) x + y + z = 5; 3x + y = 5; 2x + y = 5; y = 0; z = 0.
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