IDZ Ryabushko 4.2 Variant 8
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№1 Build surfaces and determine their type a) 4x2 - 5y2 - 5z2 + 40 = 0; b) y = 5x2 + 3z2.
№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) 3x2 - 5z2 = 15; Oz b) z = - 1; y = 3; Ox.
№3 Build a body bounded by the indicated surfaces: a) y = 2x; y = 0; x = 2; z is xy; z = 0.
b) x2 + y2 = z2; 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) 3x2 - 5z2 = 15; Oz b) z = - 1; y = 3; Ox.
№3 Build a body bounded by the indicated surfaces: a) y = 2x; y = 0; x = 2; z is xy; z = 0.
b) x2 + y2 = z2; x2 + y2 = 1; y ≥ 0; z ≥ 0.
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