IDZ Ryabushko 4.2 Option 11

No. 1. It is necessary to construct surfaces and determine their type: a) x² – 7y² – 14z² – 21 = 0; b) 2y = x² + 4z².

No. 2. It is necessary to write down the equation and determine the type of surface obtained by rotating this line around the specified coordinate axis and draw a picture: a) x² = –4z; 0z; b) y² + 4z² = 4; Oy.

No. 3. It is necessary to construct a body limited by the indicated surfaces: a) y = x; y = 0; x = 1; z = 3x² + 2y²; z = 0. b) z = 10·(x² + y²) + 1; z = 1 – 20y.

IDZ Ryabushko 4.2 Option 11

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IDZ Ryabushko 4.2 Option 11 is a product containing mathematics tasks for schoolchildren and students. It includes problems on various topics such as algebra, geometry, calculus and probability. The assignments also contain requirements for constructing surfaces and determining their type, writing equations and determining types of surfaces, as well as constructing bodies bounded by the specified surfaces. IDZ Ryabushko 4.2 Option 11 is intended for independent work and preparation for exams, and can be useful for improving understanding of the material and developing skills in solving complex mathematical problems.

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IDZ Ryabushko 4.2 Option 11 is a set of problems in mathematical analysis and analytical geometry. Tasks include constructing surfaces, determining their type, writing equations for surfaces when rotating a line around coordinate axes, and constructing bodies bounded by given surfaces.

In the first problem, you need to construct two surfaces given by the equations x^2 – 7y^2 – 14z^2 – 21 = 0 and 2y = x^2 + 4z^2, and determine their appearance.

In the second problem, it is necessary to write down equations and determine the type of surfaces obtained by rotating a given line around the specified coordinate axes.

In the third problem, it is necessary to construct bodies bounded by given surfaces, which are given by equations.

To complete the tasks, it is recommended to use knowledge of analytical geometry, in particular, constructing surfaces in space, determining their type, finding the equations of surfaces when rotating a line around coordinate axes, as well as knowledge of mathematical analysis, in particular, constructing bodies bounded by given surfaces.

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