Option 13 IDZ 4.2

Task №1.13

Construct surfaces and determine their type:

1. a) –16x² + y² + 4z² – 32 = 0;

The surface has the shape of an ellipsoid.

b) 6x² + y² -3z² = 0;

The surface has the form of an elliptical paraboloid.

Task #2.13

Write down the equation and determine the type of surface obtained by rotating this line around the specified coordinate axis, make a drawing:

1. а) z² = 2y; Yes;

then the equation describes a parabolic cylinder.

b) 2x² +3z² = 6; Oz.

then the equation describes an elliptic paraboloid.

Task №3.13

Construct a body bounded by the specified surfaces:

1. a) y = x; y = 0; x = 2; z = 0.

then the equation describes a pyramid with a triangular base.

б) x + y = 2; z = 2x; z = 0.

then the equation describes a triangular pyramid with the top cut out.

Option 13 IDZ 4.2

The digital goods store offers a digital product called "Option 13 IDZ 4.2". This product represents mathematical modeling problems that can be used as homework for students of mathematical specialties. Each option contains several problems of varying complexity that allow you to test your understanding of the material and develop problem-solving skills in mathematical modeling.

• Option 13 of IDZ 4.2 includes tasks on constructing surfaces and determining their type, tasks on finding equations of surfaces, tasks on constructing bodies bounded by given surfaces.
• The tasks of this digital product are suitable for students of many mathematical specialties, including mathematics, physics, computer science, etc.
• All problems in the product are provided with detailed solutions, which allows students to better understand the material and check their answers.

"Option 13 IDZ 4.2" is a digital product that contains mathematical modeling tasks for students of mathematical specialties. It contains tasks on constructing surfaces and determining their type, finding equations for surfaces and constructing bodies bounded by given surfaces. Each option contains several problems of varying complexity, equipped with detailed solutions.

Option 13 of IDZ 4.2 includes three tasks. The first task requires constructing an ellipsoid and an elliptic paraboloid and determining their type. The second task requires writing down the equations of surfaces obtained by rotating lines around the specified coordinate axes and determining their type. The third task requires constructing a body bounded by the specified surfaces.

The tasks of this digital product are suitable for students of various mathematical specialties, such as mathematics, physics and computer science. Solving problems helps test understanding of material and develop problem-solving skills in mathematical modeling.

The digital product "Option 13 IDZ 4.2" contains mathematical modeling tasks for students of mathematical specialties. The option includes tasks on constructing surfaces and determining their type, tasks on finding equations of surfaces, tasks on constructing bodies bounded by given surfaces.

The first two tasks involve constructing surfaces and determining their appearance. In problem 1.13 it is required to construct an ellipsoid according to the equation -16x^2 + y^2 + 4z^2 - 32 = 0, and in problem 1.13 b) it is required to construct an elliptic paraboloid according to the equation 6x^2 + y^2 - 3z^2 = 0 .

In problem 2.13, you need to write down an equation and determine the type of surface obtained by rotating a given line around a specified coordinate axis and make a drawing. In problem 2.13 a) you need to write the equation of a parabolic cylinder obtained by rotating the line z^2 = 2y around the Oy axis, and in problem 2.13 b) you need to write the equation of an elliptic paraboloid obtained by rotating the hyperbola 2x^2 + 3z^2 = 6 around Oz axis.

Problem 3.13 requires constructing a body bounded by the specified surfaces. In problem 3.13 a) you need to build a pyramid with a triangular base, bounded by the planes y = x, y = 0, x = 2 and z = 0. In problem 3.13 b) you need to build a triangular pyramid with a cut out top, bounded by the planes x + y = 2 , z = 2x and z = 0.

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The product "Option 13 IDZ 4.2" is a set of problems in mathematical analysis and algebra for students of higher educational institutions. In this version, the tasks are related to constructing surfaces and determining their type, writing equations and determining the type of surfaces obtained by rotating lines around coordinate axes, as well as constructing bodies bounded by given surfaces.

Specifically, in this version the tasks are as follows:

1. Construct surfaces and determine their type: a) –16x2 + y2 + 4z2 – 32 = 0; b) 6x2 + y2 – 3z2 = 0;
2. Write down the equation and determine the type of surface obtained by rotating this line around the specified coordinate axis, make a drawing: a) z2 = 2y; Oy; b) 2x2 + 3z2 = 6; Oz.
3. Construct a body bounded by the specified surfaces: a) y = x; y = 0; x = 2; z = 0. (TYPO: no upper limit. NOT SOLVED) b) x + y = 2; ... ; z = 2x; z = 0.

The set of problems is intended to test students' knowledge in the field of mathematical analysis and algebra, as well as to develop skills in solving problems on constructing surfaces and bodies in three-dimensional space.

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