Math Problem Statement

1. Riešte maticovú rovnicu s neznámou maticou X: ( 2 -1 ) ( 0 3 ) * X = ( -1 4 ) ( 0 -3 ) 2. Načrtnite graf funkcie y = sin(x) + 1 pre x ∈ [-π/2, π/2] a y = log₂(|x|) + 5, určte ich D(f), H(f), vlastnosti ako párnosť, nepárnosť, ohraničenosť z dola a zhora. 3. Vyšetrite priebeh funkcie: y = 2x + 8/x + 2. 4. Napíšte parametrické rovnice priamej danej ako priesečnica dvoch rovín: 3x - 2y + z - 2 = 0 a 4x + y - 3z - 2 = 0. 5. Načrtnite kužeľosečku y² - 10x - 2y - 19 = 0.

Solution

This image appears to contain a set of mathematical tasks. Here's a breakdown of the questions:

  1. Solve the matrix equation with the unknown matrix X:

    2 & -1 \\ 0 & 3 \end{pmatrix} \times X = \begin{pmatrix} -1 & 4 \\ 0 & -3 \end{pmatrix}$$
  2. Plot the graph of the function: y=sin(x)+1forx[π2,π2]y = \sin(x) + 1 \quad \text{for} \quad x \in \left[ -\frac{\pi}{2}, \frac{\pi}{2} \right]

  3. Plot the function: y=2x+8x+2y = 2x + \frac{8}{x} + 2

  4. Write parametric equations of the line given by the intersection of two planes: 3x2y+z2=0and4x+y3z2=03x - 2y + z - 2 = 0 \quad \text{and} \quad 4x + y - 3z - 2 = 0

  5. Find the equation of the curve: y210x2y19=0y^2 - 10x - 2y - 19 = 0

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Math Problem Analysis

Mathematical Concepts

Matrix equations
Trigonometric functions
Logarithmic functions
Parametric equations
Conic sections

Formulas

Matrix multiplication
y = sin(x) + 1
y = log₂(|x|) + 5
y = 2x + 8/x + 2
y² - 10x - 2y - 19 = 0

Theorems

Properties of trigonometric functions
Logarithmic function properties
Conic sections analysis
Matrix solution methods

Suitable Grade Level

Grades 10-12