📘 MATHEMATICS

1. Vous souhaitez comprendre la mathématique pure en profondeur, ce qui est un objectif admirable. 2. La mathématique pure étudie les structures, les relations et les objets abstra

1. **Stating the problem:** We are given sequences of numbers and corresponding patterns. We need to complete the tables, construct the number sequences for the patterns, and state

1. The question asks about the topic in mathematics related to the previous problem or discussion. 2. Since the previous context is not provided here, generally, identifying the to

1. **Problem:** Calculate the height of a tree given two angles of elevation from points P and Q, where Q is 5 m closer to the tree than P. 2. **Formula:** Use the tangent function

1. Let's start by understanding the key concepts related to polynomial functions and circles as described. 2. For polynomial functions, these are expressions involving variables ra

1. The problem asks to classify the number 0 among the given options: (a) positive integer, (b) rational number, (c) singular, (d) binary set. 2. Let's analyze each option:

1. The problem is to identify and show only even numbers. 2. An even number is any integer divisible by 2 without a remainder.

1. The problem asks: Is 0 a number? 2. In mathematics, a number is a mathematical object used to count, measure, and label.

1. **Problem 2.1:** Determine if the statement "In a right-angled triangle, the hypotenuse is the longest side and is opposite to the right angle" is True or False. - In a right-an

1. Знайти область визначення функцій: 1.a) Функція: $$y = \sqrt{\frac{3 - x}{4x^2 - 9x - 13}}$$

1. The problem is to understand how to use Desmos 3D to find three solutions to a given problem. 2. Desmos 3D is a tool for visualizing functions and equations in three dimensions,

1. The problem is to understand the concept of the number system. 2. A number system is a writing system for expressing numbers; it is a mathematical notation for representing numb

1. Masala: 6 ta nuqta berilgan, uchtasi bir to‘g‘ri chiziqda yotmaydi. Nechta turlicha to‘g‘ri chiziq o‘tkazish mumkin? Formulasi: $\binom{n}{2} = \frac{n(n-1)}{2}$, chunki har bir

1. Énoncé du problème : Complétons les phrases mathématiques données. 2. Première phrase : "Toute fonction f continue et strictement croissante sur un intervalle K définit ........

1. **Function Definition:** A function is a relation where each input has exactly one output. It is often written as $f(x)$, where $x$ is the input and $f(x)$ is the output. 2. **E

1. **Integers:** Simplify the expression $-5 + 12 - 7 + (-3)$. 2. **Expressions:** Expand and simplify $3(x + 4) - 2(2x - 5)$.

1. **Problem:** Determine if $P \lor (P \leftrightarrow Q) \lor Q$ is a tautology or contradiction using a truth table. **Step 1:** Recall that a tautology is always true, and a co

1. **Problem:** Determine if the statement $P \lor (P \leftrightarrow Q) \lor Q$ is a tautology or contradiction using a truth table. 2. **Problem:** Calculate the cross product of

1. **Problem:** Understand the types of numbers and their properties. 2. **Types of Numbers:**

1. Let's clarify the use of actual mathematical symbols in explanations. 2. When writing math, we use symbols like $+$, $-$, $\times$, $\div$, $=$, $\sqrt{}$, $\frac{}{}$, and vari

1. Let's start by understanding what "number" means in math. Numbers are symbols used to represent quantities or values. 2. There are different types of numbers: natural numbers (1