📘 mathematics

1. The problem is to find the complete solution of a differential equation or algebraic expression (please specify the exact problem for precise solution). 2. Generally, the comple

1. Indices: Simplify $2^3 \times 2^4$. 2. Indices: Express $\frac{3^5}{3^2}$ in simplest form.

1. The problem is to provide the first 300,000 digits of the number pi ($\pi$). 2. Pi ($\pi$) is an irrational number, meaning it has an infinite number of non-repeating decimal di

1. The problem is to find the first 300,000 digits of the number $\pi$. 2. $\pi$ is an irrational number, meaning it has an infinite number of non-repeating decimal digits.

1. **Πρόβλημα:** Να χαρακτηρίσετε τις προτάσεις με Σωστό (Σ) ή Λάθος (Λ). 2. **Επεξήγηση:** Θα εξετάσουμε κάθε πρόταση βασιζόμενοι σε βασικές ιδιότητες ορίων, μονοτονίας, συνέχειας

1. You want to revise Year 9 math chapters 1 to 6. 2. Since this is a broad request, please specify a particular topic or problem from chapters 1 to 6 that you want help with.

1. **Definition of Term: Rational Numbers** Rational numbers are numbers that can be expressed as the quotient or fraction $\frac{p}{q}$ of two integers, where $p$ and $q$ are inte

1. **Definition of Term: Rational Numbers** Rational numbers are numbers that can be expressed as the quotient or fraction $\frac{p}{q}$ of two integers, where $p$ and $q$ are inte

1. **Problem Statement:** Order the given dissimilar fractions from smallest to largest (ascending) and from largest to smallest (descending) using models. 2. **Fractions to order:

1. The user requests answers rounded to 3 decimal points. 2. To round a number to 3 decimal places, identify the digit in the 4th decimal place.

1. Problem 3.4: Draw two straight lines on a grid of small squares to form two squares of different sizes and 4 rectangles. Step 1: Understand the problem. We need to draw two line

1. The problem is to understand the concept of "in number" which seems unclear. 2. If you meant to ask about the representation or properties of numbers, please specify the type of

1. Задачата: Намерете числото $x$, ако $2025 + x = 44 \cdot 46$. 2. Използваме формулата за умножение и решаваме уравнението:

1. The problem asks whether the statement "Statistics is the branch of Mathematics that deals with the collection, organization, presentation, analysis, and interpretation of data"

1. The problem is to understand the mathematical constant $e$ and its significance. 2. The number $e$ is an irrational constant approximately equal to 2.71828.

1. The problem asks: What is \( \varepsilon \)? 2. \( \varepsilon \) (epsilon) is a Greek letter commonly used in mathematics and science.

1. The problem involves three topics: Trigonometry, Indices, and Quadratics. 2. Let's start with Trigonometry: calculating angles using the tangent function, which relates the angl

1. **Problem 1a:** Prove by mathematical induction that $n(n+1)(2n+1)$ is divisible by 6 for all $n \in \mathbb{N}$. 2. **Base Case:** For $n=1$, $1\cdot 2 \cdot 3 = 6$ which is di

1. **Problem 2(a): Prove by induction that** $$\frac{1}{1\cdot 2} + \frac{1}{2\cdot 3} + \frac{1}{3\cdot 4} + \cdots + \frac{1}{n(n+1)} = \frac{n}{n+1}$$

1. **List the members of the following sets:** (i) Set: $\{x : x + 3 = 9\}$

1. Muammo: Uy bekasi 280 so‘mdan yong‘oq sotib oldi, tozalangach 70% qoldi. 1 kg tozalangan yong‘oq uchun qancha so‘m sarflangan? Formulasi: $\text{Narx per kg tozalangan} = \frac{