🧮 algebra

1. Problema cere să calculăm suma seriei infinite $$S = \sum_{n=1}^\infty \frac{2n - 1}{7^n}$$ cu o eroare mai mică de $$10^{-4}$$. 2. Observăm că seria este o sumă de termeni care

1. **Problem Statement:** Find the value of $n$ in each of the following equations from question 8. 2. **Recall the exponential rules:**

1. **State the problem:** We are given the exponential population model $$A = 663.8e^{0.024t}$$ where $A$ is the population in millions and $t$ is the number of years after 2003. W

1. Problem: Find the value of $n$ in each of the following exponential equations. 2. Formula: For equations of the form $a^n = b$, rewrite $b$ as a power of $a$ if possible, then e

1. Let's start by understanding that you asked for a clear explanation to help you understand a math problem. 2. Since you did not specify a particular problem, I will explain a co

1. The problem involves analyzing a given graph of a function $f$ and answering questions about values, domain, range, and intervals of increase. 2. (a) To find $f(-1)$, locate $x

1. **Problem statement:** (a)(i) A furniture salesman earned 36200 last year and paid 22% tax. Find how much was left after tax.

1. Stating the problem: Solve the equation $8x + 3x = 12 \times 2x$ for $x$. 2. Combine like terms on the left side: $8x + 3x = 11x$.

1. The problem asks to solve part c from the previous context, but since the previous parts are not provided, I will assume part c involves solving an algebraic expression or equat

1. **State the problem:** We need to compute $\log_{\frac{1}{8}} 6$ using the change of base formula and round the answer to the nearest thousandth. 2. **Recall the change of base

1. **Problem Statement:** Find the canonical equations of the straight line defined by the system of planes: $$\begin{cases} 3x + y + z - 2 = 0 \\ 2x - y - 3z + 6 = 0 \end{cases}$$

1. The problem asks to rewrite the mixed number \(1 \frac{1}{4}\) as an improper fraction. 2. A mixed number consists of a whole number and a fraction. To convert it to an improper

1. The problem is to calculate $\frac{15}{32} \times 4$. 2. The formula for multiplying a fraction by a whole number is:

1. **Stating the problem:** A box contains 4 bags of sugar. We want to find the total amount of sugar in the box if each bag contains a certain amount of sugar. 2. **Formula used:*

1. The problem asks to solve for each of the ratios mentioned in the data inside the link. Since the link data is not provided, I will explain how to solve for ratios generally. 2.

1. **State the problem:** Solve the equation $\tan x + 1 = 0$ using the Regula Falsi method. 2. **Rewrite the equation:** We want to find $x$ such that $f(x) = \tan x + 1 = 0$.

1. The problem states that $x = 0.999999\ldots$ and asks about the equality $0.999999\ldots = \frac{9}{9}$ and whether $\frac{9}{9} = 1$.\n\n2. First, note that $\frac{9}{9} = 1$ b

1. **State the problem:** We are given the function $f(x) = 3x^{2} - 6x$ and want to analyze it. 2. **Formula and rules:** This is a quadratic function of the form $ax^{2} + bx + c

1. Énonçons le problème : Résoudre l'exercice 14 (sans détails supplémentaires, supposons qu'il s'agit d'une équation algébrique classique). 2. Formule et règles importantes : Pour

1. **Énoncé du problème :** Montrer que la famille $B = (u_1, u_2, u_3)$ avec $u_1 = (1,0,1)$, $u_2 = (0,1,1)$, $u_3 = (1,1,0)$ est une base de $\mathbb{R}^3$. 2. **Rappel de la dé

1. **Énoncé du problème :** Dans $\mathbb{R}^3$ muni de la base canonique $B = (e_1, e_2, e_3)$, on définit $u_1 = (1,0,1)$, $u_2 = (0,1,1)$ et $u_3 = (1,1,0)$. Montrer que $B' = (