Home Question Bank Math Pre Calculus

Pre Calculus Homework Help

Pre-calculus serves as an intermediary step between algebra and calculus, covering advanced topics like trigonometry, functions and limits. Precalculus plays an essential... Load more Hide more

error msg

Questions

On étudie un groupe de 3000 sportifs qui pratiquent soit l'athlétisme dans le club A, soit le basketball dans le club B. En 2023, le club A compte 1700 membres et le club B en compte 1300. On décide de modéliser le nombre de membres du club A et du club B respectivement par deux suites a_{n} et b_{n}, où n désigne le rang de l'année à partir de 2023. L'année 2023 correspond au rang 0 . On a alors a_{0}=1700 et b_{0}=1300. Pour notre étude, on fait les hypothèses suivantes : - durant l'étude, aucun sportif ne quitte le groupe; - chaque année, 15% des sportifs du club A quittent ce club et adhèrent au club B; - chaqueannée, 10% des sportifs du club B quittent ce club et adhèrent au club A. 1) Calculer les nombres de membres de chaque club en 2024 . 2) Pour tout entier naturel n, déterminer une relation liant a_{n} et b_{n}. 3) Montrer que la suite a_{n} vérifie la relation suivante pour tout entier naturel n : a_{n+1}=0,75 a_{n}+300 4) a) Démontrer par récurrence que pour tout entier naturel n, on a: 1200 leq a_{n+1} leq a_{n} leq 1700. b) En déduire que la suite a_{n} converge. 5) Soit v_{n} la suite définie pour tout entier naturel n par v_{n}=a_{n}-1200. a) Démontrer que la suite v_{n} est géométrique. b) Exprimer v_{n} en fonction de n. c) En déduire que pour tout entier naturel n, a_{n}=500 * 0,75^{n}+1200 . 6) a) Déterminer la limite de la suite a_{n}. b) Interpréter le résultat de la question précédente dans le contexte de l'exercice.
Feb 02, 2025

Exploring Precalculus: Functions, Equations, and More

What is Precalculus?

Building a firm basis in algebra and trigonometry, precalculus is an essential course ready for study of calculus. It emphasizes on learning algebraic expressions, functions, and several mathematical ideas required for grasp of calculus. We examine closely subjects such polyn functions, logarithms, trigonometric identities, and sequences. Precalculus basically fills in for algebra and calculus, arming students with the tools they need to succeed in more complex mathematical classes.

What is 'x' in Precalculus?

In precalculus, 'x' is typically used as the independent variable in functions, equations, and formulas. It represents an input value that can vary within a specified domain. For example, in the function \(y = f(x) = 2x\), 'x' is the value you plug into the function, and it determines the corresponding 'y' value, which is the dependent variable. Mastering how to manipulate and solve for 'x' is crucial for progressing to calculus, where you'll use 'x' in more complex equations and scenarios, such as finding derivatives and integrals.

Can the Area Model Be Used in Precalculus?

Yes, the area model can be a useful tool in precalculus, especially when working with polynomial functions and visualizing multiplication. It helps break down complex expressions into manageable parts, aiding in the simplification and factorization of algebraic expressions. For instance, when dealing with quadratic functions or expanding binomials, the area model provides a visual representation of how terms are multiplied and combined. While more commonly associated with earlier algebra courses, the area model’s principles still play a role in understanding higher-level precalculus concepts.

How Can UpStudy Precalculus Homework Bank Help You?

The UpStudy Precalculus Homework Bank is an excellent resource for students seeking to grasp precalculus fundamentals. It combines real homework questions submitted by students from various schools, ensuring that you're practicing with issues that are similar to the topic you'll experience in your courses and exams. Whether you're working on polynomial equations, trigonometric identities, or function transformations, the Homework Bank provides a variety of practice problems, step-by-step answers, and extensive explanations. This boosts confidence, improves problem-solving abilities, and helps students prepare for assignments, tests, and, finally, calculus.
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy