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Home Question Bank Math Pre Calculus Archive 2024 December 14

Pre-calculus Questions from Dec 14,2024

Browse the Pre-calculus Q&A Archive for Dec 14,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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El número de manzanas que produce cada árbol en una huerta depende de la densidad de árboles plantados. Si se plantan \( n \) árboles en un terreno determinado, entonces cada árbol produce \( 900-9 n \) manzanas. a) ¿Cuántos árboles deben plantarse en el terreno para obtener una producción máxima de manzanas? b) ¿Cuál es la cantidad máxima de manzanas que pueden producirse? Find the indicated power using de Moivre's Theorem. (Express your fully simplified answer in the form \( a+b i \).) \[ (3+\sqrt{3} i)^{4} \] 1 Find the product \( z_{1} z_{2} \) and the quotient \( \frac{z_{1}}{z_{2}} \). Express your answers in polar form. \[ z_{1}=\sqrt{5}\left(\cos \left(\frac{5 \pi}{3}\right)+i \sin \left(\frac{5 \pi}{3}\right)\right), \quad z_{2}=8 \sqrt{5}\left(\cos \left(\frac{3 \pi}{2}\right)+i \sin \left(\frac{3 \pi}{2}\right)\right) \] \( z_{1} z_{2}=\square \) \( \frac{z_{1}}{z_{2}}=\square \) Check your radius. Check your radius. Find the product \( z_{1} z_{2} \) and the quotient \( \frac{z_{1}}{z_{2}} \). Express your answers in polar form. \[ z_{1}=\frac{8}{9}\left(\cos \left(40^{\circ}\right)+i \sin \left(40^{\circ}\right)\right), \quad z_{2}=\frac{1}{9}\left(\cos \left(160^{\circ}\right)+i \sin \left(160^{\circ}\right)\right) \] \( z_{1} z_{2}=\square \) \( \frac{z_{1}}{z_{2}}=\square \) A mente Determina il dominio delle seguenti funzioni. Deco \( y=2 x^{3}-\frac{1}{2} x+1 \) What is the value of \( e^{\ln 7 x} \) ? 1 \( 7 e \) \( 7 x \) 7 0 What is the domain of the function \( y=\ln \left(\frac{-x+3}{2}\right) \) ? \( \begin{array}{l}x<2 \\ x>2 \\ x<3 \\ x>3\end{array} \) \begin{tabular}{l} Exercice 2 \\ \hline Soit \( f \) la fonction numérique définie par \\ \( f(x)=|x-1|+|x+1| \) \\ 1) Etudier la parité de la fonction \( f \) \\ 2) Vérifier que \( \forall x \in \mathbb{R} f(x) \geq 2 \) \\ 3) Résoudre l'équation \( f(x)=2 \) et déduire une valeur \\ minimale de la fonction \( f \) sur \( \mathbb{R} \)\end{tabular} \begin{tabular}{l} Exercice 2 \\ \hline Soit \( f \) la fonction numérique définie par \\ \( f(x)=|x-1|+|x+1| \) \\ 1) Etudier la parité de la fonction \( f \) \\ 2) Vérifier que \( \forall x \in \mathbb{R} f(x) \geq 2 \) \\ 3) Résoudre l'équation \( f(x)=2 \) et déduire une valeur \\ minimale de la fonction \( f \) sur \( \mathbb{R} \)\end{tabular} 8. \( \operatorname{Graph} g(x)=f(x-2)+1 \)
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