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Home Question Bank Math Pre Calculus Archive 2024 December 16

Pre-calculus Questions from Dec 16,2024

Browse the Pre-calculus Q&A Archive for Dec 16,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Find the center, transverse axis, vertices, foci, and asymptotes. Graph the following equation. \( \frac{(x-2)^{2}}{4}-\frac{(y+3)^{2}}{9}=1 \) 9. \( y=\frac{\sqrt{x-3}}{\sqrt{x-6}} \quad \) Domain: \( 1- \) Use the sketch below to determine the domain and range of the function \( y=5-\frac{12}{x} \). Give your answer in interval notation. 2. On a observé qu'une forêt \( A \) perdait \( 6 \% \) de sa surface tous les 4 ans. Aujourd'hui, cette forêt \( A \) compte une surface de 250 hectares. Une enquête réalisée il y a 6 ans montre que la surface la forêt \( B \) était alors de 200 hectares. Aujourd'hui, elle s'étend encore sur 188 hectares. On suppose que la surface de ces forêts diminue de rnanière exponentielle. a) Etablir la fonction \( A(t) \) qui représentent la surface de la forêt \( A \) au temps \( t \) ( \( t \) exprimé en années). b) Etablir la fonction \( B(t) \) qui représentent la surface de la forêt \( B \) au temps \( t \) ( \( t \) exprimé en années). c) Quelle surface (arrondir à l'hectare) devrait occuper la forêt \( A \) dans 12 ans ? d) Pendant combien d'années encore la surface de la forêt \( A \) sera supérieure à celle de la forêt \( B \) ? e) Quel est le pourcentage annuel de déforestation de la forêt \( A \) ? If \( f(x) \) and \( g(x) \) are inverse functions of each other, which of the following shows the graph of \( f(g(x)) ? \) A company charges Rs. 6000 for a television set on orders of 50 or less sets. The charge is reduced on every set by Rs. 75 per set for each set ordered in excess of 50 . Find the largest size order the company should allow to receive a maximum revenue. The function \( y=\left(\frac{1}{2}\right)^{x} \) is the parent function of which of the following? (1 point) \( \begin{array}{l}f(x)=-(2)^{x} \\ f(x)=-5\left(\frac{1}{2}\right)^{x} \\ f(x)=-5 x^{2} \\ f(x)=x^{\frac{1}{2}}\end{array} \) On considère les fonctions \( f \) et \( g \) de \( \mathbb{R} \) vers \( \mathbb{R} \), telles que : \( f(x)=\frac{x+2}{x-1} \) et \( g(x)=\frac{1}{2} x^{2}-2 \) Compare \( f \) et \( g \). QUESTION 3 The equation of a hyperbola is geven by \( f(x)=\frac{3}{1-7}-4 \) Write downt the equation of the new function that is formed when \( f \) is transformed as follows \( \begin{array}{ll}3.1 & \text { Shift two units to the left } \\ 3.2 & \text { Shift } 3 \text { units up } \\ 3.3 & \text { Shift } 1 \text { unit right and } 2 \text { units down } \\ 3.4 & \text { The equation of the new hyperbola has new asymptotes at } x=-4 \text { and } y=-1\end{array} \) Find the following product, and write the product in rectangular form, \[ \left[6\left(\cos 270^{\circ}+i \sin 270^{\circ}\right)\right]\left[5\left(\cos 240^{\circ}+i \sin 240^{\circ}\right)\right] \] \( \left[6\left(\cos 270^{\circ}+i \sin 270^{\circ}\right)\right]\left[5\left(\cos 240^{\circ}+i \sin 240^{\circ}\right)\right]=\square \) (Simplify your answer, including any radicals. Use integers or fractions for any numbe
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