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Home Question Bank Math Pre Calculus Archive 2024 December 17

Pre-calculus Questions from Dec 17,2024

Browse the Pre-calculus Q&A Archive for Dec 17,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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En los ejercicios siguientes, esbozar la curva representada por las ecuaciones paramétricas, indicando su sentido de desarrollo, y escribir la ecuación rectangular correspondiente, eliminando el parámetro: \( x=3 t-1, \quad y=2 t+1 \) \( \sqrt {\sqrt [3]{79}.}\frac{\pi }{2}\div (2^{2})^{9^{2^{\pi .85^{2}}}}= \) The annual amount of energy produced in a country from dry natural gas (in trillion cubic feet) can be approximated by the function \( g(t)=18.6(1.034)^{t} \), where \( t=10 \) corresponds to the year 2010 . (a) Find the amount of dry natural gas energy produced in 2020 . (b) If the model continues to be accurate, project the amount of dry natural gas energy produced in 2026 . (a) The amount of dry natural gas energy produced in 2020 was \( \square \) trilion cubic feet. (Round to two decimal places as needed.) (b) If the model continues to be accurate, the amount of dry natural gas energy that will be produced in 2026 is trillion cubic feet. (Round to two decimal places as needed.) The annual amount of energy produced in a country from dry natural gas (in trilion cubic feet) can be approximated by the function \( 9(t)=18.6(1.034)^{\prime} \), where \( 1=10 \) corresponds to the year 2010 . (a) Find the amount of dry natural gas energy produced in 2020 . (b) If the model continues to be accurate, project the amount of dry natural gas energy produced in 2026 . (a) The amount of dry natural gas energy produced in 2020 was \( \square \) trilion cubic feet. (Round to two decimal places as needed.) (b) If the model continues to be accurate, the amount of dry natural gas energy that will be produced in 2026 is \( \square \) trilion cubic feet. (Round to two decimal places as needed.) Express \( 13.5^{\circ} \) in terms of radians. a \( \frac{2430}{\pi} \) b \( 2430 \pi \) c \( \frac{3 \pi}{80} \) d \( \frac{3 \pi}{40} \) Find two different parametric representations for the equation of the parabola. \( y=x^{2}-4 x+8 \) (a) Let one parametric equation be \( x=t \). Find the parametric equation for y . \( \mathrm{y}=\square \) for t in \( (-\infty, \infty) \) (b) Let one parametric equation be \( \mathrm{x}=\mathrm{t}+2 \). Find the parametric equation for y . \( \mathrm{y}=\square \) for t in \( (-\infty, \infty) \) (Simplify your answer.) Find the following product, and write the product in rectangular form. \[ \left(\sqrt{3} \text { cis } 60^{\circ}\right)\left(\sqrt{3} \text { cis } 210^{\circ}\right) \] \( \left(\sqrt{3}\right. \) cis \( \left.60^{\circ}\right)\left(\sqrt{3}\right. \) cis \( \left.210^{\circ}\right)=\square \) (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Type your answer in the form a bi.) Find the following product, and write the product in rectangular form. \[ \left[8\left(\cos 270^{\circ}+i \sin 270^{\circ}\right)\left[7\left(\cos 120^{\circ}+i \sin 120^{\circ}\right)\right]\right. \] \( \left[8\left(\cos 270^{\circ}+i \sin 270^{\circ}\right)\right]\left[7\left(\cos 120^{\circ}+i \sin 120^{\circ}\right)\right]=\square \) (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Type your answer in the form a + bi.) Write the complex number in trigonometric form \( r(\cos \theta+i \sin \theta) \), with \( \theta \) in the interval \( \left[0^{\circ}, 360^{\circ}\right) \). \( 6 i \) \( 6 i=\square\left(\cos \square^{\circ}+i \sin \square^{\circ}\right) \) Exercice \( \mathrm{n}^{\circ} 5 \) Soit la suite \( \left(u_{n}\right) \) définie par \( u_{0}=6 \) et, pour tout entier naturel \( n, u_{n+1}=\frac{3}{2} u_{n} \). 1 Donner la formule explicite de \( u_{n} \). En déduire la valeur exacte puis arrondie à l'unité de \( u_{11} \).
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