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Home Question Bank Math Pre Calculus Archive 2024 December 10

Pre-calculus Questions from Dec 10,2024

Browse the Pre-calculus Q&A Archive for Dec 10,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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\( x=\ln \left(\sqrt{y^{2}-1}-y\right) \) where \( -\frac{e^{2}+1}{2 e} \leq y \leq-1 \) \( y=\sqrt{-62-x^{2}+16 x}+\frac{14}{3} \) where \( 7 \leq x \leq 9 \) The total amount spent by some number of people on clothing and footwear in the years \( 2000-2009 \) can be modeled by the quadratic function \( f(x)=-4.675 x^{2}+71.83 x+97.49 \), where \( x=0 \) represents January \( 1,2000, x=1 \) represents January 1,2001 , and so on, and \( f(x) \) is in billions of dollars. According to the model, in what year during this period was the amount spent on clothing and footwear a maximum? In the year \( \square, \$ \square \) billion was spent on clothing and footwear. (Round the final answer for the amount spent to the nearest whole number as needed. Round all intermediate values to the nearest tenth as needed.) The total amount spent by some number of people on clothing and footwear in the years 2000-2009 can be modeled by the quadratic function \( f(x)=-4.675 x^{2}+71.83 x+97.49 \), where \( x=0 \) represents January \( 1,2000, x=1 \) represents January 1,2001 , and so on, and \( f(x) \) is in billions of dollars. According to the model, in what year during this period was the amount spent on clothing and footwear a maximum? \( y=\sqrt{20 x-x^{2}}+2 \) where \( 5 \leq x \leq 20 \) 1. Realiza las siguientes graficas de las funciones racionales, con valores para \( x \) de -6 a 6 , indica el dominio \( y \) el rango de las funciones indica los puntos donde la función crece \( y \) decrece, \( y \) los puntos de las asintotas. 1) \( f(x)=\frac{x}{\left(x^{2}-1\right)} \) 2) \( f(x)=\frac{x^{2}+1}{x+1} \) 3) \( f(x)=\frac{x^{2}-1}{\left(x^{2}+2\right)\left(x^{2}+3\right)} \) Determine the domain and restricted values of \( f(x)=\frac{4}{x^{3}-9 x} \) Given \( f(x)=\sqrt{2 x} \) and \( g(x)=3 x+4 \). After simplifying, a) \( (f \circ g)(x)=\square \) b) \( (g \circ f)(x)=\square \) Sketch the graph of each of the following functions. Find any intercepts and give the coordinates of the vertex in each case. 0. \( f(x)=-x^{2}+2 x+3 \) The number of bacteria \( P(h) \) in a certain population increases according to the following function, where time \( h \) is measured in hours. \[ P(h)=2200 e^{0.13 h} \] How many hours will it take for the number of bacteria to reach 2900 ? Round your answer to the nearest tenth, and do not round any intermediate computations.
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