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Home Question Bank Math Pre Calculus Archive 2025 January 07

Pre-calculus Questions from Jan 07,2025

Browse the Pre-calculus Q&A Archive for Jan 07,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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13. The sum to infinity for a geometric series is \( \frac{3}{2} \) and the sum of the first three terms is \( \frac{14}{9} \). Find the first three terms of this series. 14. For which values of \( x \) will the series \( 1+\frac{x}{2 x-1}+\left(\frac{x}{2 x-1}\right)^{2}+\left(\frac{x}{2 x-1}\right)^{3}+\ldots \) converge? 15. Express 0,342 as a common fraction. Apply De Moivre's Theorem to solve the equation \( z^{4}=1 \), thus obtaining the fourth roots of 1 . At low altitudes the altitude of a parachutist and time in the air are linearly related. A jump at 2,700 feet lasts 150 seconds. (A) Find a linear model relating altitude a (in feet) and time in the air \( t \) (in seconds). (B) Find the rate of change of the parachutist in the air (C) Find the speed of the parachutist at landing. (A) Find a linear model relating altitude a (in feet) and time in the air \( t \) (in seconds). a = (Type an equation using t as the variable.) (B) Find the rate of change of the parachutist in the air \( \square \) feet/sec (C) Find the speed of the parachutist at landing \( \square \) feet/sec Find the range of the quadratic function. \[ y=x^{2}-10 x+26 \] Find the rarge of the quadratic fontetion \[ y=-2 x^{2}+8 x-10 \] 6 Given: \( f(x)=\frac{3}{x-2} \) and \( g(x)=3^{x-2} \). Explain why \( f(x)=g(x) \) will have only ONE root. Motivate your answer. 6. En s'aidant de la question 1., déterminer comment tracer \( \Gamma \) à partir de la représentation de \( f \) sur \( [0 ; \pi] \). Draw the curve of the function \( f \) and determine its range and its monotonicity : \( f(x)=\left\{\begin{array}{lll}x^{2}+1 & , & x>0 \\ -x^{2}-1 & , & x<0\end{array} f(x)=\left|x^{2}+1\right|\right. \) The graph of \( f: x \rightarrow a^{x} \) passes through the point \( \left(2 ; \frac{9}{4}\right) \). (a) Calculate the value of \( a \). (b) Write down the equation of the inverse in the form \( f^{-1}(x)=\ldots \). (c) Determine the equation of \( g \), the reflection of \( f \) about the \( y \)-axis (d) Determine the equation of \( h \), the reflection of \( f \) about the \( x \)-axis (e) Sketch the graphs of \( f, g, h \) and \( f^{-1} \) on the same set of axes. (f) Write down the domain and range of \( f \) and \( g \). The graph of \( f: x \rightarrow a^{x} \) passes through the point \( (-2 ; 4) \). (a) Calculate the value of \( a \). (b) Write down the equation of the inverse in the form \( f^{-1}(x)=\ldots \ldots \) (c) Determine the equation of \( g \), the reflection of \( f \) about the \( y \)-axis (d) Determine the equation of \( h \), the reflection of \( f \) about the \( x \)-axis (d) Given the function \( f(x)=-\sqrt{3 x} \). (1) Write down the domain and range of \( f \). (2) Determine the equation of \( f^{-1} \). (3) Sketch the graphs of \( f \) and \( f^{-1} \) on the same set of axes. (4) Write down the equation of (i) \( g \), the reflection of \( f \) in the line \( x=0 \). (ii) \( h \), the reflection of \( f \) in the line \( y=0 \).
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