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Home Question Bank Math Pre Calculus Archive 2025 January 25

Pre-calculus Questions from Jan 25,2025

Browse the Pre-calculus Q&A Archive for Jan 25,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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The pressure of a fluid flowing through a closed system, \( P \), after \( t \) seconds can be modeled by the function \( P(t)=100+40 \sin \left(\frac{12 \pi}{5} t\right) \). Answer parts (a) through (c) below. (a) In the interval \( [0,1] \), determine the times at which the pressure of the fluid is 100 mmHg . The solution set is \( \{\square\} \). (Type an integer or decimal rounded to two decimal places as needed. Use a comma to separate answers as needed.) The pressure of a fluid flowing through a closed system, \( P \), after \( t \) seconds can be modeled by the function \( P(t)=100+40 \) sin \( \left(\frac{7 \pi}{3} t\right) \), Answer parts (a) through \( (0) \) below, (a) In the interval \( [0,1] \), determine the times at which the pressure of the fluid is 100 mmHg . The solution set is \( \{0,0,43,0.86\} \), (Type an integer or decimal rounded to two decimal places as needed. Use a comma to separate answers as needed.) (b) In the interval \( [0,1] \), determine the times at which the pressure of the fluid is 140 mmHg . The solution set is \( \square \) D. (Type an integer or decimal rounded to two decimal places as needed. Use a comma to separate answers as needed.) The pressure of a fluid flowing through a closed system, \( P \), after \( t \) seconds can be modeled by the function \( P(t)=100+40 \sin \left(\frac{7 \pi}{3} t\right) \). Answer parts (a) through (c) below. (a) In the interval \( [0,1] \), determine the times at which the pressure of the fluid is 100 mmHg . The solution set is \( \{\square \). (Type an integer or decimal rounded to two decimal places as needed. Use a comma to separate answers as needed.) QUESTION 7 Given: \( f(x)=\frac{2}{x+4}-1 \) 7.1 Write down the equation of the asymplotes of \( f \). (2) 72 Cakolate the inteceqts of the graph of \( f \) with the axes. (3) 73 Sketch the graph of \( f \), showing clearly the asymptotes and intercepts with the axes. (3) 7.4 Wrise donm the coordinates of the image of the \( x \)-intercept if it is reflected about the \( x \) is of symmergy \( =-x-5 \). (2) Find \( d \) in the equation. Do not pound ofs until the final \[ 375000=\frac{d\left[1-\left(1+\frac{0.03}{12}\right)^{-300}\right]}{\left(\frac{0.03}{12}\right)} \] Find \( d \) in the equation \[ 270000=\frac{d\left[1-\left(1+\frac{0.02}{12}\right)^{-300}\right]}{\left(\frac{0.02}{12}\right)} \] \( \$ 270,000 = \frac { d ( 1 - ( 1 + \frac { 0.02 } { 12 } ) ^ { - 25 - 12 } ) } { ( \frac { 0.02 } { 12 } ) } \) 4. Sketch the graphs of each of the following functions and identify the domain, range, intercepts and asymptotes. a) \( f(x)=\log (3-x)^{2}-1 \) b) \( f(x)=\operatorname{coth} x \) 4. Sketch the graphs of each of the following functions and identify the domain, range, intercepts and asymptotes. a) \( f(x)=\log (3-x)^{2}-1 \) b) \( f(x)=\operatorname{cothx} \) 3. Sketch the graph of \( f(x)=\frac{x^{2}-5 x+6}{x^{2}-1} \) by identifying its domain, intercepts and asymptotes.
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