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Home Question Bank Math Pre Calculus Archive 2024 November 24

Pre-calculus Questions from Nov 24,2024

Browse the Pre-calculus Q&A Archive for Nov 24,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Solve for t . \( e^{-0.49 \mathrm{t}}=0.70 \) Select the correct choice below and, if necessary, fill in the answer box to complete your c (6) A. The solution is \( \mathrm{t}=0.7279 \). (Type an integer or a decimal. Do not round until the final answer. Then round to four B. The solution is not a real number. \( a(x)=\left\{\begin{array}{ccc}3 & \text { if } & x<-3 \\ -x+2 & \text { if } & -3 \leq x \leq 3 \\ 2 x-4 & \text { if } & x>3\end{array}\right. \) Question 2 * What is the range of the function \( y=2 \csc 5\left(x+\frac{\pi}{2}\right)-9 ? \) Use transformations to graph the function \( f(x)=4^{x+4} \). Determine its domain, range, and horizontal asymptote. Which transformations must be applied to obtain the graph of \( f(x)=4^{x+4} \) ? Select all that apply. \( \square \) A. Horizontal compression or stretch \( \square \) B. Reflection about the \( x \)-axis \( \square \) C. Vertical shift \( \square \) D. Vertical compression or stretch \( \square \) E. Horizontal shift \( \square \) F. Reflection about the \( y \)-axis hs Use transformations to graph the function \( f(x)=4^{x+4} \). Determine its domain, range, and horizontal asymptote. Which transformations must be applied to obtain the graph of \( f(x)=4^{x+4} \) ? Selec all that apply. \( \square \) A. Horizontal compression or stretch \( \square \) B. Reflection about the \( x \)-axis \( \square \) C. Vertical shift \( \square \) D. Vertical compression or stretch \( \square \) E. Horizontal shift \( \square \) F. Reflection about the \( y \)-axis Sketch the graph of each function. 13) \( y=\tan ^{-1} \frac{x}{2} \) Students in a fifth-grade class were given an exam. During the next 2 years, the same students were retested several times. The average score was given by the model \( f(t)=88-15 \log (t+1), 0 \leq t \leq 24 \) where \( t \) is the time in months. Round answers to 1 decimal place. (a) What is the average score on the original exam? (b) What was the average score after 5 months? (c) After how many months does the average score drop below 72 ? The polar coordinates of a point are ( \( -10,0 \) ). Find the rectangular coordinates of this point. The rectangular coordinates are (Simplify your answer. Type an ordered pair. Type an exact answer for each coordinate, using radicals as needed. Use integers or fractions for any numbers in the expression.) The polar coordinates of a point are \( \left(8, \frac{3 \pi}{4}\right) \). Find the rectangular coordinates of this point. The rectangular coordinates are (Simplify your answer. Type an ordered pair. Type an exact answer for each coordinate, using radicals as needed. Use integers or fractions for any numbers in the expression.) The polar coordinates of a point are given. Find the rectangular coordinates of this point. \( \left(-3,-\frac{11 \pi}{6}\right) \) What are the rectangular coordinates of this point? (Type an ordered pair. Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
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