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Home Question Bank Math Pre Calculus Archive 2025 January 19

Pre-calculus Questions from Jan 19,2025

Browse the Pre-calculus Q&A Archive for Jan 19,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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\#18 ODELING REAL LIFE In a volleyball game, a player on one team spikes the ball over the net when the ball is 10 feet above re court. The spike drives the ball downward with an initial vertical velocity of 55 feet per second. Write a function that epresents the situation. Use \( h \), for height (in feet) and \( t \), for time (in seconds). ENUNCIADO: El centro de la \( C(h, k) \) de la hipérbola cuya ecuación viene dada por la expresión: \( \frac{x^{3}}{3}-\frac{y^{2}}{7}=1 \) ? es: \( \begin{array}{l}\text { a. }(1,1) \\ \text { b. }(0,0) \\ \text { c. }(0,1) \\ \text { d. }(1,0)\end{array} \) ENUNCIADO: Para la parábola \( x^{2}-6 x+9=-4 y+16 \) el vértice esta ubicado en el punto: Like humans, sea urchins grow linearly for a portion of their life, Suppose that a population of white sea urchins (Lytechimus pietus) has a mean diameter of 28 mm at the begimning of Jume (June 1) and 33 mm at the beginning of July (July 1), a) Assuming the growth is linear, use the two given data points to derive an equation for sea urchin growth as a function of time, b) Draw a graph of your model. Use your model to estimate the mean diameter for the population of Lytechimus pictus ons e) July 10, d) June 20, e) August I, and f) June 2. g) Rank your estimates in e)=f) according to your confidence in their aecuracy, 2) Multiple Choice: Officials in a town use a function, \( C \), to analyze traffic patterns. \( C(n) \) represents the rate of traffic through an intersection where \( n \) is the number of observed vehicles in a specified time interval. What would be the most appropriate domain for the function? 1) \( \{\ldots-2,-1,0,1,2,3, \ldots\} \) 2) \( \{-2,-1,0,1,2,3\} \) 3) \( \left\{0, \frac{1}{2}, 1,1 \frac{1}{2}, 2,2 \frac{1}{2}\right\} \) 4) \( \{0,1,2,3, \ldots\} \) Given the geometric series: \( \quad 2+\frac{2}{3}+\frac{2}{9}+\ldots \ldots . . . . . . . . . . \). 3.1 \( \quad \) Determine the sum to infinity. Explain how to verify if two functions are inverses of each other using compositional notation. Find the domain of each function. If the answer is all real numbers, \( e \) (a) \( f(x)=\frac{1}{1+e^{x}} \) (b) \( f(x)=\frac{1}{1-e^{x}} \) (a) \( x= \) (b) \( x \neq \square \) Sec 6.3 Natural Exp Function: Pro (1 point) Find the solutions of the exponential equation \[ e^{2 x}-5 e^{x}+6=0 \] Enter your answer as a comma-separated list, and enter none if there are no solutions. QUESTION 5 Given: \( h(x)=\frac{2}{x+3}-1 \) \( 5.1 \quad \) Write down the equations of the asymptotes of \( h \). \( 5.2 \quad \begin{array}{l}\text { Calculate the } x \text { - and } y \text {-intercepts of } h \text {. } \\ 5.4 \\ \begin{array}{l}\text { Draw a neat sketch of the graph of } h \text {. Clearly show all intercepts with axes } \\ \text { and } x+y=c \text { is an equation of the axis of symmetry of } h, ~ c a l c u l a t e ~ t h e ~ v a l u e ~\end{array} \\ \text { of } c\end{array} \)
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