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Home Question Bank Math Pre Calculus Archive 2024 November 12

Pre-calculus Questions from Nov 12,2024

Browse the Pre-calculus Q&A Archive for Nov 12,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Graph the function and determine whether the function is one-to-one using the horizontal line test. \( f(x)=-\frac{1}{x} \) Graph the function \( f(x)=-\frac{1}{x} \). Choose the correct graph on the right. Is the function one-to-one? Yes, because no horizontal line intersects the graph more than once. No, because no horizontal line intersects the graph more than once. Yes, because there is at least one horizontal line that intersects the graph more than once. 15) Realizar el gráfico de la función: \[ \begin{array}{l}\text { a) } y=x^{2}-4 x+5 \\ \text { b) } y=-x 2-4\end{array} \] \( \begin{array}{l}\text { trans formacio de una } \\ \text { evación rectangular a polar } \\ x^{2}-y^{2}=3 x\end{array} \) Express the interval using two different representations. \[ (-\infty,-5) \cup(7, \infty) \] Diseases tend to spread according to the exponential growth model. In the early days of AIDS, the growth factor (i.e. growth multiplier not growth rate) was around 2.2. In 1983, about 1900 people in the U.S. died of AIDS. If the trend had continued unchecked, how many people would have died from AIDS in 2005? people (Note: once diseases become widespread, they start to behave more like logistic growth, but don't worry about that for the purpose of this exercise) Diseases tend to spread according to the exponential growth model. In the early days of AIDS, the growth factor (i.e. growth multiplier not growth rate) was around 1.8. In 1983, about 1900 people in the U.S. died of AIDS. If the trend had continued unchecked, how many people would have died from AIDS in 2004? people The exponential function given by \( \mathrm{H}(\mathrm{t})=80,036.66(1.0488)^{\mathrm{t}} \), where t is the number of years after 2008, can be used to project the number of centenarians in a certain country. Use this function to project the centenarian population in this country in 2013 and in 2038 . The centenarian population in 2013 is approximately (Round to the nearest whole number.) The centenarian population in 2038 is approximately (Round to the nearest whole number.) (18) Calcula la suma de los 10 primeros términos de las siguientes sucesiones. \( \begin{array}{ll}\text { a. }\left(a_{n}\right)=(0,001 ; 0,003 ; 0,009 ; \ldots) & \text { c. }\left(c_{n}\right)=\left(1, \frac{1}{5}, \frac{1}{25}, \frac{1}{125}, \ldots\right) \\ \text { b. }\left(b_{n}\right)=(1,4,16,64, \ldots) & \text { d. }\left(d_{n}\right)=\left(-1,-\frac{1}{2},-\frac{1}{4},-\frac{1}{8}, \ldots\right)\end{array} \) Por tanto: \( S_{15}=\frac{r-1}{r-1}=\frac{163835}{2-1}= \) Calcula la suma de los 10 primeros términos de las siguientes sucesiones. \( \begin{array}{ll}\text { a. }\left(a_{n}\right)=(0,001 ; 0,003 ; 0,009 ; \ldots) & \text { c. }\left(c_{n}\right)=\left(1, \frac{1}{5}, \frac{1}{25}, \frac{1}{125}, \ldots\right) \\ \text { b. }\left(b_{n}\right)=(1,4,16,64, \ldots) & \text { d. }\left(d_{n}\right)=\left(-1,-\frac{1}{2},-\frac{1}{4},-\frac{1}{8}, \ldots\right)\end{array} \) For the quadratic function \( f(x)=\frac{1}{4} x^{2}+2 \), what is the focal length \( c^{\prime} \) ? What is the focal point? What is the equation of the directrix?
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