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Home Question Bank Math Pre Calculus Archive 2024 December 12

Pre-calculus Questions from Dec 12,2024

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

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The population of Sasquatch in Salt Lake County was modeled by the function \( P(t)=\frac{400 t}{t+40} \), where \( t=0 \) represents the year 1803 . When were there fewer than 200 Sasquatch in Salt Lake County? Present your answer, to the nearest whole year, in interval notation. There were fewer than 200 Sasquatch in Salt Lake City between the years Suppose that the function \( h \) is defined on the interval \( (-2,2] \) as follows. \[ h(x)=\left\{\begin{array}{ll}-1 & \text { if }-2<x \leq-1 \\ 0 & \text { if }-1<x \leq 0 \\ 1 & \text { if } 0<x \leq 1 \\ 2 & \text { if } 1<x \leq 2\end{array}\right. \] Find \( h(-1), h(-0.5) \), and \( h(1) \). \( h(-1)=\square \) \( h(-0.5)=\square \) The population of a southern city follows the exponential law. Use this information to answer parts a and b . (a) If N is the population of the city and t is the time in years, express N as a function of t . \( \mathrm{N}(\mathrm{t})= \) (Type an expression using t as the variable and in terms of \( e \).) (b) If the population doubled in size over 19 months and the current population is 50,000 , what will the population be 3 years from now? The population will be approximately \( \square \) people. (Do not round until the final answer. Then round to the nearest whole number as needed.) \( s \) denotes the length of the arc of a circle of radius \( r \) subtended by the central angle \( \theta \). Find the missing quantity. \( r=40 \) inches, \( \theta=51^{\circ}, \mathrm{s}= \) ? \( \mathrm{s}=\square \) (Type an integer or decimal rounded to three decimal places as needed.) If \( f(x)=\frac{7}{x+5} \) and \( g(x)=\frac{x+75}{x^{2}-25} \), determine \( (f+g)(x) \) \( \begin{array}{l}(f+g)(x)=\frac{x+82}{x^{2}-25} \\ (f+g)(x)=\frac{x+82}{x+5} \\ (f+g)(x)=\frac{8}{x^{2}-25} \\ (f+g)(x)=\frac{8}{x-5}\end{array} \) The function \( P(x)=\frac{120}{1+372 e^{-0.133 x}} \) models the percentage, \( P(x) \), of Americans who are \( x \) years, old and have some degree of heart disease. What is the percentage, to the nearest tenth, of 39 -year olds with some degree of heart disease? Question 9 Find all Asymptotes and Holes for \( f(x)=\frac{5 x^{2}-3 x-2}{x^{3}-3 x^{2}+2 x} \), No decimals. Use the editor to format your answer Suppose that the function \( f \) is defined on the interval \( [-2,2) \) as follows. \( f(x)=\left\{\begin{array}{ll}-2 & \text { if }-2 \leq x<-1 \\ -1 & \text { if }-1 \leq x<0 \\ 0 & \text { if } 0 \leq x<1 \\ 1 & \text { if } 1 \leq x<2\end{array}\right. \) Find \( f(-2), f(-0.75) \), and \( f(1) \) \( f(-2)=\square \) \( f(-0.75)=\square \) Suppose that the function \( h \) is defined, for all real numbers, as follows. \[ h(x)=\left\{\begin{array}{ll}-\frac{1}{4} x^{2}+5 & \text { if } x \neq-2 \\ -1 & \text { if } x=-2\end{array}\right. \] Find \( h(-4), h(-2) \), and \( h(5) \) \( h(-4)=\square \) \( h(5)=\square \) At the beginning of an experiment, a scientist has 284 grams of radioactive goo. After 90 minutes, her sample has decayed to 4.4375 grams. What is the half-life of the goo in minutes? 15 Find a formula for \( G(t) \), the amount of goo remaining at time \( t . G(t)= \) How many grams of goo will remain after 32 minutes?
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