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Home Question Bank Math Pre Calculus Archive 2024 December 07

Pre-calculus Questions from Dec 07,2024

Browse the Pre-calculus Q&A Archive for Dec 07,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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In April 1986, a flawed reactor design played a part in the Chernobyl nuclear meltdown. Approximately 14252 becqurels (Bqs), units of radioactivity, were initially released into the environment. Only areas with less than 800 Bqs are considered safe for human habitation. The function \( f(x)=14252(0.5)^{\frac{x}{32}} \) describes the amount, \( f(x) \), in becqurels, of a radioactive element remaining in the area \( x \) years after 1986 . Find \( f(40) \), to one decimal place, in order to determine the amount of becqurels in 2026 . Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form. \[ \left[5\left(\cos 15^{\circ}+i \sin 15^{\circ}\right)\right]^{4} \] 31. Escribe la ecuación de una elipse vertical, con centro en el origen y el eje mayor coincide con el eje y. La población de una ciudad crece según una función exponencial. Si en el año 2020 había 50,000 habitantes y se espera que la población duplique cada 15 años, ¿cuál será la población en el año 2035? 22. \( f(x)=(\operatorname{sen} x)^{1 / 2} \) Successive \( n \)th roots of a complex number have arguments that differ by 9. The population growth of a certain city with a current population of 27,345 is modelled by the equation \( P=27,345\left(e^{0.005}\right) \), where \( P \) is the population of the city after \( t \) years and 0.005 is the rate of growth. (i) What will the population of the city be 10 years from now? What is the definition of a logarithmic function? \( \left. \begin{array} { l } { z = \sqrt { 36 - x ^ { 2 } - y ^ { 2 } } } \\ { z = \sqrt { ( x ^ { 2 } + y ^ { 2 } ) / 3 } } \end{array} \right. \) Detrmine the rage of \( g(x)+1 \).
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