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Home Question Bank Math Pre Calculus Archive 2024 December 05

Pre-calculus Questions from Dec 05,2024

Browse the Pre-calculus Q&A Archive for Dec 05,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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\( 46^{\circ}=\square \) radians (Type an integer or a decimal. Round to the nearest hundredth.) A population of bacteria is treated with an antibiotic, It is estimated that 5,000 live bacteria existed in the sample before treatment. After each day of treatment, \( 40 \% \) of the sample remains alive. Which best describes the graph of the function that represents the number of live bacteria after \( x \) days of treatment? \( f(x)=5000(0.4)^{x} \), with a horizontal asymptote of \( y=0 \) \( f(x)=5000(0.6)^{x} \), with a vertical asymptote of \( x=0 \) \( f(x)=5000(14)^{x} \), with a horizontal asymptote of \( y=0 \) \( f(x)=5000(1.6)^{x} \), with a vertical asymptote of \( x=0 \) What is the multiplicative rate of change for the exponential function \( f(x)=2\left(\frac{5}{2}\right)^{-x} \) ? 0.4 0.6 1.5 2.5 15. \( g(x)=\operatorname{cotan}(\sqrt{5 x-1}) \) The function \( \mathrm{d}(\mathrm{x})=\sqrt{\frac{3 \mathrm{x}}{2}} \) models the distance, \( \mathrm{d}(\mathrm{x}) \), in miles, that a person x feet high can see to the horizon. A deck on a beach front house is 128 feet above the water. How far can a person on the deck see? Write the answer in simplified form. Then use the simplified radical form and a calculator to express the answer to the nearest tenth of a mile. The function \( \mathrm{d}(\mathrm{x})=\sqrt{\frac{3 \mathrm{x}}{2}} \) models the distance, \( \mathrm{d}(\mathrm{x}) \), in miles, that a person x feet high can see to the horizon. A deck on a beach front house is 128 feet above the water. How far can a person on the deck see? Write the answer in simplified form. Then use the simplified radical form and a calculator to express the answer to the nearest tenth of a mile. Ejercicio 1. Demostrar usando el Principio de Inducción que, \( \forall n \in \mathbb{N} \) \[ \frac{1}{1.2}+\frac{1}{2.3}+\cdots+\frac{1}{n \cdot(n+1)}=\sum_{i=1}^{n} \frac{1}{i(i+1)}=\frac{n}{n+1} \] Find the domain of the function. \( f(x)=\frac{\sqrt[3]{x}}{\sqrt{80-8 x}} \) Complete the table and graph the given function. Identify the function's domain and range. \( f(x)=\sqrt{x-4} \) Complete the table and graph the given function. Identify the function's domain and range. \( f(x)=\sqrt{x}+6 \)
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