Precálculo preguntas y respuestas

\( x=11 \cos t, y=11 \sin t \) The rectangular equation for the plane curve is \( \square \).

\( x=\sqrt{t}, y=2 t-3 \) for \( t \) in \( [0,4] \) The equivalent rectangular equation is \( \square \) for \( x \) over the interval \( \square \). (Simplify your answers.)

If a polynomial function has a degree of 4 and a positive leading coefficient, what can you say about its end behavior?

3. Un granjero tiene 200 metros de cerca con la cual puede delimitar un terreno rectangular. Un lado del terreno puede aprovechar una cerca ya existente. ¿Cuál es el área máxima que puede cercarse?

3. Un granjero tiene 200 metros de cerca con la cual puede delimitar un terreno rectangular. Un lado del terreno puede aprovechar una cerca ya existente. ¿Cuál es el área máxima que puede cercarse?

Which of the following equations could be the equation of the horizontal asymptote of \( y=\frac{x-3}{x^{2}-6 x-7} \) Select one: a. \( y=-1 \) b. \( y=0 \) c. \( y=3 \) d. There is no horizontal asymptote.

The exponential model \( \mathrm{A}=905 e^{0.009 \mathrm{t}} \) describes the population, A , of a country in millions, t years after 2003. Use the model to determine the population of the country in 2003 . The population of the country in 2003 was \( \square \) million.

\( 1 \leftarrow \) The formula \( A=21.2 e^{0.0413 t} \) models the population of a US state, A , in millions, t years after 2000 . a. What was the population of the state in 2000 ? b. When will the population of the state reach 29.8 million? a. In 2000 , the population of the state was \( \square \) million.

С1. Найдите область определения функции. \[ f(x)=\sqrt{9-x^{2}}-\frac{5 x-2}{\sqrt{x^{2}+3 x-4}} \]

Caladan is currently one of the world's fastest-growing countries. The exponential function \( f(x)=91(1.027)^{x} \) models the population of Caladan, \( f(x) \), in millions, \( x \) years after 1974. Using this exponential function and a calculator with a \( y^{x} \) key or a \( { }^{\wedge} \) key, answer the following questions. a. Substitute 0 for \( x \) and, without using a calculator, find Caladan's population in 1974 . 91 million Substitute 26 for \( x \) and use your calculator to find Caladan's population in the year 2000 as predicted by this function. 181.9 million (Round to the nearest tenth.) cind Caladan's population in the year 2526 as predicted by this function. million (Round to the nearest tenth.)