91Ó°ÊÓ

In Exercises 45 - 48, an object moving vertically is at the given heights at the specified times. Find the position equation \( s = \dfrac{1}{2}at^2 + v_0t + s_0 \) for the object. At \( t = 1 \) second, \( s = 132 \) feet At \( t = 2 \) second, \( s = 100 \) feet At \( t = 3 \) second, \( s = 36 \) feet

In Exercises 43-50, write the partial fraction decomposition of the improper rational expression. \( \dfrac{16x^4}{(2x - 1)^3} \)

In Exercises 45 - 48, find the equilibrium point of the demand and supply equations. The equilibrium point is the price and number of units that satisfy both the demand and supply equations. Demand \( p = 400 - 0.0002x \) Supply \( p = 225 + 0.0005x \)

In Exercises 49 - 54, use a graphing utility to solve the system of equations. Find the solution(s) accurate to two decimal places. \( \left\\{\begin{array}{l} \hspace{1cm} \hspace{1cm} y = e^x\\\x - y + 1 = 0\end{array}\right. \)

In Exercises 41-54, sketch the graph and label the vertices of the solution set of the system of inequalities. \( \left\\{\begin{array}{l} x > y^2\\\ x < y + 2\end{array}\right. \)

In Exercises 43-50, write the partial fraction decomposition of the improper rational expression. \( \dfrac{x^4 + 2x^3 + 4x^2 + 8x + 2}{x^3 + 2x^2 + x} \)

Two cheeseburgers and one small order of French fries from a fast-food restaurant contain a total of \( 830 \) calories. Three cheeseburgers and two small orders of French fries contain a total of \( 1360 \) calories.Find the caloric content of each item.

In Exercises 49 - 54, find the equation of the parabola \( y = ax^2 + bx + c \) that passes through the points. To verify your result, use a graphing utility to plot the points and graph the parabola. \( (0, 0), (2, -2), (4, 0) \)

In Exercises 41-54, sketch the graph and label the vertices of the solution set of the system of inequalities. \( \left\\{\begin{array}{l} x - y^2 > 0\\\ x - y > 2\end{array}\right. \)

In Exercises 43-50, write the partial fraction decomposition of the improper rational expression. \( \dfrac{2x^4 + 8x^3 + 7x^2 - 7x - 12}{x^3 + 4x^2 + 4x} \)