The limiting reactant is the chemical substance that determines the amount of product(s) that can ultimately be formed in a reaction. During the reaction, the limiting reactant is completely consumed or used up and therefore causes the reaction to stop. The limiting reactant can be identified through stoichiometric calculations. After comparing the results, the reactant that produces the smaller mass of product is identified as the limiting reactant. If you are going to make banana bread and the recipe calls for 1 cup of sugar, 2 cups of flour, 3 bananas, and \( 1 / 2 \) cup of butter, which of the following ingredients is the limiting reactant? \[ \begin{array}{l}4 \text { cups of sugar } \\ 2 \text { cups of flour } \\ 6 \text { bananas } \\ 3 \text { cups of butter }\end{array} \]

For the following exercises, find the values of the six trigonometric functions if the conditions provided hold. 9. \( \cos (2 \theta)=\frac{3}{5} \) and \( 90^{\circ} \leq \theta \leq 180^{\circ} \) 10. \( \cos (2 \theta)=\frac{1}{\sqrt{2}} \) and \( 180^{\circ} \leq \theta \leq 270^{\circ} \)

ข้าวสารถุงแรกหนัก \( 6 \frac{2}{5} \) กิโลกรัม ถุงที่สองหนัก \( 2 \frac{8}{10} \) กิโลกรัม ต้องการแบ่งข้าวสารใส่ถุงใหม่ 2 ถุง ถุงละเท่าๆ กันข้าวสารแต่ละถุงจะหนักทิโลกรัม \( \begin{array}{cccc}\text { ก. } 3 \frac{1}{5} \text { กิโลกรัม } & \text { ข. } 3 \frac{3}{5} \text { กิโลกรัม } & \text { ค. } 4 \frac{1}{5} \text { กิโลกรัม } & 4 \frac{3}{5} \text { กิโลกรัม }\end{array} \)

g. \( y=\ln x^{6} \)

Which set of three numbers could be the side lengths of a triangle? \( \begin{array}{l}\text { A. } 5,5,10 \\ \text { B. } 3,3,2 \\ \text { C. } 3,3,8 \\ \text { D. } 5,5,14\end{array} \)

Consider the function \( f(x)=12 x^{5}+15 x^{4}-240 x^{3}+1 \). \( f(x) \) has inflection points at (reading from left to right) \( x=D, E \), and \( F \) where \( D \) is and \( E \) is and \( F \) is