A manufacturer produces two models of toy airplanes. It takes the manufacturer 20 minutes to assemble model \( A \) and 10 minutes to package it. It takes the manufacturer 25 minutes to assemble model B and 5 minutes to package it. In a given week, the total available time for assembling is 3000 minutes, and the total available time for packaging is 1200 minutes. Model \( A \) earns a profit of \( \$ 9 \) for each unit sold and model B earns a profit of \( \$ 12 \) for each unit sold. Assuming the manufacturer is able to sell as many models as it makes, how many units of each model should be produced to maximize the profit for the given week? Note that the ALEKS graphing calculator can be used to make computations easier. Model A: \( \square \) unit(s) Model B: \( \square \) unit(s)

2. Considere o desenvolvimento do binómio seguinte: \( \left(\frac{2}{x}+\sqrt{x}\right)^{20} \), com \( x \geq 0 \). Determine o termo cuja parte literal é \( x^{7} \).

Vereinfache die Wurzelterme mithilfe der Potenzgesetze: \( \begin{array}{lll}\text { a) } \sqrt{\sqrt[3]{a}} & \text { b) } \sqrt[3]{\sqrt[4]{a}} & \text { c) } \sqrt[3]{a^{2}} \cdot \sqrt[3]{a^{5}} \\ \text { e) } \sqrt{\sqrt{\sqrt{a}}} & \text { f) } \sqrt{a \sqrt{a \sqrt{a}}} & \text { g) } \sqrt[3]{\frac{1}{\sqrt{a}}}\end{array} \)

8- Joana possui um terreno de formato retangular. O perimetro dele é igual a 140 m . a razalo entre as medidas de sua largura e seu comprimento, nessa ordem, é \( \frac{2}{5} \). Quais são as medidas de comprimento e largura desse terreno, respectivamente?

Gncontrar las derivadas de 1) \( y=2 x \operatorname{sen} x+x^{2} \cos x \)

Rotating \( M(-5,1) 180^{\circ} \) about the origin and then translating along \( \langle-3,4\rangle \) will give the same result as translating along \( \langle-3,4\rangle \) and then rotating \( 180^{\circ} \). T True Oalse