\( (\sqrt{6},-\sqrt{2}) \) une expression.) \( \cos \alpha=\frac{\sqrt{3}}{2} \) (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for the expression.) tan \( \alpha=\square \) (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for the expression.)

culate \( \sqrt{0,81}+\sqrt[3]{0,064} \) withe 2.25

b) \( \frac{3}{8}+2 \frac{1}{3}=\ldots \)

Find all solutions of the equation in the interval \( [0,2 \pi) \) \[ \cot ^{2} x+2 \csc x=-1 \] Write your answer in radians in terms of \( \pi \). If there is more than one solution, separate them with commas.

Subtract. \[ \frac{9}{2 x^{2}-15 x+27}-\frac{3}{2 x^{2}-17 x+36} \] Simplify your answer as much as possible.

WORKSHEET: ADolications of Integration For a manufacturer, the marginal cost (in dollars) per unit, \( C^{\prime}(x) \), when producing units is given by \( C^{\prime}(x)=3 x^{2}-60 x+400 \). (a) Given that the total cost of producing the first 2 units is \( \$ 900 \), use integration (b) Herme calculate the total cost of producing the first 5 units.