1. If \( \vec{A}=2 \vec{\imath}+3 \vec{\jmath}, \vec{B}=3 \vec{\imath}-\vec{\jmath} \), then \( \|\overrightarrow{2 \mathrm{~A}}-\overrightarrow{\mathrm{B}}\|=\ldots \) 2. If \( \vec{A}=(-2,1), \vec{C}=(-3, k) \) are parallel, then the value of \( \mathrm{k}=\ldots \) 3. If \( \vec{A} \perp \vec{B}, \vec{A}=(3,4), \vec{B}=(4, m) \), then \( m=\cdots \). 4. If \( \vec{A}=(2,3), \vec{B}=(-1,2) \), then \( \overrightarrow{A B}=\cdots \) 5. If \( \vec{A}=\left(10,45^{\circ}\right) \), write \( \vec{A} \) in term of fundamental unit vectors. 6. If \( \vec{A}=(4,4 \sqrt{3}) \) find in polar form the position vector of the point A respect to the origin point. 7. If \( \|-8 \overrightarrow{\mathrm{~A}}\|=5\|k \overrightarrow{\mathrm{~A}}\|=\ldots \ldots \), then find the value of k

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.

Find the least common denominator of \( \frac{5 x}{x-6} \) and \( \frac{9 x}{x-7} \)

The graph to the right shows a region of feasible solutions. Use this region to find maximum and minimum values of the given objective functions, and the locations of these values on the graph. (a) \( z=4 x+3 y \) (b) \( z=2.25 x+0.50 y \)

Dine part \( \left.\right|^{\text {D'autre part }} \)

191. La somma di due angoli alla circonferenza misura \( 130^{\circ} 18^{\prime} 24^{\prime \prime} \) e uno di essi è \( 3 / 5 \) dell'altro'. Calcola l'ampiezza dei due angoli al centro corrispondenti. \( \quad\left[97^{\circ} 43^{\prime} 48^{\prime \prime} ; 162^{\circ} 53^{\prime}\right] \)