1) Dada la ecuación de la hipérbola \( \frac{y^{2}}{25}-\frac{x^{2}}{9}=1 \) determinar sus elementos.

Find the center and radius of the circle represented by the equation below. \[ (x-4)^{2}+(y-8)^{2}=25 \] Answer Attempt 1 out of 5 Center: \( (\square, \square \) Radius:

Directions: Determine whether a triangle with sides of the given lengths is a right triangle. Justify your answer and show all wor receive full credit. 14.60 feet, 80 feet, 100 feet

lengths is a right triangle. Justify your answe receive full credit. 14.60 feet, 80 feet, 100 feet

Use the given vectors to find \( \mathbf{v} \cdot \mathbf{w} \) and \( \mathbf{v} \cdot \mathbf{v} \). \[ \begin{array}{l}\mathbf{v}=-7 \mathbf{i}-3 \mathbf{j}, \mathbf{w}=-9 \mathbf{i}-5 \mathbf{j} \\ \mathbf{v} \cdot \mathbf{w}=78 \text { (Simplify your answer.) } \\ \mathbf{v} \cdot \mathbf{v}=\square \text { (Simplify your answer.) }\end{array} \text { \$ } \]

(a) Find the dot product \( \mathbf{v} \cdot \mathbf{w} \); (b) find the angle between \( \mathbf{v} \) and \( \mathbf{w} \); (c) state whether the vectors are parallel, orthogonal, or neither. \( \mathbf{v}=\sqrt{3} \mathbf{i}+3 \mathbf{j}, \quad \mathbf{w}=-\mathbf{i}+\mathbf{j} \) (a) \( \mathbf{v} \cdot \mathbf{w}=3-\sqrt{3} \) (Simplify your answer. Type an exact answer, using radicals as needed.) (b) The angle between \( \mathbf{v} \) and \( \mathbf{w} \) is \( \square^{\circ} \). (Type your answer in degrees.)