91Ó°ÊÓ

Find the component form and magnitude of the vector v. $$\begin{array}{cc}\text{Initial Point} && \text{Terminal Point} \\ (-3,11) && (9,40) \end{array}$$

Use the Law of cosines to solve the triangle. Round your answers to two decimal places. $$C=101^{\circ}, \quad a=\frac{3}{8}, \quad b=\frac{3}{4}$$

Use the Law of sines to solve the triangle. Round your answers to two decimal places. \(C=95.20^{\circ}, \quad a=35, \quad c=50\)

Use the vectors \(\mathbf{u}=\langle\mathbf{3}, \mathbf{3}\rangle, \mathbf{v}=\langle-\mathbf{4}, \mathbf{2}\rangle,\) and \(\mathbf{w}=\langle 3,-1\rangle\) to find the indicated quantity. State whether the result is a vector or a scalar. $$(\mathbf{v} \cdot \mathbf{u})-(\mathbf{w} \cdot \mathbf{v})$$

Trigonometric Form of a Complex Number Represent the complex number graphically. Then write the trigonometric form of the number. $$5+2 i$$

Use the Law of Sines to solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places. \(A=110^{\circ}, \quad a=125, \quad b=100\)

Use the dot product to find the magnitude of u. $$\mathbf{u}=\langle-8,15\rangle$$

Use the Law of Sines to solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places. \(A=110^{\circ}, \quad a=125, \quad b=200\)

Use the dot product to find the magnitude of u. $$\mathbf{u}=\langle 4,-6\rangle$$

Trigonometric Form of a Complex Number Represent the complex number graphically. Then write the trigonometric form of the number. $$8+3 i$$