91Ó°ÊÓ

In Exercises 31-38, find (a) \(\small{\mathbf{u}} + \small{\mathbf{v}}\), (b) \(\small{\mathbf{u}} - \small{\mathbf{v}}\), and (c) \(\small{2\mathbf{u}} - \small{3\mathbf{v}}\), Then sketch each resultant vector. \(\mathbf{u} = \langle -5, 3 \rangle\), \(\mathbf{v} = \langle 0, 0 \rangle\)

In Exercises 33-42, find the standard form of the complex number. Then represent the complex number graphically. \(2(\cos\ 60^{\circ} + i\ \sin\ 60^{\circ})\)

In Exercises \(25-34,\) use the Law of Sines to solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places. $$ A=45^{\circ}, \quad a=b=1 $$

In Exercises 25-34, use the Law of Sines to solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places. \(A\ =\ 25^{\circ}4'\), \(a\ =\ 9.5\), \(b\ =\ 22\)

In Exercises 31-38, find (a) \(\small{\mathbf{u}} + \small{\mathbf{v}}\), (b) \(\small{\mathbf{u}} - \small{\mathbf{v}}\), and (c) \(\small{2\mathbf{u}} - \small{3\mathbf{v}}\), Then sketch each resultant vector. \(\mathbf{u} = \langle 0, 0 \rangle\), \(\mathbf{v} = \langle 2, 1 \rangle\)

In Exercises 33-42, find the standard form of the complex number. Then represent the complex number graphically. \(5(\cos\ 135^{\circ} + i\ \sin\ 135^{\circ})\)

In Exercises 31-40, find the angle \(\theta\) between the vectors. \(\mathbf{u} = 2\mathbf{i} - 3\mathbf{j}\) \(\mathbf{v} = \mathbf{i} - 2\mathbf{j}\)

In Exercises 33-40, use Heron's Area Formula to find the area of the triangle. \(a = 33\), \(b = 36\), \(c = 25\)

In Exercises 33-40, use Heron's Area Formula to find the area of the triangle. \(a = 2.5\), \(b = 10.2\), \(c = 9\)

In Exercises 31-40, find the angle \(\theta\) between the vectors. \(\mathbf{u} = 2\mathbf{i} - \mathbf{j}\) \(\mathbf{v} = 6\mathbf{i} + 4\mathbf{j}\)