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Chapter 7: Problem 37
Find the area of the triangle having the indicated angle and sides. \(A=150^{\circ}, \quad b=8, \quad c=10\)
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Find a unit vector in the direction of the given vector. Verify that the result has a magnitude of 1.$$\mathbf{v}=\langle-9,12\rangle$$.
Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form. $$(\cos 0+i \sin 0)^{20}$$
Find \(\mathbf{u} \cdot \mathbf{v},\) where \(\theta\) is the angle between \(\mathbf{u}\) and \(\mathbf{v}.\) $$\|\mathbf{u}\|=100,\|\mathbf{v}\|=250, \theta=\frac{\pi}{6}$$
Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form. $$\left[6\left(\cos 15^{\circ}+i \sin 15^{\circ}\right)\right]^{4}$$
The vector \(\mathbf{u}=\langle 1225,2445\rangle\) gives the numbers of hours worked by employees of a temp agency at two pay levels. The vector \(\mathbf{v}=\langle 12.00,10.25\rangle\) gives the hourly wage (in dollars) paid at each level, respectively. (a) Find the dot product \(\mathbf{u} \cdot \mathbf{v}\) and explain its meaning in the context of the problem. (b) Identify the vector operation used to increase wages by 2 percent.
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