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Magazine Problem 48
Use set-builder notation to describe the polar region. Assume that the region contains its bounding curves. The region inside the circle \(r=5\) but outside the circle \(r=3\).
Problem 49
In Exercises \(32-52,\) for the given vector \(\vec{v}\), find the magnitude \(\|\vec{v}\|\) and an angle \(\theta\) with \(0 \leq \theta<360^{\circ}\) so that \(\vec{v}=\|\vec{v}\|\langle\cos (\theta), \sin (\theta)\rangle\) (See Definition 11.8.) Round approximations to two decimal places. $$ \vec{v}=\hat{\imath}-4 \hat{\jmath} $$
Problem 49
Use set-builder notation to describe the polar region. Assume that the region contains its bounding curves. The region which lies inside of the circle \(r=3 \cos (\theta)\) but outside of the circle \(r=\sin (\theta)\)
Problem 49
For Exercises \(41-52,\) use \(z=-\frac{3 \sqrt{3}}{2}+\frac{3}{2} i\) and \(w=3 \sqrt{2}-3 i \sqrt{2}\) to compute the quantity, Express your answers in polar form using the principal argument. $$ \frac{w}{z^{2}} $$
Problem 49
Convert the point from rectangular coordinates into polar coordinates with \(r \geq 0\) and \(0 \leq \theta<2 \pi\) (-8,1)
Problem 50
Convert the point from rectangular coordinates into polar coordinates with \(r \geq 0\) and \(0 \leq \theta<2 \pi\) \((-2 \sqrt{10}, 6 \sqrt{10})\)
Problem 50
In Exercises \(32-52,\) for the given vector \(\vec{v}\), find the magnitude \(\|\vec{v}\|\) and an angle \(\theta\) with \(0 \leq \theta<360^{\circ}\) so that \(\vec{v}=\|\vec{v}\|\langle\cos (\theta), \sin (\theta)\rangle\) (See Definition 11.8.) Round approximations to two decimal places. $$ \vec{v}=\langle 123.4,-77.05\rangle $$
Problem 50
For Exercises \(41-52,\) use \(z=-\frac{3 \sqrt{3}}{2}+\frac{3}{2} i\) and \(w=3 \sqrt{2}-3 i \sqrt{2}\) to compute the quantity, Express your answers in polar form using the principal argument. $$ \frac{z^{3}}{w^{2}} $$
Problem 51
In Exercises \(32-52,\) for the given vector \(\vec{v}\), find the magnitude \(\|\vec{v}\|\) and an angle \(\theta\) with \(0 \leq \theta<360^{\circ}\) so that \(\vec{v}=\|\vec{v}\|\langle\cos (\theta), \sin (\theta)\rangle\) (See Definition 11.8.) Round approximations to two decimal places. $$ \vec{v}=\langle 965.15,831.6\rangle $$
Problem 51
For Exercises \(41-52,\) use \(z=-\frac{3 \sqrt{3}}{2}+\frac{3}{2} i\) and \(w=3 \sqrt{2}-3 i \sqrt{2}\) to compute the quantity, Express your answers in polar form using the principal argument. $$ \frac{w^{2}}{z^{3}} $$
