Answer:
a) See the file below, b) [tex]s = \int\limits^{0.5\pi}_{-0.25\pi} {[\left( 3\cdot \cos t\right)^{2}+\left(-5\cdot \sin t \right)^{2}]} \, dx[/tex], c) [tex]s \approx 9.715[/tex]
Step-by-step explanation:
a) Points moves clockwise as t increases. See the curve in the file attached below. The parametric equations describe an ellipse.
b) The arc length formula is:
[tex]s = \int\limits^{0.5\pi}_{-0.25\pi} {[\left( 3\cdot \cos t\right)^{2}+\left(-5\cdot \sin t \right)^{2}]} \, dx[/tex]
c) The perimeter of that arc is approximately:
[tex]s \approx (\frac{1}{4} + \frac{1}{8})\cdot 2 \pi\cdot \sqrt{\frac{3^{2}+5^{2}}{2} }[/tex]
[tex]s \approx 9.715[/tex]
