검증된 단계별 안내
08:02
7:42
02:5953–56. Circular motion Find parametric equations that describe the circular path of the following objects. For Exercises 53–55, assume (x, y) denotes the position of the object relative to the origin at the center of the circle. Use the units of time specified in the problem. There are many ways to describe any circle.
A bicyclist rides counterclockwise with constant speed around a circular velodrome track with a radius of 50 m, completing one lap in 24 seconds.
Tangent lines for a hyperbola Find an equation of the line tangent to the hyperbola x²/a² + y²/b² = 1 at the point (x₀, y₀)
11–20. Slopes of tangent lines Find the slope of the line tangent to the following polar curves at the given points.
r = 4 + sin θ; (4, 0) and (3, 3π/2)
31–38. Equations of parabolas Find an equation of the following parabolas. Unless otherwise specified, assume the vertex is at the origin.
A parabola with focus at (3, 0)
9–13. Graph the points with the following polar coordinates. Give two alternative representations of the points in polar coordinates.
(-4, 3π/2)
Spiral arc length Consider the spiral r=4θ, for θ≥0.
a. Use a trigonometric substitution to find the length of the spiral, for 0≤θ≤√8.
