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05:43
3:40
5:47Air drop A plane traveling horizontally at 80 m/s over flat ground at an elevation of 3000 m releases an emergency packet. The trajectory of the packet is given by
x = 80t, y = −4.9t² + 3000, t ≥ 0
where the origin is the point on the ground directly beneath the plane at the moment of the release (see figure). Graph the trajectory of the packet and find the coordinates of the point where the packet lands.
Explain why the slope of the line θ=π/2 is undefined.
41–44. Intersection points and area Find all the intersection points of the following curves. Find the area of the entire region that lies within both curves
r = 3 sin θ and r = 3 cos θ
102–104. Spirals Graph the following spirals. Indicate the direction in which the spiral is generated as θ increases, where θ>0. Let a=1 and a=−1.
Spiral of Archimedes: r = aθ
15–30. Working with parametric equations Consider the following parametric equations.
a. Eliminate the parameter to obtain an equation in x and y.
b. Describe the curve and indicate the positive orientation.
x = √t + 4, y = 3√t; 0 ≤ t ≤ 16
45–60. Areas of regions Find the area of the following regions.
The region inside the curve r = √(cos θ) and inside the circle r = 1/√2 in the first quadrant
