Can anyone help me with these problems please?
1) Set up and find the volume of the solid bounded by the plane P: x + y + z = 1 and the cone C: z = sqrt[(x - 1)^2 + (y + 3)^2].
2) Incy moves according to r = <t^2, t^3, 2^t>. Find the velocity and acceleration vectors.
Mincy moves with s = <t + 2, t^2 + 4, 4>. Would they ever meet? If so, where?
If they hit each other, what would be their relative velocities in each direction at the impact?
Starting from t = -2, how long would the creatures move before hitting each other? Re-parametrize Incy's path in terms of the length of his journey to Mincy.
For the second question, I already found the velocity and acceleration vectors, and have determined that they will collide, when t = 2, at point <4, 8, 4>. But I do not know where to go from there. Any help is appreciated. Thank you!
1) Set up and find the volume of the solid bounded by the plane P: x + y + z = 1 and the cone C: z = sqrt[(x - 1)^2 + (y + 3)^2].
2) Incy moves according to r = <t^2, t^3, 2^t>. Find the velocity and acceleration vectors.
Mincy moves with s = <t + 2, t^2 + 4, 4>. Would they ever meet? If so, where?
If they hit each other, what would be their relative velocities in each direction at the impact?
Starting from t = -2, how long would the creatures move before hitting each other? Re-parametrize Incy's path in terms of the length of his journey to Mincy.
For the second question, I already found the velocity and acceleration vectors, and have determined that they will collide, when t = 2, at point <4, 8, 4>. But I do not know where to go from there. Any help is appreciated. Thank you!
