The base of a solid is the segment of the parabola y2
= 12x cut off...
The base of a solid is the segment of the parabola y2
= 12x cut off by the latus rectum. A section of the solid
perpendicular to the axis of the parabola is a square. Find its
volume.
Let PQ be a focal chord of the parabola y2 = 4px. Let
M be the midpoint of PQ. A perpendicular is drawn from M to the
x-axis, meeting the x-axis at S. Also from M, a line segment is
drawn that is perpendicular to PQ and that meets the x-axis at T.
Show that the length of ST is one-half the focal width of the
parabola.
1. Find p and graph the parabola y+12x−2x^2=16
2. Find e, d and determine which conic that has the equation r=
4 / 5 - 4sin(theta)
Please show steps. Thanks a lot.
The end of a stopped pipe is to be cut off so that the pipe will be open. If the stopped pipe has a total length L, what fraction of L should be cut off so that the fundamental mode of the resulting open pipe has the same frequency as the fifth harmonic (n=5) of the original stopped pipe?
Express your answer in terms of L.
A solid S occupies the region of space located outside the
sphere x2 + y2 + z2 = 8 and inside
the sphere x2 + y2 + (z - 2)2 = 4.
The density of this solid is proportional to the distance from the
origin.
Determine the center of mass of S.
Is the center of mass located inside the solid S ?
Carefully justify your answer.