The Subaru telescope is a large optical-infrared telescope at the summit of Mauna Kea, Hawaii. The telescope has a parabolic mirror 8.2 m in diameter with a focal length of 15 m . a. Suppose that a cross section of the mirror is taken through the vertex, and that a coordinate system is set up with 0 , 0 placed at the vertex. If the focus is 0 , 15 , find an equation representing the curve. b. Determine the vertical displacement of the mirror relative to horizontal at the edge of the mirror. That is, find the y value at a point 4.1 m to the left or right of the vertex. c. What is the average slope between the vertex of the parabola and the point on the curve at the right edge?
The Subaru telescope is a large optical-infrared telescope at the summit of Mauna Kea, Hawaii. The telescope has a parabolic mirror 8.2 m in diameter with a focal length of 15 m . a. Suppose that a cross section of the mirror is taken through the vertex, and that a coordinate system is set up with 0 , 0 placed at the vertex. If the focus is 0 , 15 , find an equation representing the curve. b. Determine the vertical displacement of the mirror relative to horizontal at the edge of the mirror. That is, find the y value at a point 4.1 m to the left or right of the vertex. c. What is the average slope between the vertex of the parabola and the point on the curve at the right edge?
The Subaru telescope is a large optical-infrared telescope at the summit of Mauna Kea, Hawaii. The telescope has a parabolic mirror
8.2
m
in diameter with a focal length of
15
m
.
a. Suppose that a cross section of the mirror is taken through the vertex, and that a coordinate system is set up with
0
,
0
placed at the vertex. If the focus is
0
,
15
,
find an equation representing the curve.
b. Determine the vertical displacement of the mirror relative to horizontal at the edge of the mirror. That is, find the
y
value at a point
4.1
m
to the left or right of the vertex.
c. What is the average slope between the vertex of the parabola and the point on the curve at the right edge?
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
Write the given third order linear equation as an equivalent system of first order equations with initial values.
Use
Y1 = Y, Y2 = y', and y3 = y".
-
-
√ (3t¹ + 3 − t³)y" — y" + (3t² + 3)y' + (3t — 3t¹) y = 1 − 3t²
\y(3) = 1, y′(3) = −2, y″(3) = −3
(8) - (888) -
with initial values
Y
=
If you don't get this in 3 tries, you can get a hint.
Question 2
1 pts
Let A be the value of the triple integral
SSS.
(x³ y² z) dV where D is the region
D
bounded by the planes 3z + 5y = 15, 4z — 5y = 20, x = 0, x = 1, and z = 0.
Then the value of sin(3A) is
-0.003
0.496
-0.408
-0.420
0.384
-0.162
0.367
0.364
Question 1
Let A be the value of the triple integral SSS₂ (x + 22)
=
1 pts
dV where D is the
region in
0, y = 2, y = 2x, z = 0, and
the first octant bounded by the planes x
z = 1 + 2x + y. Then the value of cos(A/4) is
-0.411
0.709
0.067
-0.841
0.578
-0.913
-0.908
-0.120
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Finding The Focus and Directrix of a Parabola - Conic Sections; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=KYgmOTLbuqE;License: Standard YouTube License, CC-BY