The Hubble Space Telescope was launched into space in 1990 and now orbits the Earth at 5 mi/sec at a distance of 353 mi above the Earth. From its location in space, the Hubble is free from the distortion of the Earth's atmosphere, enabling it to return magnificent images from distant stars and galaxies. The quality of the Hubble's images results from a large parabolic mirror, 2.4 mi 7.9 ft in diameter, that collects light from space. Suppose that a coordinate system is chosen so that the vertex of a cross section through the center of the mirror is located at 0 , 0 . Furthermore, the focal length is 57.6 m . a. Assume that x and y are measured in meters. Write an equation of the parabolic cross section of the mirror for − 1.2 ≤ x ≤ 1.2 See figure. b. How thick is the mirror at the edge? That is, what is the y value for x = 1.2 ?
The Hubble Space Telescope was launched into space in 1990 and now orbits the Earth at 5 mi/sec at a distance of 353 mi above the Earth. From its location in space, the Hubble is free from the distortion of the Earth's atmosphere, enabling it to return magnificent images from distant stars and galaxies. The quality of the Hubble's images results from a large parabolic mirror, 2.4 mi 7.9 ft in diameter, that collects light from space. Suppose that a coordinate system is chosen so that the vertex of a cross section through the center of the mirror is located at 0 , 0 . Furthermore, the focal length is 57.6 m . a. Assume that x and y are measured in meters. Write an equation of the parabolic cross section of the mirror for − 1.2 ≤ x ≤ 1.2 See figure. b. How thick is the mirror at the edge? That is, what is the y value for x = 1.2 ?
Solution Summary: The author calculates the equation of the parabolic cross section of a mirror for the Hubble Space telescope.
The Hubble Space Telescope was launched into space in
1990
and now orbits the Earth at
5
mi/sec
at a distance of
353
mi
above the Earth. From its location in space, the Hubble is free from the distortion of the Earth's atmosphere, enabling it to return magnificent images from distant stars and galaxies. The quality of the Hubble's images results from a large parabolic mirror,
2.4
mi
7.9
ft
in diameter, that collects light from space. Suppose that a coordinate system is chosen so that the vertex of a cross section through the center of the mirror is located at
0
,
0
. Furthermore, the focal length is
57.6
m
.
a. Assume that
x
and
y
are measured in meters. Write an equation of the parabolic cross section of the mirror for
−
1.2
≤
x
≤
1.2
See figure.
b. How thick is the mirror at the edge? That is, what is the
y
value for
x
=
1.2
?
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.
8. For x>_1, the continuous function g is decreasing and positive. A portion of the graph of g is shown above. For n>_1, the nth term of the series summation from n=1 to infinity a_n is defined by a_n=g(n). If intergral 1 to infinity g(x)dx converges to 8, which of the following could be true? A) summation n=1 to infinity a_n = 6. B) summation n=1 to infinity a_n =8. C) summation n=1 to infinity a_n = 10. D) summation n=1 to infinity a_n diverges.
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13: If the perimeter of a square is shrinking at a rate of 8 inches per second, find the rate at which its area is changing when its area is 25 square inches.
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11: A rectangle has a base that is growing at a rate of 3 inches per second and a height that is shrinking at a rate of one inch per second. When the base is 12 inches and the height is 5 inches, at what rate is the area of the rectangle changing?
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY