The James Webb Space Telescope (JWST) is a new space telescope currently under construction. The JWST will orbit the Sun in an orbit roughly 1.5 million km from the earth, in a position with the Earth between the telescope and the Sun. The primary mirror of the JWST will consist of 18 hexagonally shaped segments that when fitted together will be 6.5 min diameter (over 2.5 times the diameter of the Hubble). With a larger mirror, the JWST will be able to collect more light to “see" deeper into space. The primary mirror when pieced together will function as a parabolic mirror with a focal length of 131.4 m . Suppose that a coordinate system is chosen with 0 , 0 at the center of a cross section of the primary mirror. Write an equation of the parabolic cross section of the mirror for − 3.25 ≤ x ≤ 3.25 . Assume that x and y are measured in meters.
The James Webb Space Telescope (JWST) is a new space telescope currently under construction. The JWST will orbit the Sun in an orbit roughly 1.5 million km from the earth, in a position with the Earth between the telescope and the Sun. The primary mirror of the JWST will consist of 18 hexagonally shaped segments that when fitted together will be 6.5 min diameter (over 2.5 times the diameter of the Hubble). With a larger mirror, the JWST will be able to collect more light to “see" deeper into space. The primary mirror when pieced together will function as a parabolic mirror with a focal length of 131.4 m . Suppose that a coordinate system is chosen with 0 , 0 at the center of a cross section of the primary mirror. Write an equation of the parabolic cross section of the mirror for − 3.25 ≤ x ≤ 3.25 . Assume that x and y are measured in meters.
The James Webb Space Telescope (JWST) is a new space telescope currently under construction. The JWST will orbit the Sun in an orbit roughly
1.5
million km from the earth, in a position with the Earth between the telescope and the Sun. The primary mirror of the JWST will consist of
18
hexagonally shaped segments that when fitted together will be
6.5
min diameter (over
2.5
times the diameter of the Hubble). With a larger mirror, the JWST will be able to collect more light to “see" deeper into space.
The primary mirror when pieced together will function as a parabolic mirror with a focal length of
131.4
m
. Suppose that a coordinate system is chosen with
0
,
0
at the center of a cross section of the primary mirror. Write an equation of the parabolic cross section of the mirror for
−
3.25
≤
x
≤
3.25
. Assume that x and y are measured in meters.
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