A typical dish antenna is built as a surface of revolution obtained by revolving a parabola about an axis of symmetry. One of the main benefits of this design is that the resulting antenna exhibits very high gains in the direction towards which it points, making it well-suited for applications in which a strong directionality is needed-such as TV reception and radar. We can model such a parabolic antenna as the surface of revolution obtained by revolving the function 1/2 ㅠ O / [(1 + KR²) ¹/² − 1] K 퓸 [(1 2π 3K about the y-axis. Here R is the radius of the antenna, and K-the curvature at the tip-controls how flat it is. Compute the surface area of this antenna in terms of the parameters R and K. y = 1 +2RK)¹/² − 1] 2π 3K O 4√2 R³/2 K-1/4 3 [(1 + KR²) ³/2 − 1] [(₁1 (1+2RK)³/2 O 2√2 R¹/2 K-3/4 3 K - 1] _x²³, 0 ≤ x ≤ R
A typical dish antenna is built as a surface of revolution obtained by revolving a parabola about an axis of symmetry. One of the main benefits of this design is that the resulting antenna exhibits very high gains in the direction towards which it points, making it well-suited for applications in which a strong directionality is needed-such as TV reception and radar. We can model such a parabolic antenna as the surface of revolution obtained by revolving the function 1/2 ㅠ O / [(1 + KR²) ¹/² − 1] K 퓸 [(1 2π 3K about the y-axis. Here R is the radius of the antenna, and K-the curvature at the tip-controls how flat it is. Compute the surface area of this antenna in terms of the parameters R and K. y = 1 +2RK)¹/² − 1] 2π 3K O 4√2 R³/2 K-1/4 3 [(1 + KR²) ³/2 − 1] [(₁1 (1+2RK)³/2 O 2√2 R¹/2 K-3/4 3 K - 1] _x²³, 0 ≤ x ≤ R
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![A typical dish antenna is built as a surface of revolution obtained by
revolving a parabola about an axis of symmetry. One of the main benefits
of this design is that the resulting antenna exhibits very high gains in the
direction towards which it points, making it well-suited for applications in
which a strong directionality is needed-such as TV reception and radar.
We can model such a parabolic antenna as the surface of revolution
obtained by revolving the function
O / [(1 +KR²) ¹/² − 1]
K
ㅠ
[(1 +2RK)¹/² − 1]
K
y =
about the y-axis. Here R is the radius of the antenna, and K-the
curvature at the tip-controls how flat it is. Compute the surface area of
this antenna in terms of the parameters R and K.
2π
O / [(1 + KR²) ³/² - 1]
3K
3
2π
3K
R³/2 K-1/4
[(1+2RK) ³/2 - 1]
2√2
O 22 R¹/2 K-3/4
3
K
-x²,
0 ≤ x ≤ R](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa82ab235-0403-49ff-b89c-b564bdf9f108%2F5601f06c-b4b9-4074-bfe4-4a6f514c1042%2Ffxdu5mg_processed.png&w=3840&q=75)
Transcribed Image Text:A typical dish antenna is built as a surface of revolution obtained by
revolving a parabola about an axis of symmetry. One of the main benefits
of this design is that the resulting antenna exhibits very high gains in the
direction towards which it points, making it well-suited for applications in
which a strong directionality is needed-such as TV reception and radar.
We can model such a parabolic antenna as the surface of revolution
obtained by revolving the function
O / [(1 +KR²) ¹/² − 1]
K
ㅠ
[(1 +2RK)¹/² − 1]
K
y =
about the y-axis. Here R is the radius of the antenna, and K-the
curvature at the tip-controls how flat it is. Compute the surface area of
this antenna in terms of the parameters R and K.
2π
O / [(1 + KR²) ³/² - 1]
3K
3
2π
3K
R³/2 K-1/4
[(1+2RK) ³/2 - 1]
2√2
O 22 R¹/2 K-3/4
3
K
-x²,
0 ≤ x ≤ R
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