The DNA molecule comes in the form of a double helix, meaning two helices that wrap around one another. Suppose a single one of the helices has a radius of 6 A (1 angstrom = 10-8 cm) and one full turn of the helix has a height of 31 A. Find the paremetrization r(t) of the helix. r(t) = (6 cos(1), a, b) (Use symbolic notation and fractions where needed.) a= b= Find the arc length L of one full turn of the helix. L=
The DNA molecule comes in the form of a double helix, meaning two helices that wrap around one another. Suppose a single one of the helices has a radius of 6 A (1 angstrom = 10-8 cm) and one full turn of the helix has a height of 31 A. Find the paremetrization r(t) of the helix. r(t) = (6 cos(1), a, b) (Use symbolic notation and fractions where needed.) a= b= Find the arc length L of one full turn of the helix. L=
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Helical Structure of DNA
The DNA molecule is known to have the structure of a double helix, consisting of two helices that wrap around each other. In this exercise, we consider a single helix with the following parameters:
- The radius of the helix is 6 Å (1 angstrom = \(10^{-8}\) cm).
- One full turn of the helix has a height of 31 Å.
### Problem Statement
Find the parametrization \( r(t) \) of the helix, given by:
\[ r(t) = \langle 6 \cos(t), a, b \rangle \]
**(Use symbolic notation and fractions where needed.)**
1. Determine the values of \( a \) and \( b \).
\[ a = \quad \text{(Answer box)} \]
\[ b = \quad \text{(Answer box)} \]
2. Find the arc length \( L \) of one full turn of the helix.
\[ L = \quad \text{(Answer box)} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff95e890f-a45d-49ff-801b-f76192665ba7%2F3ef24252-549a-4ee5-8d1a-2e4e9ef924fc%2Fxx6i3vh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Helical Structure of DNA
The DNA molecule is known to have the structure of a double helix, consisting of two helices that wrap around each other. In this exercise, we consider a single helix with the following parameters:
- The radius of the helix is 6 Å (1 angstrom = \(10^{-8}\) cm).
- One full turn of the helix has a height of 31 Å.
### Problem Statement
Find the parametrization \( r(t) \) of the helix, given by:
\[ r(t) = \langle 6 \cos(t), a, b \rangle \]
**(Use symbolic notation and fractions where needed.)**
1. Determine the values of \( a \) and \( b \).
\[ a = \quad \text{(Answer box)} \]
\[ b = \quad \text{(Answer box)} \]
2. Find the arc length \( L \) of one full turn of the helix.
\[ L = \quad \text{(Answer box)} \]
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