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 33 A. Find the paremetrization r(t) of the helix. r(t) = (6 cos(t), a, b) (Use symbolic notation and fractions where needed.) a = 6 sin((t)) b = 33t 2π 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 33 A. Find the paremetrization r(t) of the helix. r(t) = (6 cos(t), a, b) (Use symbolic notation and fractions where needed.) a = 6 sin((t)) b = 33t 2π 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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![**DNA Structure and Parametrization of a Helix**
**Overview:**
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 33 A.
**Helix Parametrization:**
Find the parametrization \( \mathbf{r}(t) \) of the helix.
\[ \mathbf{r}(t) = \langle 6 \cos(t), a, b \rangle \]
(Use symbolic notation and fractions where needed.)
**Solution:**
\[ a = 6 \sin(t) \]
\[ b = \frac{33t}{2\pi} \]
**Arc Length Calculation:**
Find the arc length \( L \) of one full turn of the helix.
\[ L = \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F717f4d87-5a32-4cdf-855f-90bb556622e3%2Fed9b912a-c985-416c-bff2-534e77939432%2Fcpceis_processed.png&w=3840&q=75)
Transcribed Image Text:**DNA Structure and Parametrization of a Helix**
**Overview:**
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 33 A.
**Helix Parametrization:**
Find the parametrization \( \mathbf{r}(t) \) of the helix.
\[ \mathbf{r}(t) = \langle 6 \cos(t), a, b \rangle \]
(Use symbolic notation and fractions where needed.)
**Solution:**
\[ a = 6 \sin(t) \]
\[ b = \frac{33t}{2\pi} \]
**Arc Length Calculation:**
Find the arc length \( L \) of one full turn of the helix.
\[ L = \]
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