67. The DNA (see Figure 3 on page 850). The radius of each helix is about 10 angstroms (1 Å= 10-8 cm). Each helix rises about 34 Å during each complete turn, and there are about 2.9 × 108 complete turns. Estimate the length of each helix.
67. The DNA (see Figure 3 on page 850). The radius of each helix is about 10 angstroms (1 Å= 10-8 cm). Each helix rises about 34 Å during each complete turn, and there are about 2.9 × 108 complete turns. Estimate the length of each helix.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
67
![= -T(S)N
the curve.
g of a curve.)
s) = 0.
et formulas,
ometry:
3 comes
0
e follow-
art as in
+ KT(S')³B
(a cos t, a sin t, bt),
64. Show that the circular helix r(t)
where a and b are positive constants, has constant curvature
and constant torsion. [Use the result of Exercise 63(d).]
65. Use the formula in Exercise 63(d) to find the torsion of the
curve r(t) = (1, 1², 1³).
66. Find the curvature and torsion of the curve x =
y = cosh t, z = t at the point (0, 1, 0).
=
67. The DNA molecule has the shape of a double helix (see
Figure 3 on page 850). The radius of each helix is about t
10 angstroms (1 Å
108 cm). Each helix rises about 34 Å
during each complete turn, and there are about 2.9 × 108
complete turns. Estimate the length of each helix.
=
sinh tạ
68. Let's consider the problem of designing a railroad track to
make a smooth transition between sections of straight track.
Existing track along the negative x-axis is to be joined
smoothly to a track along the line y = 1 for x ≥ 1.
(a) Find a polynomial P
function F defined by
=
P(x) of degree 5 such that the
(o
F(x) = P(x)
d Acceleration
if x ≤ 0
if 0<x< 1
if x ≥ 1
is continuous and has continuous slope and continuous
curvature.
(b) Graph F.
we show how the ideas of tangent and normal vectors and curvature can
ysics to study the motion of an object, including its velocity and accelera-
space curve. In particular, we follow in the footsteps of Newton by using
to derivo K](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8e478c4b-4364-44bb-80a1-5284f424b563%2Fdcb4f61b-a4b6-44d8-b8ff-75ac92946cd8%2F7sotop_processed.jpeg&w=3840&q=75)
Transcribed Image Text:= -T(S)N
the curve.
g of a curve.)
s) = 0.
et formulas,
ometry:
3 comes
0
e follow-
art as in
+ KT(S')³B
(a cos t, a sin t, bt),
64. Show that the circular helix r(t)
where a and b are positive constants, has constant curvature
and constant torsion. [Use the result of Exercise 63(d).]
65. Use the formula in Exercise 63(d) to find the torsion of the
curve r(t) = (1, 1², 1³).
66. Find the curvature and torsion of the curve x =
y = cosh t, z = t at the point (0, 1, 0).
=
67. The DNA molecule has the shape of a double helix (see
Figure 3 on page 850). The radius of each helix is about t
10 angstroms (1 Å
108 cm). Each helix rises about 34 Å
during each complete turn, and there are about 2.9 × 108
complete turns. Estimate the length of each helix.
=
sinh tạ
68. Let's consider the problem of designing a railroad track to
make a smooth transition between sections of straight track.
Existing track along the negative x-axis is to be joined
smoothly to a track along the line y = 1 for x ≥ 1.
(a) Find a polynomial P
function F defined by
=
P(x) of degree 5 such that the
(o
F(x) = P(x)
d Acceleration
if x ≤ 0
if 0<x< 1
if x ≥ 1
is continuous and has continuous slope and continuous
curvature.
(b) Graph F.
we show how the ideas of tangent and normal vectors and curvature can
ysics to study the motion of an object, including its velocity and accelera-
space curve. In particular, we follow in the footsteps of Newton by using
to derivo K
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