Differential Geometry (4) Show that the helix α(t) = (2 cos(3t), 2sin(3t), 3t) lies on a...
Differential Geometry
(4) Show that the helix α(t) = (2 cos(3t), 2sin(3t), 3t) lies on a circular cylinder, and find the arc-length of the helix. Determine β(s), the Reparametrized the helix by using the arc-length as the parameter.
Homework Answers
Add Answer to:
Differential Geometry
(4) Show that the helix α(t) = (2 cos(3t), 2sin(3t), 3t) lies on
a...
16. Find a set of parametrie equations t d) r(t)-(4t,3 cos(t).2sin(t) the line tangent to the gra...
Solve for 14(b,c) and 18 (b,c) please
16. Find a set of parametrie equations t d) r(t)-(4t,3 cos(t).2sin(t) the line tangent to the graph of r(t) (e.2 cos(t).2sin(t)) at to-0. Use the qu tion to approximate r(0.1). tion function to find the velocity and position vectors at t 2. 17. Find the principal unit normal vector to tih curve at the specified value of the parameter v(0)-0, r(0)-0 (b) a(t)cos(t)i - sin(t)i (a) r(t)-ti+Ij,t 2 (b) rt)-In(t)+(t+1)j.t2 14. Find the...
Consider the parametric curve given by x(t) = 16 sin3(t), y(t) = 13 cos(t) − 5 cos(2t) − 2 cos(3t...
Consider the parametric curve given by x(t) = 16 sin3(t), y(t) = 13 cos(t) − 5 cos(2t) − 2 cos(3t) − cos(4t), where t denotes an angle between 0 and 2π. (a) Sketch a graph of this parametric curve. (b) Write an integral representing the arc length of this curve. (c) Using Riemann sums and n = 8, estimate the arc length of this curve. (d) Write an expression for the exact area of the region enclosed by this curve.
4. Consider the nonhomogeneous linear system of differential equations / 4 3 4t / cos(3t) +...
4. Consider the nonhomogeneous linear system of differential equations / 4 3 4t / cos(3t) + 2te4t / l - sin(3t) / + 4tºe4t / sin(3t)) 43.4t sin(3) ( cos(3t) ) Given a particular solution t²4t / t th 4t / Find the general solution of the nonhomogeneous system. Hint: det(A – XI) = 12 – 81 + 25.
2. Consider the circular helix r(t)- (a cos t, a sin t, bt) where a > 0,b > 0. Let P(0, a, T) be ...
please answer all the 4 parts
of this question
2. Consider the circular helix r(t)- (a cos t, a sin t, bt) where a > 0,b > 0. Let P(0, a, T) be a point on the helix (a) Find the Frenet frame (T, N, B) at the point P (b) Find equations for the tangent and normal line at P (c) Find equations for the normal plane and the osculating plane at P (d) What is the curvature at...
The general solution to the second-order differential equation d2ydt2−4dydt+7y=0 is in the form y(x)=eαx(c1cosβx+c2sinβx). Find the values of α and β, where β>0. Answer: α= and β=
The general solution to the second-order differential equation d2ydt2−4dydt+7y=0d2ydt2−4dydt+7y=0 is in the form y(x)=eαx(c1cosβx+c2sinβx).y(x)=eαx(c1cosβx+c2sinβx). Find the values of αα and β,β, where β>0.β>0.Answer: α=α= and β=β=
Find the unit tangent vector T and the curvature k for the following parameterized curve. r(t)...
Find the unit tangent vector T and the curvature k for the following parameterized curve. r(t) = (3t+2, 5t - 7,67 +12) T= 000 (Type exact answers, using radicals as needed.) JUNIL Score: 0 of 2 pts 42 of 60 (58 complete) HW Score: 72.17%, 7 X 14.4.40 Ques Determine whether the following curve uses arc length as a parameter. If not, find a description that uses arc length as a parameter. r(t) = (7+2,8%. 31), for 1sts Select the...
Let α = {1 + 2t, t − t 2 , t + t 2} (a)...
Let α = {1 + 2t, t − t 2 , t + t 2}
(a) Show that α is a basis for P2(R).
(b) Let p(t) = 1 + 3t + t 2 . Find [p(t)]α.
(c) Define the transformation T : P2(R) → P2(R) as T (p(t)) = p
0 (t) − p(t) i.e., the difference of p(t) and its first derivative.
Determine whether this transformation is a linear
transformation.
(d) Find [T]α
Problem 4. Let a =...
Find the general solution x(t) of: x'' + 4x = 3 cos(2t) + 4 cos(3t) using...
Find the general solution x(t) of: x'' + 4x = 3 cos(2t) + 4 cos(3t) using the method of undetermined coefficients.
Decompose the signal s(t) = 5cos(2t) • cos(3t + π/4) into a linear combination and determine...
Decompose the signal s(t) = 5cos(2t) • cos(3t + π/4) into a linear combination and determine the amplitude, frequency, and phase shift of each component after decomposition. (Show all work and explain why.) Be Neat Please.
2. Find the Laplace transform of the following functions (a) f(t)3t+4 (b) cos(2Tt) (c) sin(2t T)...
2. Find the Laplace transform of the following functions (a) f(t)3t+4 (b) cos(2Tt) (c) sin(2t T) (d) sin(t) cos(t) "Use Trig. Identity" (e) f(t) te 2t use first shifting theorem
Solve for 14(b,c) and 18 (b,c) please
16. Find a set of parametrie equations t d) r(t)-(4t,3 cos(t).2sin(t) the line tangent to the graph of r(t) (e.2 cos(t).2sin(t)) at to-0. Use the qu tion to approximate r(0.1). tion function to find the velocity and position vectors at t 2. 17. Find the principal unit normal vector to tih curve at the specified value of the parameter v(0)-0, r(0)-0 (b) a(t)cos(t)i - sin(t)i (a) r(t)-ti+Ij,t 2 (b) rt)-In(t)+(t+1)j.t2 14. Find the...
4. Consider the nonhomogeneous linear system of differential equations / 4 3 4t / cos(3t) + 2te4t / l - sin(3t) / + 4tºe4t / sin(3t)) 43.4t sin(3) ( cos(3t) ) Given a particular solution t²4t / t th 4t / Find the general solution of the nonhomogeneous system. Hint: det(A – XI) = 12 – 81 + 25.
please answer all the 4 parts
of this question
2. Consider the circular helix r(t)- (a cos t, a sin t, bt) where a > 0,b > 0. Let P(0, a, T) be a point on the helix (a) Find the Frenet frame (T, N, B) at the point P (b) Find equations for the tangent and normal line at P (c) Find equations for the normal plane and the osculating plane at P (d) What is the curvature at...
Find the unit tangent vector T and the curvature k for the following parameterized curve. r(t) = (3t+2, 5t - 7,67 +12) T= 000 (Type exact answers, using radicals as needed.) JUNIL Score: 0 of 2 pts 42 of 60 (58 complete) HW Score: 72.17%, 7 X 14.4.40 Ques Determine whether the following curve uses arc length as a parameter. If not, find a description that uses arc length as a parameter. r(t) = (7+2,8%. 31), for 1sts Select the...
Let α = {1 + 2t, t − t 2 , t + t 2}
(a) Show that α is a basis for P2(R).
(b) Let p(t) = 1 + 3t + t 2 . Find [p(t)]α.
(c) Define the transformation T : P2(R) → P2(R) as T (p(t)) = p
0 (t) − p(t) i.e., the difference of p(t) and its first derivative.
Determine whether this transformation is a linear
transformation.
(d) Find [T]α
Problem 4. Let a =...
2. Find the Laplace transform of the following functions (a) f(t)3t+4 (b) cos(2Tt) (c) sin(2t T) (d) sin(t) cos(t) "Use Trig. Identity" (e) f(t) te 2t use first shifting theorem
Most questions answered within 3 hours.
-
Calculate the number of valence electrons for
[Mo(C6H6)(CO)3]
asked 1 minute ago -
MGT-201: Marketing Management
Before deciding on the structure of the channel marketers must
take several factors...
asked 2 minutes ago -
1. ACLs allow a router to control traffic within a network. The
concept is very similar...
asked 4 minutes ago -
Raising a heavy load requires work. Raising it in half the time
requires:
asked 3 minutes ago -
35. When the electron in a hydrogen atom falls from its first
excited energy level to...
asked 5 minutes ago -
A man is dragging a box of mass "m" by using a rope which rests
on...
asked 22 minutes ago -
Liquid octane
(CH3(CH2)6CH3) will
react with gaseous oxygen (O2) to produce gaseous carbon
dioxide (CO2) and...
asked 23 minutes ago -
For the reaction N2(g) +
O2(g) --> 2NO(g), if the initial
concentration of NO was 0.00M...
asked 26 minutes ago -
On a recent quiz, the class mean was 75 with a standard
deviation of 2.2. Calculate...
asked 42 minutes ago -
Discuss the Coefficient of Restitution in an elastic collision
compared to the Coefficient of Restitution in...
asked 46 minutes ago -
Pretend that you are
the audit manager on an annual financial statement audit engagement
for a...
asked 55 minutes ago -
A certain lens focuses light from an object 1.65 m away as an
image 41.8 cm...
asked 55 minutes ago