Arclength
Homework Answers
First, take the derivative of the function with respect to x and that is your value for r'(t).
After you've taken the derivative of the function, the arclength of the function
s(t) = sqrt (1+(r'(t))^2)
Therefore that is your answer for the arclength, now to compute it with the initial point, substitute 0 for t.
Assignment 4 - Vector Functions: Problem 7 Previous Problem Problem List Next Problem (1 point) Consider...
Assignment 4 - Vector Functions: Problem 7 Previous Problem Problem List Next Problem (1 point) Consider the curve r = (e-44 cos(—2t), e-4t sin(–2t), e-4). Compute the arclength function s(t): (with initial point t = 0). 2(14)^(1/2)*(1/4-(e^(-4t))/4) Preview My Answers Submit Answers You have attempted this problem 1 time. Your overall recorded score is 0%. You have unlimited attempts remaining.
(1 point) Find the arclength s(t) of the curve r(t) Don't forget to submit your answer as a function of t. 9t21+ 8t3j + 4t4k from r(0) to r(t). You can assume that t is positive. s(t) (1 poi...
(1 point) Find the arclength s(t) of the curve r(t) Don't forget to submit your answer as a function of t. 9t21+ 8t3j + 4t4k from r(0) to r(t). You can assume that t is positive. s(t)
(1 point) Find the arclength s(t) of the curve r(t) Don't forget to submit your answer as a function of t. 9t21+ 8t3j + 4t4k from r(0) to r(t). You can assume that t is positive. s(t)
2. Reparameterize each of the following paths in terms of their arclength S. a)(t)(t2, t,) b) )(sin(t), t, cos(t))...
2. Reparameterize each of the following paths in terms of their arclength S. a)(t)(t2, t,) b) )(sin(t), t, cos(t)) c)E(t)=(tcos(t), t sin(t))
2. Reparameterize each of the following paths in terms of their arclength S. a)(t)(t2, t,) b) )(sin(t), t, cos(t)) c)E(t)=(tcos(t), t sin(t))
(1 point) Evaluate s(t) du for the Bermoulli spiral r(t) -(e cos(5t), e sin(5t,) It is convenient...
(1 point) Evaluate s(t) du for the Bermoulli spiral r(t) -(e cos(5t), e sin(5t,) It is convenient to take -oo as the lower limit since s(-oo) 0. Then use s to obtain an arc length parametrization of r (t).
(1 point) Evaluate s(t) du for the Bermoulli spiral r(t) -(e cos(5t), e sin(5t,) It is convenient to take -oo as the lower limit since s(-oo) 0. Then use s to obtain an arc length parametrization of r (t).
1 point) Find the arclength of the curve r(t)=(2t2,2y2t,int), for 1-t-6. 1 point) Find the arclength of the curve r(t)=(2t2,2y2t,int), for 1-t-6.
1 point) Find the arclength of the curve r(t)=(2t2,2y2t,int), for 1-t-6.
1 point) Find the arclength of the curve r(t)=(2t2,2y2t,int), for 1-t-6.
1 point) Consider the initial value problem dy 29y--9e cos( dt dt2 dt Write down the Laplace transform of the left-hand...
1 point) Consider the initial value problem dy 29y--9e cos( dt dt2 dt Write down the Laplace transform of the left-hand side of the equation given the initial conditions Y(sA2-10s+29)+3s-24 Your answer should be a function of s and Y with Y denoting the Laplace transform of the solution y. Write down the Laplace transform of the right-hand side of the equation -9(s-5(S-5)A2+9) Your answer should be a function of s only. Next equate your last two answers and solve...
e.) What is the equation of the tangent plane to the function z = x2 +...
e.) What is the equation of the tangent plane to the function z = x2 + 4y2 at the point with x = 2, y = -1? [8 points) f.) For the curve through space F(t) =< sin(3t), cos(3t), 2t>, what is the unit tangent vector at t = 7/2? [8 points] g.) Starting from t= 0, reparameterize the curve r(t) = (1 - 2t) î +(-4+ 2t)ſ+(-3 – t)k in terms of arclength. [8 points]
The arclength of the curve r(t) = (2 cos(at/2), 2 sin"(at/2),1), between the points r =...
The arclength of the curve r(t) = (2 cos(at/2), 2 sin"(at/2),1), between the points r = (2,0,1) and r = (0,2,1), is given by the expression -] . a37 sin(a4nt/2) cos(azat/2) dt = 06. 02 Fill in the blank for ai, i = 1,...,6. Answers should be integers, no spaces, no punctu- ation, the only non-numeric symbol allowed is a minus sign. where a1, 22, 23, 24, 25 and 26 are integers given by: 01 = A2 = A3 =...
NOTE: PLEASE DO Q.3 Part d and e Answers are given below: Question 3 (16 marks)...
NOTE: PLEASE DO Q.3 Part d and e
Answers are given below:
Question 3 (16 marks) Consider the periodic signal T v(t)24 cos(2t ) - 4 sin(5t - 2 The signal v is given as an input to a linear time-invariant continuous-time system with fre- quency response 4 0 lwl 2 2 jw H(w) lwlT 2, 1 2 jw (a) 3 marks] Find the fundamental period To and frequency wo of v (b) [3 marks] Express v in cosine sine...
(4) Evaluate the line integral F dr where C is the epicycloid with parametrization given by r(t) 5 cos t - gradient of...
(4) Evaluate the line integral F dr where C is the epicycloid with parametrization given by r(t) 5 cos t - gradient of the function f(x, y) = 3 sin(ry) + cos(y2) cos 5t and y(t) = 5 sin t - sin 5t for 0 < t < 2« and F is the (5) EvaluateF dr where F(x, y) with counterclockwise orientation (2y, xy2and C is the ellipse 4r2 9y2 36 _ F dr where F(r, y) = (x2 -...
Assignment 4 - Vector Functions: Problem 7 Previous Problem Problem List Next Problem (1 point) Consider the curve r = (e-44 cos(—2t), e-4t sin(–2t), e-4). Compute the arclength function s(t): (with initial point t = 0). 2(14)^(1/2)*(1/4-(e^(-4t))/4) Preview My Answers Submit Answers You have attempted this problem 1 time. Your overall recorded score is 0%. You have unlimited attempts remaining.
(1 point) Find the arclength s(t) of the curve r(t) Don't forget to submit your answer as a function of t. 9t21+ 8t3j + 4t4k from r(0) to r(t). You can assume that t is positive. s(t)
(1 point) Find the arclength s(t) of the curve r(t) Don't forget to submit your answer as a function of t. 9t21+ 8t3j + 4t4k from r(0) to r(t). You can assume that t is positive. s(t)
2. Reparameterize each of the following paths in terms of their arclength S. a)(t)(t2, t,) b) )(sin(t), t, cos(t)) c)E(t)=(tcos(t), t sin(t))
2. Reparameterize each of the following paths in terms of their arclength S. a)(t)(t2, t,) b) )(sin(t), t, cos(t)) c)E(t)=(tcos(t), t sin(t))
(1 point) Evaluate s(t) du for the Bermoulli spiral r(t) -(e cos(5t), e sin(5t,) It is convenient to take -oo as the lower limit since s(-oo) 0. Then use s to obtain an arc length parametrization of r (t).
(1 point) Evaluate s(t) du for the Bermoulli spiral r(t) -(e cos(5t), e sin(5t,) It is convenient to take -oo as the lower limit since s(-oo) 0. Then use s to obtain an arc length parametrization of r (t).
1 point) Find the arclength of the curve r(t)=(2t2,2y2t,int), for 1-t-6.
1 point) Find the arclength of the curve r(t)=(2t2,2y2t,int), for 1-t-6.
1 point) Consider the initial value problem dy 29y--9e cos( dt dt2 dt Write down the Laplace transform of the left-hand side of the equation given the initial conditions Y(sA2-10s+29)+3s-24 Your answer should be a function of s and Y with Y denoting the Laplace transform of the solution y. Write down the Laplace transform of the right-hand side of the equation -9(s-5(S-5)A2+9) Your answer should be a function of s only. Next equate your last two answers and solve...
e.) What is the equation of the tangent plane to the function z = x2 + 4y2 at the point with x = 2, y = -1? [8 points) f.) For the curve through space F(t) =< sin(3t), cos(3t), 2t>, what is the unit tangent vector at t = 7/2? [8 points] g.) Starting from t= 0, reparameterize the curve r(t) = (1 - 2t) î +(-4+ 2t)ſ+(-3 – t)k in terms of arclength. [8 points]
The arclength of the curve r(t) = (2 cos(at/2), 2 sin"(at/2),1), between the points r = (2,0,1) and r = (0,2,1), is given by the expression -] . a37 sin(a4nt/2) cos(azat/2) dt = 06. 02 Fill in the blank for ai, i = 1,...,6. Answers should be integers, no spaces, no punctu- ation, the only non-numeric symbol allowed is a minus sign. where a1, 22, 23, 24, 25 and 26 are integers given by: 01 = A2 = A3 =...
NOTE: PLEASE DO Q.3 Part d and e
Answers are given below:
Question 3 (16 marks) Consider the periodic signal T v(t)24 cos(2t ) - 4 sin(5t - 2 The signal v is given as an input to a linear time-invariant continuous-time system with fre- quency response 4 0 lwl 2 2 jw H(w) lwlT 2, 1 2 jw (a) 3 marks] Find the fundamental period To and frequency wo of v (b) [3 marks] Express v in cosine sine...
(4) Evaluate the line integral F dr where C is the epicycloid with parametrization given by r(t) 5 cos t - gradient of the function f(x, y) = 3 sin(ry) + cos(y2) cos 5t and y(t) = 5 sin t - sin 5t for 0 < t < 2« and F is the (5) EvaluateF dr where F(x, y) with counterclockwise orientation (2y, xy2and C is the ellipse 4r2 9y2 36 _ F dr where F(r, y) = (x2 -...
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