(1 point) If C is the curve given by r(t)=(1+5sint)i+(1+3sin2t)j+(1+3sin3t)k, 0≤t≤π2 and F is the radial...

(1 point) If C is the curve given by r(t)=(1+5sint)i+(1+3sin2t)j+(1+3sin3t)k, 0≤t≤π2 and F is the radial vector field F(x,y,z)=xi+yj+zk, compute the work done by F on a particle moving along C.

Solutions

Expert Solution

milcah answered 1 year ago

Next > < Previous

Related Solutions

Find the length of the curve. 2 t i + et j + e−t k, 0 ≤...

Find the length of the curve. 2 t i + et j + e−t k, 0 ≤ t ≤ 5

The curve C is given by the parameterization ⃗r(t) = <−t , 1 − t^2> for...

The curve C is given by the parameterization ⃗r(t) = <−t , 1 − t^2> for −1 ≤ t ≤ 1. a) Choose any vector field F⃗ (x, y) = 〈some function , some other function〉 and setup the work integral of F⃗ over C. b)Choose any vector field G⃗(x,y) which has a potential function of the form φ(x,y)= x^3 + y^3 + some other stuff and compute the work done by G⃗ over C. Please use a somewhat basic...

Given the curve −→r (t) = <sin3 (t), cos3 (t),sin2 (t)> for 0 ≤ t ≤...

Given the curve −→r (t) = <sin3 (t), cos3 (t),sin2 (t)> for 0 ≤ t ≤ π/2 find the unit tangent vector, unit normal vector, and the curvature.

Find T(t), N(t), and B(t) for r(t) = t^2 i + (2/3)t^3 j + t k...

Find T(t), N(t), and B(t) for r(t) = t^2 i + (2/3)t^3 j + t k at the point P ( 1, (2/3) , 1)

f(t) = 1- t 0<t<1 a function f(t) defined on an interval 0 < t <...

f(t) = 1- t 0<t<1 a function f(t) defined on an interval 0 < t < L is given. Find the Fourier cosine and sine series of f and sketch the graphs of the two extensions of f to which these two series converge

Given the following economy: Y = C(Y - T) + I(r) + G C(Y - T)...

Given the following economy: Y = C(Y - T) + I(r) + G C(Y - T) = a + b(Y - T) I(r) = c - dr M/P = L(r,Y) L(r,Y) = eY - fr i. Solve for Y as a function of r, the exogenous variables G and T, and the model's parameters a, b, c, and d. ii. Solve for r as a function of Y, M, P, and the parameters e and f. iii. Derive the aggregate...

(1 point) For the given position vectors r(t)r(t) compute the unit tangent vector T(t)T(t) for the...

(1 point) For the given position vectors r(t)r(t) compute the unit tangent vector T(t)T(t) for the given value of tt . A) Let r(t)=〈cos5t,sin5t〉 Then T(π4)〈 B) Let r(t)=〈t^2,t^3〉 Then T(4)=〈 C) Let r(t)=e^(5t)i+e^(−4t)j+tk Then T(−5)=

a) ty’ −y/(1+T) = T,(T>0),y(1)=0 b) y′+(tanT)y=(cos(T))^2,y(0)=π2 Solve the above equations.

Let f: [0 1] → R be a function of the class c ^ 2 that...

Let f: [0 1] → R be a function of the class c ^ 2 that satisfies the differential equation f '' (x) = e^xf(x) for all x in (0,1). Show that if x0 is in (0,1) then f can not have a positive local maximum at x0 and can not have a negative local minimum at x0. If f (0) = f (1) = 0, prove that f = 0

Calculate the arc length of the indicated portion of the curve r(t). r(t) = i +...

Calculate the arc length of the indicated portion of the curve r(t). r(t) = i + (9t sin t)j + (9t cos t)k ; -3 ≤ t ≤ 7

Subjects