Question1:x=2-t, y=3-2t, z=4-3t a) Explain why the work done by a force field ?(?, ?, ?)...

Question1:x=2-t, y=3-2t, z=4-3t

a) Explain why the work done by a force field ?(?, ?, ?) is the line integral ∫c ? ∙ ?? where C is a curve defined by ?(?) = ?(?) ? + ?(?)? + ?(?)?

b) Find the work done by the force field ?(?, ?) = −?? + ?? on a particle moving along the straight line y = 2x + 3 from A(0,3) to B(1,5)

Expert Solution

milcah answered 2 years ago

given the curve x(t)=t^2+3 and y(t)=2t^3-3t^2 find the following: a.) find the derivative of the curve...

given the curve x(t)=t^2+3 and y(t)=2t^3-3t^2 find the following: a.) find the derivative of the curve at t=1 b.) dind the concavity of the curve c.) graph the curve from t=0 to t=2 d.) find the area if the curve on the interval 0<=t<=2

Find the work done by the force field F(x,y,z) =8x^2yzi+5zj-4xyk r(t)=ti+t^2j+t^3k (0

3. Given the parametric equations x = 3t /1 + t^3 and y = 3t^2 /1...

3. Given the parametric equations x = 3t /1 + t^3 and y = 3t^2 /1 + t^3 . a) Show that the curve produced also satisfies the equation x^3 + y^3 = 3xy. b) Compute the limits of x and y as t approaches −1: i. from the left ii. from the right c) To avoid the issue in part b), graph the curve twice in the same command, once for −5 < t < −1.5 and once for...

Velocity field for this system is: V=[X^2-(yz^1/2/t)]i-[zy^3+(x^1/3z^2/t^1/2)j+[-x^1/3t^2/z*y^1/2]k find the components of acceleration for the system.

Velocity field for this system is: V=[X^2-(y*z^1/2/t)]i-[z*y^3+(x^1/3*z^2/t^1/2)j+[-x^1/3*t^2/z*y^1/2]k find the components of acceleration for the system.

Determine whether the lines and are parallel, skew, or intersecting. L1:X=1+2t, Y=2+3t , z=3+4t L2: X=-1+6s,...

Determine whether the lines and are parallel, skew, or intersecting. L1:X=1+2t, Y=2+3t , z=3+4t L2: X=-1+6s, Y=3-s ,z=-5+2s

An object moves along the x-axis according to the equation x = 3t ^ 3 - 2t ^ 2 + t along the x-axis.

An object moves along the x-axis according to the equation x = 3t ^ 3 - 2t ^ 2 + t along the x-axis. Find the instantaneous velocity at t = 2 s.A) 29 B) 18 C) 48 D) 43

The temperature at a point (x,y,z) is given by T(x,y,z)=200e^(-x^2-y^2/4-z^2/9) , where T is measured in...

The temperature at a point (x,y,z) is given by T(x,y,z)=200e^(-x^2-y^2/4-z^2/9) , where T is measured in degrees Celsius and x,y, and z in meters. just try to keep track of what needs to be a unit vector. a) Find the rate of change of the temperature at the point (1, 1, -1) in the direction toward the point (-5, -4, -3). b) In which direction (unit vector) does the temperature increase the fastest at (1, 1, -1)? c) What is...

Determine whether it is linear or nonlinear system: 1. y(t) = 3 + x(2t) 2. y(t)...

Determine whether it is linear or nonlinear system: 1. y(t) = 3 + x(2t) 2. y(t) = x(4t) 3. y(t) = -4t[x(2t)] 4. y(t) = e^2[x(2t)] 5. y(t) = x^5(t) 6. y(t) = cost[x(2t)]

Let L be the line parametrically by~r(t) = [1 + 2t,4 +t,2 + 3t] and M...

Let L be the line parametrically by~r(t) = [1 + 2t,4 +t,2 + 3t] and M be the line through the points P= (−5,2,−3) and Q=(1,2,−6). a) The lines L and M intersect; find the point of intersection. b) How many planes contain both lines? c) Give a parametric equation for a plane Π that contains both lines

Given the two lines (x, y, z) = (4, -3, 5) + t(2, 0, -3) (x,...

Given the two lines (x, y, z) = (4, -3, 5) + t(2, 0, -3) (x, y, z) = (4, -3, 5) + s(5, 1, -1) a) determine a vector equation for the plane that combines the two lines b) parametric equations of the plane that contains the two lines c) Cartesian equation of the plane that contains the two lines

Question