Consider the vector Field 7 and the curve C below. F(x,y) = (3 +4 ху?) 1 + 4x²yј, C is the arc of the hyperbola y=¹/x from (1,1) to (2/2)

Q: vector-valued function 7(t) the parametric equations of the line.) b) Find the distance of the point…

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Q: 5. (a) (b) The surfaces (x - 2)² + z² = 9 and y = z² intersect along the curve C. Find a vector…

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Q: Without finding T and N, write the acceleration of the motion a(t) to the position vector r(t) =…

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Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

A: Given that v=<x-y, z+y+9, z2> and the given curve is y=1-x2-z2,y≥0 To find: The value of ∬S…

Q: The figure shows the vector field F (x,y) = {2xy,x2 } and three curves that start at (1,2) and end…

A: Given, vector field F→x,y=2xy,x2 and three curves that start at 1,2 and end at 3,2.

Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

A: Adding the plane surface y=0 to close the surface and apply the gauss divergence theorem.

Q: Find a vector parametric equation r(t) for the line through the points P = (4, -3, 4) and Q = (3,…

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Q: Find a vector parametric equation F(t) for the line through the points P = (5,-5, -5) and Q = (10,…

A: The given points are P=5, -5, -5 and Q=10, -6, -9. (a) We have to find r→t when r→0=5, -5, -5 and…

Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

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Q: Solution r(t) = 6 cos(t) i + 6 sin(t)j + 3tk. The parametric equations for this curve are x= y = 6…

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Q: bee with a velocity vector r' (t) starts out at (7, -3, 7) at t = 0 and flies around for 6 sec me t…

A: We know position vector of bee if it has a velocity vector  is We are given

Q: 10. A drop of water falls on the surface z³x+z¹y² + x²y³ = 79 at the point (3, 2, 1). Find a three-…

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Q: Match the vector field with its graph. F(x, y) = yi -5+ -5+

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Q: 2) Let r(t) = (t, t² , e'). Find an equation for the unit tangent vector T(t).

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Q: Suppose that over a certain region of space the electrical potential V is given by the following…

A: Given that, Vx,y,z=4x2-3xy+xyz Find Vx,Vy,Vz:  Vx=8x-3y+yzVy=-3x+xzVz=xy Gradient of V at P(6,6,5)…

Q: An object moves in space with acceleration a(t) = 12t²i+6tj+2k. When t = 0, the object is at (1, 0,…

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Q: Find r'(t), r(t), and r'(to) for the given value of to. r(t) = 3 cos(t)i + 3 sin(t)j, to r'(t) =…

A: The given vector valued function

Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

A: Given data net velocity (v) V=x-y, z+y+9, z2 net equation  y=1-x2-z2   , y≥0 find  ∫∫sv.ds= ? in…

Q: A particle traveling in a straight line is located at the point (1, -1, 2) and has speed 2 at time t…

A: Given: A particle traveling in a straight line is located at the point (1, -1, 2) and has speed 2 at…

Q: express the parametric curve in the form y = f (x) c(t) = (4t − 3, 10 − t)

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Q: 3. (a) Find an equation for the tangent line to the curve parameterized by 3(t) = (. e"-) at the…

A: Given data: s→(t)=t3+t+2t2+1, et2-1 point p→=<0,1> So, x=0, y=1⇒t3+t+2t2+1=0et2-1=1=e0…

Q: At which point P does the curve r(t) = ( 2t+3, 3t², t* ) given in vector form have the tangent…

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Q: 19) Consider the vector function 7 (t) = (cos (3t), sin (3t) , 3t). Write 7" () in the form at () T…

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