Question
In: Math
The electrical voltage in a certain region of space is given by the function V(x,y,z)=80+xz−sin(yz). If...
The electrical voltage in a certain region of space is given by the function V(x,y,z)=80+xz−sin(yz). If the directional derivative of V at (1,1,π) in the direction 〈a,−1,π〉 is π, what is the value of a?
Group of answer choices
π22
−π22
π2
−π2
None of the above.
Solutions
milcah answered 1 year agoRelated Solutions
The vector field given by E (x,y,z) = (yz – 2x) x + xz y +...
The vector field given by E
(x,y,z) = (yz – 2x)
x + xz y + xy
z may represent an electrostatic field?
Why? If so, finding the potential F a from which E may be
obtained.
Suppose that over a certain region of space the electrical potential V is given by the...
Suppose that over a certain region of space the electrical
potential V is given by the following equation.
V(x, y,
z) = 4x2 −
4xy + xyz
(a) Find the rate of change of the potential at P(3, 6,
6) in the direction of the vector v =
i + j − k.
???
(b) In which direction does V change most rapidly at
P?
???
(c) What is the maximum rate of change at P?
???
Compute the derivative of the given vector field F. Evaluate the line integral of F(x,y,z) = (y+z+yz , x+z+xz , x+y+xy )
Compute the derivative of the given vector field F. Evaluate the line integral of
F(x,y,z) = (y+z+yz , x+z+xz , x+y+xy )over the path C consisting of line segments joining (1,1,1) to (1,1,2), (1, 1, 2) to (1, 3, 2), and (1, 3, 2) to (4, 3, 2) in 3 different ways, along the given path, along the line from (1,1,1) to (4,3,2), and finally by finding an anti-derivative, f, for F.
Consider F and C below. F(x, y, z) = yz i + xz j + (xy...
Consider F and C below.
F(x, y, z) = yz i + xz j + (xy + 14z) k
C is the line segment from (3, 0, −1) to (6, 4, 2)
(a) Find a function f such that F =
∇f.
f(x, y, z) =
(b) Use part (a) to evaluate
C
∇f · dr along the given curve C.
Consider F and C below. F(x, y, z) = yz i + xz j + (xy...
Consider F and C below.
F(x, y, z) = yz i + xz j + (xy + 14z) k
C is the line segment from (3, 0, −3) to (5, 5, 1)
(a) Find a function f such that F =
∇f.
f(x, y, z) =
(b) Use part (a) to evaluate
C
∇f · dr along the given curve C.
Consider the scalar functions f(x,y,z)g(x,y,z)=x^2+y^2+z^2, g(x,y,z)=xy+xz+yz, and=h(x,y,z)=√xyz Which of the three vector fields ∇f∇f, ∇g∇g and...
Consider the scalar functions
f(x,y,z)g(x,y,z)=x^2+y^2+z^2,
g(x,y,z)=xy+xz+yz,
and=h(x,y,z)=√xyz
Which of the three vector fields ∇f∇f, ∇g∇g and ∇h∇h are
conservative?
Which of the following are correct for P(x,y,z)= xyz + x(yz)' + x'(y + z) +...
Which of the following are correct for P(x,y,z)= xyz +
x(yz)' + x'(y + z) + (xyz)' ?
1) P(0, 0, 1) = 0
2) P(0, 1, 0) = 1
3) P(0, 0, 0) = 1
4) P(1, 1, 1) = 1
5) P(1, 0, 0) = 0
Use implicit differentiation to find ∂z/∂x and ∂z/∂y if xz = cos (y + z).
Use implicit differentiation to find ∂z/∂x and ∂z/∂y if xz = cos
(y + z).
Find the maximum and minimum of the function f(x, y, z) = (x^2)(y^2)z in the region...
Find the maximum and minimum of the function f(x, y, z) =
(x^2)(y^2)z in the region D = {(x, y, z)|x^2 + 2y^2 + 3z^2 ≤
1}.
Calculate the integral of the function f (x, y, z) = xyz on the region bounded...
Calculate the integral of the function f (x, y, z) = xyz on the
region bounded by the z = 3 plane from the bottom, z = x ^ 2 + y ^
2 + 4 paraboloid from the side, x ^ 2 + y ^ 2 = 1 from the top.
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