F = <0, 1, z> . Without doing any calculations determine whether the flux across each sphere is positive, negative or zero. (a) Sphere with radius 2 and center at the origin. (b) Sphere with radius 1 and center at (1, 2, 3) (c) Sphere with radius 1 and center at (3, –2, 1).

Q: Let a = (-3, –4, –4) and b = (2, 2, 4) . Find scalars s and t so that sa + tb = (20, 4, 32) %3D %3D

A: We have to find the values of scalers s and t for a=-3,-4,-4 and b=2,2,4.

Q: Given S as a quadric with equation 4x^2 - (y-3)^2 + 4z^2 = 4 Find a generating curve for S (as a…

A: Given S as a quadric with equation 4x^2 - (y-3)^2 + 4z^2 = 4 Find a generating curve for S (as a…

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A: In this question, we have to calculate the line integral in both parts.

Q: Integrate counterclockwise dz, C the circle with z2 + 12z + 35 center –5 and radius 2. dz z2 + 12z +…

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Q: Match each parametrization with the corresponding surface. (i) (ii) (iii) (iv) (v) Answer Bank (u,…

A:

Q: let angle thetha be measured from x1 axis counterclockwise to a line drawn normal to the boundary…

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Q: 6) x² + (y – 4)² = 4 Center Radius

A: The given equation is x2+(y-4)2=4This is in the form of (x-h)2+(y-k)2=r2 which is a circle equation…

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Q: A bee starts at the point (5, 7, -3) (with units in meters) and travels at a constant speed of 9 m/s…

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Q: 36 for 0 <= u <= 6 and 0 <= v <= 2(pi) where <= is less then equal too where pi = 3.1415

A: Introduction: An ellipse is the locus of all points that satisfy the equations.x = a sint,  y = b…

Q: Transform (0, 5, 2) from rectangular into spherical form (here z is any negative number).

A: given rectangular coordinates is of the form (x, y, z) are (0,5,z) Now we are going to find…

Q: Prove x = cos x for some x € (0, π/2).

A: Intermediate value theorem: Let [a,b] be a closed and bonded interval and  f: [a,b]→R be a function…

Q: 6. The point V (3,-5) is rotated 270° clockwise around the origin. Find the coordinates of the…

A: The given point is V(3, -5).

Q: Consider the three following points of R'. A = (0, 2, 2) B = (1, 1, 1) C = (-1, 1,2) (a) Find the…

A: The scalar equation of a plane is of the form: ax+by+cz+d=0, where a, b, c ,d are constants. The…

Q: Find the equation of the sphere of radius at centered at (1, 4, 5)

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Q: Find a vector perpendicular to the surface described by the following equation at the point 2zy= =…

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Q: convert parametrici equation in rectangualr form  x=5sin t, y=4cos t

A:

Q: Let F = –9zi+ (xe"² – 2xe³) }+ 12 . Find ſg F ·dÃ, and let S be the portion of the plane 2x + 3z = 6…

A: The vector field is F→=-9zi→+xexz-2xex2j→+12k→ The equation of the plane is 2x+3z=6⇒ gx, y=6-2x3.…

Q: Let T be the tetrahedron with vertices at the origin and (4,0,0), (0,4,0) and (0,0,1). A fluid flows…

A: Given, function is, The rate of flow of the tetrahedron can be calculated by the flux. So, the…

Q: Parametrize the circle of radius 7 centered at (-2, 3) in the clockwise direction starting at…

A: Here I am attaching image so that you understand each and every step.

Q: y2 f(x, y)dx dy Let f(x, y) = e-x2-y² and

A: answer is in next step

Q: Describe the loci zz−2z−2z+8 = 0 expressed in terms of conjugate coordinates z, z.

A: It is given thatzz¯-2z-2z¯+8=0Where,z¯ is the conjugate co-ordinate of z.We have describe the locus.