5. Consider a parabolic solar panel which lies in the part of z = x2 + y? below the plane z = 1, which is oriented downwards. A field of photons is given by (x2, y?, -2). Calculate the flux of the photon field through the solar panel.

Q: 4. Find the work done by the force field F (x,y) = (x + y)î + (xy)ĵ in moving a particle along the…

A: The force field is given by F→ = x+yi^+xyj^ The end points of the straight line along which the…

Q: What is an equation for the largest ball centred at (0,0, 1) that can fit in the paraboloid z = 3 -…

A: To find the equation for the largest ball centered at (0, 0, 1) that can fit in the below equation…

Q: If KN=2x+1 and NJ=3x+5, what value of x makes point N the centroid? K, J M

A: (1).   If in the given triangle N is the centroid then the point N divides the line HL, JK and LM in…

Q: Find a parametrization for the cylinder x2 + y2 = 1.

A:

Q: What is the flux of the vector field F(x, y, z) = [9y, 2xy, 4yz + 234xy] through the unit cube [0,1]…

A: We find the flux of the vector field F(x, y, z) = [9y, 2xy, 4yz + 234xy] through the unit cube [0,1]…

Q: Given two points A(3, 0) and B(), find the work done by the following force field in moving a…

A:

Q: Suppose we have part of a hyperboloid of two sheets -4x? -4y? + z? = 9 where z 20 (so the upper…

A: Equation of hyperboloid of two sheets is: −4x2−4y2+z2=9 Where z≥0 and z≤15

Q: Find the path of a heat-seeking particle placed at point P on a metal plate with a temperature field…

A:

Q: 4. Where does the curve r(t) = ti + t²j+ (3 t2)k intersect the paraboloid z = x2 +y² ?

A:

Q: Is the two-dimensional vector field V = -2y 2x a possible velocity field x²+y² 'x² +y² for an…

A: For a two dimensional incompressible for a vector field V=ui+vj. ∂u∂x+∂v∂y=0

Q: The magnetic field along a solenoid is conservative and given by 2xy 7- (2 x ₁-2x, (x²+1)-2). ¡−2x,…

A: Given a vector field as F=2xyx2+1-2x,lnx2+1-2 We need to find the scalar potential from which this…

Q: Find the flux of F = yi + 2zxj – z²k through the parabolic cylinder y = x2,0 < x < 1,0 < z< 4, in…

A:

Q: Show that the value of ∮C xy2 dx + (x2y + 2x) dy around any square depends only on the area of the…

A:

Q: 2) Given the vector field F = (- Vx²+y² 2z2) write the integral to calculate the outward x²+y² flux…

A: We have to find the outward flux across the cylinder x2+y2=100.

Q: 6. What is an equation for the largest ball centred at (0,0, 1) that can fit in the paraboloid z…

A:

Q: Consider the force field F = (ev – e2" , (x + })ev) and the curve C = C¡U C2 where Cı is the line…

A: As per our guidelines we are allowed to do 1 question at a time. Please post other questions next…

Q: Sketch the surface z = 3x? + y? +1 and find its linear approximation at P-(0, -1)

A:

Q: The work done by the force field F(x, y) = 5y'i + (x² – 2)j in moving a particle along the arc y =…

A: As per the company's guidelines, we are supposed to solve first question for you, kindly repost…

Q: C is the intersection curve between the paraboloid z=x²+y² and

A: Given that C is the intersection curve between the paraboloid z=x2+y2 and the cylinder x2+y2=1.

Q: Find the work done by the force field F→(x,y)=54x^2y^2i→+(36x^3y−2)j→in moving an object from the…

A:

Q: 1)calculate a*yz dædydz where D is the rectangular parallelepiped 1< « < 2,1 < y < 2,1 < z < 5

A:

Q: Find the flux of F = 3zi + 5y? i+ 3x k out of the closed cone y = Væ2 + z2, with 0 < y < 1. flux =

A:

Q: (8) Find the point(s) where the line r(t) = ti+(1+t)j+5k intersects the paraboloid z = x² + y?.

A: A detailed solution is given below.

Q: Distinguish briefly the Skewness and kurtosis

A: Skewness is a measure of symmetry where symmetry means equal proportion to the left and right to the…

Q: 1. Use isoclines to sketch the direction field for y' = x+ 2y and sketch the solution curve that…

A:

Q: Find the outward flux of F = (4x +25y*,0,) 10z through the surface 25 4 9

A: Solution:-

Q: Find the outward flux across the domain D xi + yj + zk x2 +y? + z? F(x,v,z) = across the sphere x2…

A:

Q: Suppose that v = (0, y, 0) is the velocity field of a fluid and let S be the surface defined by y =…

A: Given, the velocity field v→=0, y, 0and S be the surface defined by y=x2+z2, with y≤1.

Q: Evaluate both sides for the field- rectangular parallelepiped X = 0 and 1 Y=0 and 2 and Z=0 and 3.…

A:

Q: Find the flux of the field F up through the part of the 1+ xy paraboloid z = 1 – x² – y? that…

A: FORMULA: Flux=∬F.n^ dS According to Stokes theorem, ∬F.n^ dS =∬∇×F . n^ dS According to the…

Q: 1 Evaluate dV, where E lines between the spheres a? + y? + z² = 25 and %3D x² + y? + z2 49 in the…

A:

Q: Sketch the bifurcation diagram for y = (A– 4t)y (where A is a parameter, as usual). 2

A: To find- Sketch the bifurcation diagram for y' = λ - 4t2y (where λ is a parameter, as usual)

Q: Find the work done by the force field F(x, y) = xi + 2yj on a particle moving along the path C:x =…

A:

Q: The work done in moving a particle in the force field F= x- i+ 3xy j from (0,0) to (1,2) along the…

A:

Q: Given the radial field (x, y, z) (x² + y² + z²)³/2 |r|3/2 Find the outward flux across the sphere of…

A: Image is attached with detailed solution.

Q: Evaluate € fff.₂²². e² dV where E is enclosed by the paraboloid z = 3 + z² + y², the cylinder z² +…

A: We need to find integral.

Q: A=(2x-3y)ax+(2xy-y2)ay Prove the Stokes theorem for the triangular linear path in the shape that is…

A: The general form of a vector valued function in a plane is given by A=Axax+Ayay, where Ax and Ay are…

Q: Find the work done by the force field F in moving an object from P(-4, 8) to Q(6, 4). F(x,y) = 2* 1…

A:

Q: he temperature in a temperature-controlled chamber is given by a 3D scalar field Tlx, y, 2) = Ax®yz…

A: Note- Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Find the work done in moving a particle in the force field F = (2r + y)i + (3y – 2)j along the…

A: Work done in moving a particle in the force field along along the curve C is:  ∫CF→·dr→ here F→ is…

Q: 6) Given the vector field F = (-x,-y,-z) '(x²+y2+z²)3/2! write the integral to calculate the outward…

A: First we parameterize field F then we calculate the Flux across the sphere using following formula:

Q: 43 Find the work done by the force field F(x, y) = (x² ln(y + 5), -) on a particle 3(y + 5) that…

A: Given force field F(x,y)=x2ln(y+5),x33(y+5) and circle x2+y2=4. The objective is to find the work…

Q: 3. Show that every sphere through the circle x2 +y-2ax+r²=0, z=0 cuts orthogonally every sphere…

A: This is a co-ordinate geometry problem

Q: 1. Calculate the work done when a force F = 3xyî – y?j moves a particle in the xy-plane from (0,0)…

A: Take dot product along limit of integration and integrate

Q: Compute the flux of the vector field F = 2xi + yj through the cylindrical 5 and b = 4 and it is…

A:

Q: A fluid has density 600 kg/m3 and flows with velocity ū = ri + y. measured in meters, and the…

A: Here we have, Velocity v→=xi^+yj^+zk^ where x,y, and z are measured in meters.  the equation of…

Q: Find the work done by the force field F(z,y,2) = Ir+v,rs, y+:) on a particle that moves along the…

A:

Q: Find the work done by the force field F(x,y) = x²yi + y²j around the circle with radius 2.

A:

Q: Evaluate +y² 1 Ez² + y² JJJ₁² dV, where E lies between the spheres z² + y² + 2² +2² 16 in the first…

A: Given that,

Q: Let F(x, y) that starts at (0, 0)and ends at (1, 2). (6æ? + 4y) 7 + (4x + 3) j. Calculate la F . dř,…

A: