Use Divergence Theorem to evaluate .(v²z²i +z²x²j+x²y²k).ds, where S is the upper part of the sphere x + y + z² = 9 above xy- plane.

Q: HW Find the valume af theSelid beunded abave the Planc 2= x+2y+2,belw the X-y plane and Taterally…

A:

Q: Which of the following planes is tangent to the sphere x² + y + z' = 17 at the point (2, -2, 3)? %3D…

A:

Q: Use Divergence Theorem to evaluate ,0i +rj +ryh) ds, Q#3(a) where S is the upper part of the sphere…

A: As per bartleby instruction when more then one question is given only one has to be answered. Please…

Q: parametrizes the portion of the sphere x² + y² + z² = 9 that is above the xy-plane and below the…

A:

Q: Evaluate both sides of divergence theorem for A = pa,+pcos(@)a , + za , through the closed surface…

A: Given vector field is  Divergence theorem

Q: Find the area of the part of the sphere x2 + y2 + z2 = 4z that lies inside the paraboloid z = x2 +…

A: Given, x2+y2+z2=4z  and  z=x2+y2 Equation of the sphere and paraboloid in cylindrical coordinates is…

Q: Use the divergence theorem to evaluate ]] F .dɔ̃ where F = xyi – ¹⁄y²j+zk and the surface consists…

A: Here, the surface consists of the three surface z=4-3x2-3y2; 1≤z≤4 on the top x2+y2=1, 0≤z≤1 and z=0…

Q: Let f(x, y, z) = x² + 2y? + 4z2. Find the point on the plane x + y + z = 14 at which f has its…

A: Given: fx,y,z=x2+2y2+4z2and the plane equation x+y+z=14 To find the point x,y,z The Lagrange's…

Q: Let D be the half-disc in the xy-plane given by x +y <9. Calculate e-(x2+v)dA

A:

Q: The half-space consisting of the points on and below the xy-plane

A: Concept:

Q: Use Divergence Theorem to evaluate ,0²z²i + z²x²j+ x²y²k).ds, 1. where S is the upper part of the…

A:

Q: (a) Compute directly I = S Ss F-dS, where S is the surface of the sphere x? +y? +z? = 4 and F =…

A: X²+y²+z²=4=2² Therefore radius of sphere is 2.

Q: Sketch the space curve r(t) = i + t2j + t3k and find its length over the given interval [0, 2] .

A: If r=x(t)i+y(t)j+z(t)k then length of r over [a, b] is L=∫ab[x'(t)]2+[y'(t)]2+[z'(t)]2dt

Q: Find the area of the plane xtay-zt 10=0 that lies above the disk xy-plare

A: Given that, Area of plane is x+2y-z+10=0 It lies above the disk {(x,y)/x2+y2≤4} in x,y plane. The…

Q: Use Lagrange's multiplier(s) to find the maximum and minimum for f(x, y, z) = x² + 2x + 2y2 + 3z2 on…

A:

Q: Use Gauss Divergence theorem to calculate (5zi+ 4yj- 2z k).n dA over the sphere S: 2 + y? + 22 = 9.

A: This is a problem related to vector calculus. Based on the general formula of gauss divergence…

Q: Use the Divergence Theorem to evaluate (5x + 10y + z) ds where S is the sphere x2 + y2 + z2 = 1.

A: In the given problem, S is the sphere x2+y2+z2=1Divergence Theorem:∬SF·n dS=∭Ediv F dVNow, the…

Q: Apply the divergence Theorem,with the surface of F = 4xzỉ – y²j + yzk and S being the cube surface…

A:

Q: Verify Stoke's for F = (2x – y)i – yz²j – y²zk where S is the upper half of the sphere x? + y? +z² =…

A: Solution is given below

Q: F. dS, where F(x, y, z) = z²xi + 2) + (x2z + y2)k and S is the top half of the sphere x² + y² + z? =…

A:

Q: 7. Use the Divergence Theorem to evaluate ff(F n) dS, where S is the top half of the sphere r+y + z…

A:

Q: (a) Show that the two surfaces S₁: z = xy and S₂ : z = ³x² - y² intersect perpendicularly at the…

A: As per our guideline, we are supposed to solve only first question. Kindly repost other questions as…

Q: Use Divergence Theorem to evaluate [0²z?i+z?x²j+x*y²k).ds, where S is the upper part of the sphere…

A: To evaluate the below integral using the divergence theorem. ∫∫Sy2z2i+z2x2j+x2y2kds Here S is the…

Q: evaluate $ A. dš over the sphere R = 3 and show whether Divergence theorem holds or not. %3D

A: Calculate surface integral over R=3 or dr=0 ∮A→×ds→=∮R cos2θ,π,0×r2sinθdθdϕ,rdϕdr,rsinθdrdθ…

Q: 7. Use the Divergence Theorem to evaluate ff(F n) dS, where S is the top half of the sphere r2 +y +…

A:

Q: Q5. Analyze and Verify Gauss divergence theorem for F 2 xz i+ yzj+ z? k over the upper half of the…

A: Here, F=2xzi+yzj+z2k Given upper half of the sphere x2+y2+z2=a2. Let ∅=x2+y2+z2-a2=0…

Q: State what the Divergence Theorem says, using your own words. You may assume that E is a solid in R³…

A: We can state the Divergence theorem .

Q: Find /| F-dS if F(x, y, z) = 2xi+2yj+2zk and S is the part of the paraboloid z = = 8-x?-y? lying…

A:

Q: Let C be the boundary curve counterclockwise of the semidisk x² + y? < 9, y 2 0. Then f.(-2ydx +…

A: A detailed solution is given below.

Q: Q7. Use Green's theorem to evaluate fy² dx + 3xy dy, where c is the boundary of the semi annular…

A:

Q: The flux of F(x, y, z) = 2³î – r³}+ y®k, where o is the sphere | x2 + y? + z2 = a² with outward…

A:

Q: Use the Divergence Theorem to evaluate F. dS , where F(r, y, z) = (2x(y - z), x? – y, z) and S is…

A:

Q: Use Divergence Theorem to evaluate .v²z²i +z²x²j+x²y²k).ds, where S is the upper part of the sphere…

A: To evaluate the below integral. ∫∫sy2z2i+z2x2j+x2y2kds¯

Q: Let C be the boundary curve counterclockwise of the semidisk x2 + y? < 9,y 2 0. Then f (-2ydx +…

A: Given Information -  C is the boundary curve counterclockwise of the semi disk x2 + y2 ≤ 9 , y ≥ 0…

Q: Let F(x, y, z) = 2z? xi + (y + tan(z))j + (2x²z – 2y²)k. Use the Divergence Theorem to evaluate F.…

A:

Q: Find the maximum value of  f(x,y,z)=27x+7y+3z on the sphere x2+y2+z2=81

A: For this question we will use Lagrange multipliers where f(x,y,z)=given function and…

Q: Use the Divergence Theorem to evaluate (3x + 2y + z2) ds where S is the sphere x2 + y2 + z² = 1.

A:

Q: Use the Divergence Theorem to evaluate (4x + 7y + z²) dS where S is the sphere x2 + y2 + z² = 1.

A:

Q: Consider the following space curve r (t) = t²i + 2tj – v2 43/2 k %3D 3

A: The given space curve isrt=t2i^+2tj^-423t32k^.To find:The time period when rt intersects xt+zt=0 and…

Q: Given F = ryx – ỳ + zà, use the divergence theorem to evaluate f, F. dS over the closed surface…

A: Given F→=xyx^-12y2y^+zz^The closed surface consisting of the three surfacesfz=z-4+3x2+3y2when…

Q: Use the Divergence Theorem to evaluate (4x + 3y + z) dS where S is the sphere x2 + y2 + z2 = 1.

A: The divergence theorem establishes the equality between surface integral and volume integral.

Q: evaluate both sides of divergence theorem for A= ra,+rcos(8)a , +r²a, through the closed surface…

A: Given problem is :

Q: a) Evaluate /| (-ri-yj+2: k) · n dS, where o is the portion of the paraboloid z = 3x2 + 3y? between…

A: Define a function fx,y=z or fx,y=3x2+3y2.  So, the flux integral is:…

Q: Use the Divergence Theorem to find F- ndS, where F = (y°z,x²z,z') and the surface S is the sphere x…

A: See the details solution below

Q: Find the maximum value of f(x,y,z)=9x+14y+29z on the sphere x2+y2+z²=25

A:

Q: Verify the divergence theorem for A = R²ag + Rsin0ag and S is the surface of a quarter of a sphere…

A: The geometry is as follows:

Q: Let C be the boundary curve counterclockwise of the semidisk x² + y? 0. Then § (-2ydx + 3xdy) = a)…

A:

Q: Use t = y to parametrize the part of the line of intersection of the two planes y = 2x – 4 and z =…

A:

Q: Find the points on the surface xy – z2 = 1 that are closed to the origin.

A: Given surface is xy-z2=1. let xy-z2-1=0⇒z2-xy+1=0 Now distance from origin is…

Q: Let F(x, y, 2) = 32?ai+ (y³ + tan(z))j+ (3x²z- 4y?)k. Use the Divergence Theorem to evaluate fs F dS…

A:

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related. 

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.