Evaluate 3ydx 5xdy, where C is the boundary of the square [-2,3] x [-2,3], oriented in the counterclockwise direction, using Green's theorem

Q: Calculate F. dĩ, where C is the square of (1,1, 1), (–1, 1, 1), (–1, –1,1) and (1, –1,1), with…

A:

Q: Calculate F . dr, where C is the square of (1,1, 1), (–1,1, 1), (-1,–1,1) and (1,–1,1), with…

A: Let F→x,y,z=zex-yezi→+2cosy-xezj→+ex-xyezk→ and C is the square with vertices…

Q: 1. Explain why (b x c) must be a linear comnbination of b and c. a X

A: We will use properties of cross product of two vectors

Q: Use Lagrange multipliers to find the distance from the point (3, 0, -1) to the plane 6x - 4y + 7z +…

A:

Q: Let r(t) be a positively oriented rectangle with corners (0,0), (0,1), (2,1) and (2,0) and F(r, y)…

A:

Q: Find the area of the band cut from the paraboloid x2 + y2 - z = 0 by the planes z = 2 and z = 6.

A:

Q: ® Find the_functian that satisfies the following conditions for some constant Eceficients c,and c…

A:

Q: Find the trace of the plane 8x – 9y + 2z = -11 in the coordinate xz-plane.

A:

Q: Sketch the surfaces PARABOLOIDS AND CONES z = 8 - x2 - y2

A: Consider the equation of the surface, z = 8 - x2 - y2

Q: Let C be the positively oriented square with vertices (0,0) (2,0), (2,2), (0,2) Use Green's Theorem…

A: Consider the provider question,

Q: Evaluate / x2 zdS, where S is the part of the plane z = 4+ 3x + y above the rectangle [0, 4] x [0,…

A:

Q: Use the given transformation to evaluate the integral. (8x + 8y) da, where R is the parallelogram…

A: Given that vertices of parallelogram is −3,9,3,−9,4,−8  and −2,10 And transformation is x=14u+v  and…

Q: use green's theorem to evaluate ∫c 5y^3dx-5x^3dy where C is the circle x^2+y^2=4 counterclockwise

A: Given: ∫c 5y^3dx-5x^3dy where C is the circle x^2+y^2=4

Q: Find the trace of the plane 3x − 2y + 5z = 4 in the xy-plane.

A: The given equation of the plane is 3x-2y+5z=4. The trace of the plane in the xy-plane is the…

Q: Use the transformation u = y – 3x, v = y + 6x to evaluate // (2y + 12x) dA on the parallelogram R…

A:

Q: Use the given transformation to evaluate the integral. (12x + 12y) dA, where R is the parallelogram…

A:

Q: Bounded by the coordinate planes and the plane 3x + 2y + z = 6

A:

Q: EX Find the reglon in the z-plane represented bye

A: Given

Q: Draw the bifurcation diagram for à = (x + 1)(x² – 2.x +r).

A: We are given : Now, the bifurcation diagram for this is :

Q: Find the area of the part of the paraboloid z=x +y² that lies under the plane 2=9.

A:

Q: 5. Evaluate f (x²zdx – yx²dy + 3dz) where C is the boundary of the triangle with vertices (0,0, 0),…

A:

Q: A(n)________ is the collection of points in the plane the difference of whose distances from two…

A: The given statement is "A(n)________ is the collection of points in the plane the difference of…

Q: Verify that the operation {x, y} = x1y1 − x1y2 − x2y1 + 3x2y2 where x = (x1, x2) and y = (y1, y2) is…

A: Given : The operation on ℝ2 is defined as  x, y = x1y1 - x1y2 - x2y1 + 3x2y2 ,  where x = (x1 , x2)…

Q: Find all planes in R3 whose intersection with the xz-plane is theline with equation 3x + 2z = 5.

A: Find all planes in ℝ3 whose intersection with the xz-plane is the line with equation 3x + 2z = 5.

Q: Enclosed by the paraboloid z = x² + 3y? and the planes x = 0, y = 1, y = x, z = 0

A: We know that, volume under surface z=fx,y and above the region D in xy-plane is given as…

Q: Evaluate // x² zdS, where S is the part of the S 1 + 4x + 3y above the rectangle plane z = [о, 2] x…

A:

Q: Find the barycentric coordinates of p with respect to the affinely independent set of points that…

A: Given 11, 35, 06, p=23 let a=11, b=35, c=06, p=23 Now we write the points in augmented matrix form…

Q: What are the perpendicular generators on (D) 좋 =3 %3D2 (P) 16 2. of the surface

A:

Q: In the xy plane mark all nine of these linear combinations: c[2/1]+d[0/1] with c=0, 1 , 2 and d=0, 1…

A:

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: to find the use lagrange Multiplier Point p (x1s,Z) Closest to the origion on the Plane 2x +y - 2=5…

A:

Q: Let F = (16xy, (8x^2 + 8z^2), (8y*2z)). What is the curl of F?

A:

Q: must use linear algebra to find the parametric equations of a line of intersection in R3 for x1 + x2…

A:

Q: Find the area of the cap cut from the paraboloid y2 + z2 = 3x by the plane x = 1.

A:

Q: Use the given transformation to evaluate the integral. (12x + 12y) dA, where R is the parallelogram…

A:

Q: (b) Are the polynomials x + 5, x – 5, 2x +1 linearly independent in P1(R)? Explain.

A: The vectors a1, ..., an are called linearly independent if there are no non-trivial combination of…

Q: Use Lagrange Multiplier to find the Point P (x,y,z) closest to the origin on the plane containing…

A: The equation of the plane passing through the three points can be obtained using the matrices. The…

Q: Find the area of the portion of the paraboloid x = 4 - y2 - z2 that lies above the ring 1<=y2 +…

A: Given surface is  The required surface area is given by where

Q: Consider P2 with the inner product = f (x)g(x) dr. Then d(x, 2) Jo

A: d(x,2) represents distance between the vectors x and 2 P2 is the set of all polynomials with degree…

Q: Use Lagrange multipliers to find all points on the cone z2 = x² + y² that are closest to the point…

A: The solution has been given below.

Q: Let C be the rectangle in the xy-plane with vertices (0,0), (1,0), (0, 2) and (1, 2), and let F(r,…

A:

Q: (c) Use Green's Theorem to evaluate 3xydx + 2xydy, where C is a counterclockwise C oriented…

A:

Q: What are the perpendicular generators on (D) 등 =D3 %3D (P) -= of the surface

A: Given equations are  x216-y24=z ......(1)x3=y2=z-4  ......(2) Equation of generators of the…

Q: Let C be the boundary curve counterclockwise of the semidisk æ? + y? 0. Then fc(-2ydx + 3xdy) 5dydx…

A:

Q: -:Q1 Evaluate , (x- 2y) dA, where R is the parallelogram in the xy-plane with vertices (0,0), (4,1),…

A: The objective is to evaluate ∫∫Rx-2ydA where R is the parallelogram in the xy plane with vertices…

Q: Find the average haight of the Paraboloid z- xry* over the square osx <2, osd<2

A: We need to find the average height of paraboloid

Q: Evaluate JJ (² where o is the first-octant portion of the plane 2x + y + 2z = 6 (x² + 2yz)dS

A:

Q: Use Gramer's Rule to Find K,y and Z -y-22 = -8 %3D + 32 = 2 %3D 7X +y+Z = 0

A: As per our guidelines we are supposed to answer only one question at a time. So submit the other…

Q: Given F(x.y.z) (x+y+Zi +(x-yj+(xz-2)k what is CurlF at the point (1,-1,3)? You should write your…

A:

Q: Let ƒ (x, y) = x² - y² . Find all all points (x, y) such that Vf(x,y) =±(1, 1).

A:

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.