Transform pentagon BEARS according to (x, y) → (x +6,y+B). Write the coordinates for pentagon B'E'A'R'S' and sketch pentagon B'E'A'R'S' on the same coordinate plane

Q: Find the work done by the force F = 4xyi + (2x² – 3xy)j by pushing a particle along the line segment…

A:

Q: Parametrize a path for the curve that is a circle in the x-y plane that has radius 2 (a) with center…

A:

Q: 25 at the point ( 1, -1, 2 ).

A: Given that : The surface  8x2+y2+4z2 = 25 , point = ( 1, -1, 2 ).

Q: Determine the orthogonal trajectories of the hyperbola 3xy= 5 at the point (2, 5/6). Sketch the…

A:

Q: find a parametrization of the curve. The line passing through (1, 0, 4) and (4, 1, 2)

A: Given: A line is passing through the points 1, 0, 4 and 4, 1, 2.

Q: he transformation from Cartesian to plane coordinates in x-direction is given by x=rsine x=rcos20…

A:

Q: Find the angle between the planes 3x – 2y + z + 4 = 0 and x + 4y – 3z – 3 = 0. Express your answers…

A: The angle between two planes is equal to the angle between their normals.

Q: where does this concave up and down?

A: A graph is concave up if f''x>0 and concave down if f''x<0. When f''x>0, it means…

Q: 7x + 8y2 and the planex = 3. At what rate is z changing with A point moves along the intersection of…

A:

Q: 55. A point moves along the intersection of the elliptic parab- oloid z = x+ 3y and the plane y = 1.…

A:

Q: F - dr where F(x, y, z) = (4.25yz cos(xyz), 4.25xz cos(xyz), 4.25zy cos(ryz)) Evaluate п 1 and Cis…

A:

Q: Find the distance from the point (-4, 5, 1) to the plane – kr – ly – 2 = 5.

A:

Q: Picture attached. Thanks in advance!

A:

Q: 4. Determine the orthogonal trajectories of the hyperbola 3xy = 5 at point (2, 5/6). Sketch the…

A: To find the trajectories of the hyperbola write dydx by dxdy  and solve the system.

Q: Find a parametrization of the curve. The vertical line passing through the point (3, 2, 0)

A: Consider the given point  3 , 2 , 0

Q: A point moves along the intersection of the elliptic paraboloid z = x + 3y² and the plane y = 3. At…

A: z=x2+3y2 and y=3 Point of Intersection : Curve z:x2+3y2=x2+3(3)2=x2+27 dzdx=2x+0 =2x

Q: Consider the curve C parametrized by x = -1 + 6 sin t and y 6 cos t for -n <t< 9n. %3D Then C is a…

A:

Q: The value of the line integral I- [Adl where A-(2x+y)£+(y-x)ý along the parabola y=x^2 and form…

A: Evaluate: I=∫A.dl              ...(1)WhereA=2x+yx∧+y-xy∧

Q: Find the points on the hyperbolic cylinder x2 - z2 -1 = 0 that are closest to the origin. please…

A:

Q: 3. Calculate the centroid of the given illustration below. y-axis 7.5ft- 4ft 2ft 5ft- х-ахis 2ft

A:

Q: 4. Determine the orthogonal trajectories of the hyperbola 3xy = 5 at point (2,5/6). Sketch the…

A:

Q: Find the equation for the tangent plane to the surface x2 - 5xyz + y² = 7z2 at the point (-1, -1,…

A: Simplify the given equation of the surface in the form F(x,y,z)=0. x2-5xyz+y2=7z2x2-5xyz+y2-7z2=0…

Q: (2) The distance from the point (1, 2, -1) to the plane 3x - y + 2z = 6 is. (3) Consider the…

A:

Q: find a parametrization for the curve. the ray (half line) with initial point (2, 3) that passes…

A:

Q: A line segment bounded by two points (0,0,0) and (2,2,0) is rotated about the y-axis by 270 degrees.…

A: We will first parametrize the line as a function of t , then with the help of rotation (u) matrix we…

Q: Find an equation of the tangent plane to the surface z = In(x - 2y) at the point (3, 1,0) %3D

A: Given that, z = ln (x - 2y) we have to find the equation of tangant at point (3, 1, 0).

Q: Find the distance between the point (0,0, 8) and the plane given by 2x – y + 2z – 1 = 0.

A:

Q: Find the lateral surface area of the cone generated by revolving the line segment 5x-8y+40=0 about…

A: Find lateral surface area.

Q: An equation for the tangent plane to the surface z + 3 = xy cos (2) at the point (3, 1, 0) is:

A:

Q: 1)If the 15 kilogram object is resting on a table tilted at 40 °. indicate the decomposition of the…

A: Consider the provided question,

Q: The plane tangent to the surface z+1= ze" cos z at (1,0,0) can be represented by the equation Z= 1.…

A: As per our guidelines, we are allowed to answer only one question. Since you have posted multiple…

Q: 5 – 4z Show that the reactiob w= transformation the circle z =1 4z -2 in to a circle of a radius…

A:

Q: Find the equation of the osculating plane of the helix x = sin 2t, y = t, z = cos 2t at the point…

A: The helix is given as x=sin 2t, y=t, z=cos 2t. We have to find the equation of the osculating plane…

Q: c. Based on the orientation of your rectangle would we integrate with respect to x or y? С.

A: Follow the procedure given below.

Q: A particle moves along a circular path over a horizontal xy coordinate system, at constant speed. At…

A: Given Motion is a circular motion. r = radius of the circlea = x-cordinate of the centreb =…

Q: Find the distance from the point S(0,0,0) to the plane 20x+10y+5z=70 (approxmate to two decimal…

A:

Q: A point moves along the intersection of the elliptic paraboloid z = 10x? + 3y² and the plane y = 1.…

A:

Q: Determine the surface of revolution if the arc y^3 + y = x^2 + 6x on the interval [−5, −1] is…

A: The curve will appear like this

Q: Find a parametrization of the circle of radius 7 with center (5, 3, 9) in a plane parallel to the…

A:

Q: Find the points on the hyperbolic cylinder x2 - z2 -1 =0 that are closest to the origin. please…

A: The parametric equation of hyperbolic cylinderx2-z2-1=0 is , x=cos hθ                          y=y…

Q: (a) Obtain the equation of the tangent plane and the condition for tangency to the conicoid Ar? +…

A: Conicoid given is- Ax2+By2+cz2=1 at the point (α,β,γ) We have to obtain the equation of the tangent…

Q: Evaluate fc 2x ds, where consists of the arc of the parabola y= x2 from to followed by the vertical…

A: The given line integral is ∫C2xdS where C is the arc of the parabola y=x2 from (0,0) to (1,1) and…

Q: A point moves along the intersection of the elliptic paraboloid z = 4x + 11y and the plane y = 4. At…

A: given information is z=4x2+11y2 The plane y=4To find :Rate of change of z with respect to x when the…

Q: A point moves along the intersection of the elliptic paraboloid z = 2x? + 7y² and the planex = 4. At…

A:

Q: The plane tangent to the surface z +1= re" cos z at (1,0,0) can be represented by the equation X + y…

A: Given: z+1=xey cosz

Q: The curve y = (64x – 4x³ )m bounds the shaded section on top and the x-axis on the bottom. Determine…

A: Given curve, y=64x-4x3 The shaded region is shown as: Formula for the centroid x, y in a region is…

Q: What does parseval's identity imply about relationship between the dot products x · y and [x]ẞ·…

A: Concept: A branch of mathematics which deals with symbols and the rules for manipulating those…

Q: Give arc-lengtu porametriz atian of the line which an Hhe tangent planes of and (1,2,9). is Hhe…

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.