Rule: (x, y) → ( Reflection: Across Line y = -X YA

Q: The equation of the area of the plane region bounded by y = x^3 and the lines x = 1 and y =0 is…

A: Detail solution written below

Q: Sketch the surface..........CYLINDERS.............x2 + 4z2 = 16

A: Here we have to draw the surface of cylinder having equation  x2+4z2=16

Q: Find the point(s) on x=3-y² that are closest the point A=(1,0)

A: Our Aim is to find the points on x=3-y2 that are closest the point A=(1,0).

Q: Suppose XY has coordinates X( -2, 5) and Y(3, -9). What are the coordinates for the midpoint of XY?

A: To find the Midpoint of the line.

Q: nissile is propelled from the origin of a coordinate system with the x units

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Q: A heat-seeking particle is located at the point (2, −3) on a metal plate whose temperature at (x, y)…

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Q: Find the points on the cone z2 = x2 + y2 that are closest to the point (6, 2, 0). (x, y, z) (smaller…

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Q: Find the distance from the point (−3,0,2) to the plane - 3x + y + 5z = 0

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Q: 4.) y = VT, y = 3, x = 0 around the y axis %3D

A: Given, y = x1/2, y = 3, x = 0, we have to find the volume by rotating about the y-axis.

Q: Find the areas of the shaded regions

A: The area of the shaded region of the left is:

Q: Find the points on the cone z = x² + y that are closest to the point (-3,-2,0) %3D

A:

Q: What is the ALGEBRAIC RULE for REFLECTION over the y-axis? (х, у) —

A: Use reflection rule

Q: Let us consider the level curve f(x, y) = 2. Does the point %3D (1, 2) belong to this curve.

A: Given function is, fx,y=y2x2+1....(1) Since, the level of the curve is, fx,y=2

Q: Find the solution u(t, x) to the system Jau +30₂u+u²=0 for t≥0, 20, u(t = 0, x) = cos(x). Start by…

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Q: Determine the location of a point (x, y, z) that satisfies the condition y < 0

A: With the given condition there are 4 scenarios 1) x>0,y<0,z>0 2) x<0,y<0,z<0 3)…

Q: Find the point(s) on x = 3 - y that are closest to point A = (1,0).

A: Given: Curve x=3-y2 and a point A(1,0).

Q: What is the ALGEBRAIC RULE for REFLECTION over the line y = x? (х, у) —

A: This question is related to reflection of coordinates, We will solve it using given information.

Q: Find the distance from the point (2, 0, 0) to the plane x + 2y + 2z = 0.

A: Given a point, (2, 0, 0) and the equation of the plane x + 2y + 2z = 0.

Q: ди ди + x - Əx %| ду 0 =

A:

Q: What is the ALGEBRAIC RULE for a REFLECTION over the x-axis? (х, у) —

A:

Q: The change in the relative configuration of point within a solid is called strain

A: Strain is a description of deformation in terms of relative displacement of particles in the body.

Q: Find the point on the line y = 3x + 5 that is closest to the origim %3D (x, y) = %3D

A: We have to solve

Q: b) Explain when an external flow is two-dimensional, three-dimensional, and axisymmetric. What type…

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Q: Tind he latance from the pomt (-2, 4) to tu plane 37+2y4 6E5

A: Given a point (1, -2, 4) and a plane 3x + 2y + 6z = 5

Q: find the distance from the point to the plane. (1, 0, -1), -4x + y + z = 4

A: Concept -Let the equation of plane be -Ax+By+Cz+D = 0And the coordinates of a point be - (x1, y1,…

Q: y = VT, y = 2 - x and r O about the x-axis?

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Q: The temperature at the point (x, y) on a metal plate is x² + y? " Find the direction of greatest…

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Q: b) Use chain rule 1 - arctan u, where u = e* y =

A: Given y=1u - arctan u, where u=ex apply derivatives on both sides…

Q: Eliminate the parameter to obtain an equation in x and y: x=-2cos2t, y=-2sin2t

A: x=-2cos2t y=-2sin2t using trigonometric property,               sin2t+cos2t=1

Q: Find the image of the line y =-x under the mapping = f(z) =2² + 4z %3D %3D

A: We need to find the image of the line y = - x under the given mapping.

Q: Double integrate under z=xy, above the triangle with vertices (0,1),(0,4),(1,1).

A: We have to find the volume by double integration

Q: Find the Second appoximation for the System. X Sin y at (xo,,)= (1, 1). y=Cosx

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Q: -axis. 5. Evaluate dV, where E is the solid tetrahedron with vertices at (0,0, 0), (2, 0, 0),…

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Q: Find the points that are minimum to the origin and lie on the lines of intersection of planes: y +…

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Q: Iz+ai| rupriants Prove that the equation Iz+2] = 5V13 the origin is distance from pror line and its

A: Prove that the equation z+2=z+3i represents a line and its distance from the origin is 51326.

Q: Find y': %3D Oy =- Oy=--

A: A detailed solution is given below

Q: (a) Assume that traffic flows at a rate of 240 vehicles per hour on the stretch of road between…

A: The number of vehicles coming and leaving the signal is same in all the signals. That is, Total…

Q: At what points (x, y, z) in space are the functions in continuous? ƒ(x, y, z) = x2 + y2 - 2z2

A: Solution:-  At what points (x, y, z) in space are the functions in continuous? Let (m,n,p) is the…

Q: 2-g(%,y)%3D플-플 * at (VT ,1)

A:

Q: Integrate f(x,y,z) = x-3y + z over the line segment joining the points (0,0,0) and (2,2,2). %3D

A: Here, we need to integrate f(x, y, z)=x-3y2+z over the line segment joining the points (0, 0, 0) to…

Q: Rule: (x, y) → ( Reflection: Across Line y = x

A: Actually the rule of reflection along y=x is simply writing the points (x,y) as (y,x). See for the…

Q: Findauihtvectorhermat to thesuFace X Y +X2=1 et the Point (-1,1,1)

A:

Q: Find the distance from the point (0,8,9) to the plane – 2y + 3z = 11.

A: In this question, we will find the distance from the given point to the given plane.

Q: 1+iz if w= Find the image |z|<1 1-iz

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Q: y = x', y = 4x, x > 0 about the line y = 0 using the method of disks or washers. 2 Volume…

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Q: Show that f(-ydx + xdy) where C is the line segment joining (x, y) and (x₂, y2).

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Q: Exercise : Find dy O y = 10x+3 Cosx O y =cscx -4VX+7 Cotx 3y =- (3) I+ Cotx

A: To differentiate the following: 1) y=10x + 3 cos x 2) y= cosec x -4x +7 3) y=cot x1+ cot x

Q: 8. y- -x+4 , x=0, y=o, about the (x 20) y axis

A: y=-x2+4 and x≥0 ,x=0,y=0 about y axis

Q: Find the length of curve along y = x² from (0,0) into (2,4).

A: