Write a function from r ^2 to r that has a plane with normal (1,1,1) exactly one point.give an example for why this is the case

Q: Let S be a sphere centered at the origin. Show that the normal line at any point on the sphere goes…

A: we are given a sphere S centered at the origin

Q: Determine the centroid (x, ỹ) of shaded area. Im

A: The given figure is  We have to find the co-ordinates of the centroid of the shaded region.

Q: Calculate integrate integrate sinx/x da Where R is the triangle in the xy plane bounded by the…

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Q: What are the new coordinates of the point (-5, 25) under the dilation (x, y) - (2x, 2y)? O (-10,…

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Q: Define Vector Line Integral.

A: A line integral is the integral of some function along a curve. One can integrate a scalar-valued…

Q: Find the Contour integration to

A: ∫-π-π11+sin2xdx∫aafxdx=0, a≠∞=0

Q: bounded by the curve f(x)= Vx-1, y-axis, line y =1 and line y =

A: We will find the area bounded by the curves.

Q: area between the curves :- x=y^2 , x = 0 , y=3

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Q: Find the centroid of the region above the X axis that is bounded by the Y axis and the line Y = 3 -…

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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: Calculate the area of the plane region bounded by the function Y=X²-4X +5, and the line that passes…

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Q: Find the centroid of the region cut from the first quadrant by the curve y = 1/sqrt(x + 1) and the…

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Q: What is the area bounded by the curve x² = -9y and the line y + 1 = 0?

A: Given curve is x2=-9y Line is y+1=0 We need to find the area bounded by the curve

Q: .Determine the distance from the y-axis of the centroid of the area bounded by the curve y = x³, the…

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Q: Find the equations of the tangent plane and the normal line at point (1,1,-2) to surface z^2 =…

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Q: Find parametric equations for the normal line to the surfacez=ln(3x2 +7y2 +1)  at the point…

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Q: Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat…

A: Diameter=60 meters⇒radius=30 meters                         ∵Radius is half of the…

Q: Find the centroid of the region that is bounded by the line Y = 3X, the line X 2 and the X axis.

A: To find the centroid

Q: Find parametric equations of the normal line to the surface z = 4 + y² at the point (2, –2, 5) |

A:

Q: Find the centroid of the triangular region cut from the first quadrant by the line x + y = 3.

A: We will find the x and y-intercept of the triangle.  To find x-intercept we plug y=0 and find x…

Q: Find an equation of the plane passing through the point (1,4,2) with a normal vector of the form n=…

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Q: What is the Net Change Theorem? What does it say about theintegral of velocity? The integral of…

A: What is the Net Change Theorem? What does it say about the integral of velocity? The integral of…

Q: What relationship do you see between the segments of the median that are formed by the centroid?

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Q: Find the number 6 such that the line y = 6 divides the region bounded by the curves y = x2 and y =…

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Q: Explain the meaning of the surface integral in the Divergence Theorem.

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Q: Find the area of a triangle bounded by they axis, the line f(x) r, and the line perpendicular to…

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Q: Show that the gradient vector is perpendicular to the tangent at a point of an isovalue curve

A: According to question                                     Let,  w=f(x, y, z)  be a function in…

Q: What is a parametrization of a curve in the xy-plane?

A: we have to tell what is parametrization of a curve in the xy-plane?

Q: The area of the region bounded by y = v9- x² , the x-axis and the line y-x in the first quadrant is:

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Q: Find a set of symmetric equations for the normal line to the surface xyz = 12 at the point (2, −2,…

A: The normal line to the surface xyz = 12 at the point (2, −2, −3).

Q: Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat…

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Q: How do I find the bounds in which I integrate a curve that is rotated about an axis?

A: To find the bounds, it is necessary to check whether we have to find the surface area or volume. In…

Q: – 4V5 )ds]

A:

Q: give two example of tangent vector on manifold

A: Manifold is a topological space that which is almost similar to a euclidean space near to each of…

Q: Exercise 2 Find symmetric equations of the normal line to the surface 4 + y – 162 = 0 at (2,4,2).…

A: Given surface is     4x2+y2-16z = 0We will find the symmetric equation of the normal line to the…

Q: Find the centroid of the region cut from the first quadrant by the circle x +y =

A: Given x2 + y2 = 81 y=81-x2 Area of Quadrant(A) = πr24                              A  = 81π4

Q: The region is bounded by the curves y = x² and y = 4x - x² and is rotated about the line X = 4. %3D…

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Q: What are the new coordinates of the point (-10, 10) under the dilation (x, y) (4x, 4y)? O (40, 40) O…

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Q: does the default area of curve is the region under it?

A: Query- does the default area of curve is the region under it? Answer- The area under a curve between…

Q: Find the centroid of the region that is bounded by the line Y = 3X, the line X = 2 and the X axis.

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Q: Regions under the curve can be described in terms of area. True or False

A: We want to tell you above statement is true or false

Q: Find equation of plane normal to line = = and pass through line x = y = z.

A: The equation of a plane passing through the point: x0, y0, z0 is defined as ax-x0+by-y0+cz-z0=0,…

Q: A bee was flying upward along the curve that is the intersection of z = x⁴+xy³+12 with the plane…

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Q: 4

A: We have to find the equation of plane according to the given information

Q: Find the average distance from a point in a ball of radius to its center.

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Q: How to calculate the pseudo-surface integral from a line? Please explain it in your multivariable…

A: How to calculate surface integral from line?

Q: What are the new coordinates of the point (3, -4) under the dilation (x, y) (0.25x, 0.25y)? O (3,…

A: We have to find the new coordinates of the point (3,-4) under the dilation (x, y) ----> (0.25x,…

Q: Sketch the region that is bounded by y = 8 - x² and y = 2 – x. Then, find the coordinates of the…

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Q: Use a linear approximation to estimate V29. Show the work. Do not round your

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.