How can we ensure that the decision boundary (separating hyperplane) of a perceptron does not always pass through the origin?

Q: Obtain all the umbilical point of the Hyperboloid of two sheets {x^2+y^2-z^2=1}.

A: consider the equation {x2+y2-z2=1}

Q: Sketch the surface.......... ASSORTED ............... 4y2 + z2 - 4x2 = 4

A: Given :             The given function is 4y2 + z2 - 4x2 = 4 And can be written as,…

Q: Find the dimensions of the box of maximum volume with its sides parallel to the coordinate planes…

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Q: A suspension bridge with weight uniformly distributed along its length has twin towers that extend…

A: A suspension bridge with weight uniformly distributed along its length has twin towers that extend…

Q: Find the maximum volume of a rectangular box with faces parallel to the coordinate planes if one…

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Q: Find the orthogonal trajectories of family of hyperbola with center at the original and the length…

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Q: Find the orthogonal trajectories for the family of ellipses with centers at the origin and…

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Q: Calculate the point on the surface z =1 - x2 - y2 that has a maximum value for the sum of its…

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Q: A suspension bridge with weight uniformly distributed along its length has twin towers that extend…

A: The general equation for a parabola is given as, y=kx2 Let the x-axis represents the road surface…

Q: Given a sphere in center-radius form, how will you get an equation tangent to only one of the…

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Q: The surface z - - = 1 is a hyperboloid of one sheet. Select one: True False

A: The general form of the equation of hyperboloid of one sheet is: x2a2+y2b2-z2c2=1

Q: Find the maximum volume of a box that is resting on the xy-plane with one vertex at the origin and…

A: Given the plane is 3x+4y+2z=12

Q: A reflecting telescope contains a mirror shaped like a paraboloid of revolution.If the mirror is 4…

A: When we draw the parabola  to form the mirror on a rectangular coordinate system  we find…

Q: Find a parametrization for the sphere of radius 2.

A: Consider the equation of the sphere x2+y2+z2=22. Here the sphere is centered at origin.

Q: Find equations of two spheres that are centered at the ori- gin and are tangent to the sphere of…

A: Given radius=r=1 centered sphere at (3,-2,4) find the equations of sphere that are centered at…

Q: Find the equation of the sphere of radius at centered at (1, 4, 5)

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Q: What is the definition of a parabolic cylinder?

A: The parabolic cylinder functions are the solutions to the differential equation d2ydx2 + ax2 + bx +…

Q: What is the highest point on the ellipse that is the intersection of the plane z+y+ 2z = 2 and the…

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Q: Must two rays with a common endpoint be coplanar? Must three rays with a common endpoint be…

A: We know that two rays with a common endpoint must be coplanar and three rays with a common endpoint…

Q: Find the equations of all spheres in R 3 of radius R = 3 passing through the point (7 ,8, 9) that…

A: To find the equation of spheres Given that, from the question  Radius R = 3  with Passing through…

Q: Sketch the surfaces PARABOLOIDS AND CONES x = 4 - 4y2 - z2

A: The given equation is x = 4 - 4y2 - z2

Q: Show that the maximum value of a2b2c2 on a sphere of radius r centered at the origin of a Cartesian…

A: Let fa,b,c=a2b2c2 subject to a2+b2+c2 =r2  The gradient equation is…

Q: Just like in a projective plane, two distinct lines always intersect on the spherical plane.

A: Straight lines in spherical plane are the great circles. So, any two different lines meets at two…

Q: 2.5 What is the distance between two parallel hyperplanes {r E R" | a"x = b1} and {r E R" | a"x =…

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Q: Maximize xyz on the ellipsoid

A: See the details solution in below

Q: 3. Find the area of the surface cut from the nose of the paraboloid x = 1-y²-z2 by the yz-plane. Do…

A: Surface area in yz-plane

Q: Must the centroid of an isosceles triangle lie on the altitude to the base?

A: The centroid of an isosceles triangle lie on the altitude.

Q: 3. Find the area of the surface cut from the nose of the paraboloid x = 1-y²-z² by the yz-plane. Do…

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Q: What is the highest point on the ellipse that is the intersection of the plane z +y+ 2z = 2 and the…

A: I am going to solve the given problem by using the Lagrange's Multiplier method to get the highest…

Q: A mirror for a reflecting telescope has the shape of a finite paraboloid of diameter 0.3 meters and…

A: Equation of a circular paraboloid  f=r24d here, f= focal length along the axis of symmetry from the…

Q: Is it possible to angle the flashlight in such way that the boundary of the lighted area is a…

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Q: What is the minimum amount of unique shapes that could tessellate a plane?

A: Only three unique shape form tessalate

Q: (a) Where does the normal line to the ellipse x2- x   y + y 2 = 3 at the point (1, -1) intersect the…

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Q: Classify the quadric surface ² - y² - x² + 4x = 5. 2 य

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Q: determine a and b as to make the cylinder y^2=4ax orthogonal to the ellipsoid at point (1,2,1)

A: Given equation of the cylinder is  y2=4ax, say φ1=y2-4ax=0 and the general equation of the ellipsoid…

Q: A suspension bridge with weight uniformly distributed along its length has twin towers that extend…

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Q: Find the points on the ellipse 2x +y 1 where f(x,y)= xy has its extreme values. %3D

A: Solution:- Here we have to find the extreme value of  f(x,y)=xy subject to constraint…

Q: What is the general process to fit random 3D points to a surface?

A: Hint: Here 3D points are given we need to plot them on a surface. Write the general process to plot…

Q: Find the orthogonal trajectories of family of hyperbola with center at the original and the length…

A: The solution are next step

Q: Show that the ellipse x = a cos t, y = b sin t, a > b > 0, has its largest curvature on its…

A: Consider the given equation as x=acost, y=bsint and a>b>0

Q: A long suspension bridge 180 meters from end,has towers 60 meters tall,where suspension cables are…

A: Given : from the data given above  the graph of the parabola is:

Q: Find the points on the curve of intersection of the ellipsoid x²+4y²+4z²=4 and the plane x-4y-z=0…

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Q: What is a flat surface that extends infinitely in all directions?

A: Plane.

Q: What is the surface generated by a straight line which moves along a fixed curve, and which remains…

A: To determine the name of the surface generated by a straight line which moves along a fixed curve,…

Q: xplain

A: Given: Hypercube Qn,   n≥2 We have to find the reason behind that why hypercube is hamiltonian.

Q: What is the surface of the box formed by the net above

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Q: Find the equation of the tangent plane to the hyperboloid in 2 sheets x2 - y2 - z2 = 4 at the point…

A: We have to find the equation of the tangent plane to the hyperboloid x2-y2-z2=4 at the point 3,2,4.

Q: What coordinate system is suggested if the integrand of a tripleintegral involves x2 + y2?

A: Given: The integrand of a triple integral involves x2 + y2

Q: A suspension bridge with weight uniformily distributed along its length has twin towers that extend…

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