Find the points on the cone z^2=x^2+y^2 closest to the point (4, 2, 0).

Q: Find the surface area of the portion of the half ball with a radius a which cuts off by the cylinder…

A: To Find: The surface area of the portion of the half ball with a radius a which cuts off by the…

Q: Find the dimensions of the rectangular box of maximum volume that has three of its faces in the…

A: Let say that(a,b,c) is point in plane 4x+3y+z=12 and it is one vertex of requested rectanglar box.…

Q: A cylinder is inscribed in a right circular cone of height 5 and radius (at the base) equal to 2 .…

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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: Find the centroid of the region bounded by y = 9 – x² and the x-axis.

A: Given, y=9-x2or let fx=9-x2and x-axis y=0or let gx=0

Q: 2. Show that an equilateral triangle can be inscribed in the epitrochoid and that its centroid is on…

A: An equilateral triangle can be inscribed in the epitrochoid and that its centroid is onthe circle of…

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

A: Given,

Q: what is the formula to find centroid of triangular prism

A: Centroid of triangular prism is determined as shown below.

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: A container with a height of 3/2 is made by rotating the curve y = 3/2x^2, Osx<1, about the axis x =…

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Q: A rectangle with perimetee 18 cm is rotated about one of its sides forming a a right circular…

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Q: Find the points on the cone z = x + y that are closest to the point (8, 2, 0) (x, y, z) (smaller…

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Q: A metal rain gutter is made from sheets of aluminum that are 12 inches wide by using a machine that…

A: Given that  sheets of aluminum that are 12 inches wide by using a machine that turns up the edges to…

Q: find the centroid of the solid formed by revolving about the x-axis the solid formed by the curve…

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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 right triangle who's hypotenuse is square root 3 m long is revolved around one of its legs to…

A: Given data is : Hypotenuse is 3 m To find the radius, height, and the volume of a cone of greatest…

Q: Find the dimensions (radius r and height h) of the cone of maximum volume which can be inscribed in…

A: According to our company policy, I am supposed to answer only one question at a time so for the rest…

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: Find the volume of the solid above the triangle with vertices (0, 0), (1, 0) and (1, 2), below the…

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Q: Find theirelume of the largest. right circular Cone that can be inscribed in a sphere of radius 3.

A: we know,     The volume  of right circular cone is:      V =1/3 pi*r2*h  , where r is the radius of…

Q: under the cone Z =Vx²+y² and above the region bounded by the semicircle X=-V 4-y and the y-axis.

A: The circle and a cone is given as,

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: Differentiate, and make sure to show all your work: y = exin(2z) %3D

A: The given question is taken from the derivative of the function in which we have to find the…

Q: A region in the xy-plane is bounded by y = 2x + 2, X = y + 2, y = -2, 2 y = 2. and

A: Given curves are y=2x+2 and x=y22+2 The limits are y=-2 and y=2 We isolate x from the first curve,…

Q: Find the area of the portion of the plane in the first octant passing through the points (0,0,6),…

A: This question can be solved using the area of triangle in three dimensional geometry.

Q: Find the height of the cylinder that can be put into a cone with radius 7 cm and height 12 cm and…

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Q: Find the dimensions of a right circular cylinder of maximum volume which can be inscribed in a…

A: NOTE: Refresh your page if you can't see any equations. . the radius of the sphere is R=12 the…

Q: 9. Determine the position of the centroid of a sheet of metal formed by the curve y = 4x - x² which…

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Q: Find the centroid of the region bounded by the given curves. y = 8 sin(5x), у 38 cos(5x), х-D0, х 3…

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Q: Find the tangent plane to the surface 8x2+y2+4z2 = 25 at the point ( 1, -1, 2 )

A: To find: The equation of the tangent plane at the point  1,-1,2. The given function for the surface…

Q: Find the lateral (side) surface area of the cone generated by revolving the line segment y = x/2, 0…

A: The given line segment is y=x2 where 0≤x≤4. The line segment is revolved around x-axis, thus it…

Q: Find the tangent plane to surface 8x2 + y2 + 4z2 = 25  at the point ( 1, -1, 2 )

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Q: What is the average distance between the parabola y = 7x(20 – x) and the x-axis on the interval…

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Q: Find the dimensions of the closed rectangular box with maximum volume that can be inscribed in the…

A: Let 2x, 2y, 2z be the dimensions of rectangular box. Then Let

Q: A thin plate has mass 3. What is the x-moment of the plate if its center of mass has coordinates (2,…

A:

Q: find the lateral (side) surface area of the cone generated by revolving the line segment y=7/3x, 0…

A: What is Solid of Revolution: A solid can be formed by revolving a region in two dimensional…

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: Find the dimensions of the rectangular box of maximum volume that can be inscribed inside the sphere…

A: Given sphere is

Q: Find volume y=3x^2, x=1, and y=0 about x axis

A: y=3x^2, x=1, and y=0 about x axis

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

A: We have to find the closest points near to the point (2,2,0).

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: A frustum of a cone is generated by revolving the graph of y = 4x on the interval 32, 64 about the…

A: The surface area A=∫ab2π f(x) 1+f'(x)2dx

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: Consider the region in the first quadrant bounded by y=x^2, the y-axis, and y=4. -the y-axis using…

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Q: Find the centroid of the region bounded by the graphs of the equations using any method y = √(1 −…

A: Consider the given equations y=fx=1-x2y=gx=0 First, find the point of intersection of the given…

Q: 2

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Q: What is the average distance between the parabola y = 10x(22 - x) and the x-axis on the interval…

A: From the average of a curve to x axis in an interval.

Q: 5. Find the moment of inertia of a plate covering the first-quad rant region bounded by y2- x, x-:…

A: Plot the given conditions for finding the boundary limits.

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) ----&gt; (0.25x,…

Q: Use geometry to calculate (without integraung). o V16 - x2 dx Note that f (x) = v16 – x² is the top…

A: The integral of a function form a point x=a to an other point x=b is the area under the graph of the…