Which graph shows the intersection curve, in the first octant, between a cylinder of equation: (x − 3)2/a2 + (z − 2)2/b2 =1, where a > b > 0, with the equation plane z = 4 − y

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

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Q: B4. Find the dimensions of the right circular cylinder of maximum lateral surface area which can be…

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

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: A The roots of Characteristic equetion f oreler, lineor homopeneous-equation with constant…

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Q: 4.x² + y = 4

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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: Sketch typical solution curves in the regions in the xy-plane determined by the graphs of the…

A: Given: f(y)=y2(9−y2)  To find: Solution

Q: Find the points on the cone z2 = x² + y² that are closest to the point (1,-1,0) %3D

A: Given that, z2=x2+y2 and the point is (1, -1,0). Form the equation of distance as follows.…

Q: Determine the surface of revolution of arc y³+y=x²+6x on the interval [-5,-1] if it is revolved…

A: Use the formula of arc length to determine its length. Now use to it determine the volume generated…

Q: 3. For curve y ==x +4x2 - 12x , locate the possible maximum and minimum %3D points.

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Q: What is the total length of the curve of intersection of the surfaces x2 + y2 + z2 = 4 and y2 + 2z2…

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Q: sketch the graph xyz plane x^2+z^2=4

A: GIVEN: x2 + z2 = 4

Q: As a hardworking student, plagued by too much homework, you spend all night doing math homework. By…

A: First we consider the volume of small disk and integrate this across the given region to get the…

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: A cylindrical surface in an xyz-coordinate system is an equation that contains only two of the…

A: In this question we have to state whether the given statement is true or false.

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 point on the plane x−3 y+3 z =−8 that is closest to the point (−2,−2,0) .

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

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Q: oil storage tank can be described as the volume generated by revolving the area bounded by…

A: We have to find out volume of tank

Q: As a hardworking student, plagued by too much homework, you spend all night doing math homework. By…

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

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Q: 4 and the plane Find the point on the curve of intersection of the paraboloid x- + y- x - y + 2z = 0…

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Q: 1. y = x², x = 0 , x = 2, y = 0, about the x – axis - 2. V9 - y?, у %3 1, у %3 3, а %3D 0, about the…

A: Use formula to calculate volume

Q: The line through the origin whose projection on the xy-plane is a line of slope 3 and whose…

A: In this type of questions we assume a line an points on that line. Suppose we have a line and points…

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: As a hardworking student, plagued by too much homework, you spend all night doing math homework. By…

A: GIVEN: y = 9 x2 x = 0 x = 1 y = 0

Q: 9. In the ry-plane, a particle moves along the parabola y = x? – x with a constant speed of 2/10…

A: Given:-  In the xy-plane, a particle moves along the parabola y = r²r with a constant speed of 2√10…

Q: Find the points on the cone z = x² + y² that are closest to the point (-5,-2,0)

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Q: Find the intersection of the two planes with equations 3(x – 1) + 2y + (z + 1) = 0 and (x – 1) + 8y…

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Q: This sphere has a diameter of 20 feet. The center of the sphere is 12 ft from the ground. (x – 0)² +…

A: Volume of the sphere in cubic feet

Q: A triangle has vertices (1, 1), (3, 7) and (5, 4). What is the distance between the centroid and the…

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Q: an isosceles triangle has a baseline between (0,0) and (x,0), while the third corner is placed in y=…

A: Let's find.

Q: intersection of the paraboloid z=x^2+5y^2 and the plane x=3. At what rate is z changing with y when…

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Q: The 50 g bullet travelling at 100 ms-1 strikes the 2 kg block centrally and is embedded within it.…

A: Please check step 2 for the solution.

Q: 8. Consider the parabola whose equation is y=x² -4x and the line whose equation is y=2x+b, where b…

A: y=x2-4x  &  y=2x+b Put y=2x+b in y=x2-4x, we get ⇒2x+b=x2-4x⇒x2-4x-2x-b=0⇒x2-6x-b=0 To intersect…

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: As a hardworking student, plagued by too much homework, you spend all night doing math homework. By…

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Q: Charlie and Alexandra are running around a circular track with radius 60 meters. Charlie started at…

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Q: A miniature quadcopter flies in a curve line from one point to another. Suppose that the path of the…

A: The path of the quadcopter is given by the equation y=2.15+2.09x-0.41x2, 0≤x≤3.6 (i) The distance of…

Q: Find the shortest distance from the point (2,0,–3) to the plane x + y + z = 1. . Use Lagrange…

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Q: A package in the shape of a rectangular solid is to be delivered. However, it can only have a…

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

A: The solution are next step

Q: Find the minimum distance from the surface x2 -y2 -z2= 1 to the origin.

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Q: 1. A closed box, with a rectangular base, whose length is twice its width, is to have a surface of…

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Q: A variable straight line of slope 4 intersects the hyperbola xy = 1 at two points. The locus of the…

A: Introduction :

Q: The maximum vertical distance between the parabola y = 3-z and the line y = 3x+2 on the interval…

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Q: True or false (and explain): A solution to y′ = y(4 − y)(y + 2) that includes the point (1, 100)…

A: Solve, as follows:

Q: Find the volume of the largest rectangular box in the first octant with three faces in the…

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Q: Find the orthogonal trajectories of the families of Parabolas y a + 8az + 16a, which passes through…

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