caculate and generate the graph of following general cylinders and surfaces in three dimensions. 1.9x^2 + 4y^2 =36 2.z=16-x^2 3.9x^2 + 4y^2 +z^2 =36 4.9x^2 + 9z^2 - 4y^2 =36

Q: There is a line through the origin that divides the region bounded by the parabola y = 6x x-axis…

A: We will find the slope

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

A: The given equation of plane is : x+2y+3z=6 x=6-2y-3z                   …(1) Volume of a rectangular…

Q: Determine the diameter of a hole that is drilled vertically through the center of the solid bounded…

A:

Q: Describe the relationship between the graphs of the quadric surfaces x2 + y2 - z2 + 2z = 1 and x2 +…

A: Given: The quadratic surfaces,   To describe the relationship between given two graphs and to state…

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

A:

Q: what are the dimensions of the right hexagonal prism of minimum surface whose volume is 36 cubic…

A: This is a problem of optimization.

Q: There is a line through the origin that divides the region bounded by the parabola y = 2x and the…

A: Answer

Q: Find the dimensions of the rectangular box of maximum volume with faces parallel to the coordinate…

A:

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

A:

Q: 3. What are the dimensions of the closed cylindrical can that has surface area 280 square…

A:

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: There is a line through the origin that divides the region bounded by the parabola y = 7x – 3? and…

A: The equation of the line passing through the origin is y=mx where m is the slope of the line. The…

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

A:

Q: Determine the maximum highest point (x, y,=) the surface on z = 1+ 4x + 4y- x* - y*

A:

Q: Find the area of ​​the rotating surface that occurs by turning circle x2+y2=4 around line x=2 .

A:

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

A:

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

A:

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

A: We have to find the volume of the largest rectangular box in the first octant with three faces in…

Q: Find the area of the ellipse x^2+14 x y+245 y^2=4 by using a suitable transformation that maps to…

A: Given equation is, x2+14xy+245y2=4 The equation can be written as,…

Q: A rectangle is inscribed in a parabola y²=8x with one of its vertical side passes through the point…

A:

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

A:

Q: Determine the diameter of a hole that is drilled vertically through the center of the solid bounded…

A:

Q: Determine the center and the radius: X2 + Y2 + 2X +10Y + 1 = 0 O (-1,-5) Radius 5 O (1,5) Radius 5 O…

A: Topic-circle

Q: the solid cut from the first octant by the surface z = 81-x2-y

A:

Q: Find the centroid of a thin, flat plate covering the region enclosed by the parabolas y = 2x2 and y…

A:

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

A: The equation of a ball with radius a is x2+y2+z2=a2. The surface area of the function z=fx,y over…

Q: There is a line through the origin that divides the region bounded by the parabola y 7z 5x and the x…

A:

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

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

Q: To calculate: The dimension of the rectangular solid with a square base that yields the minimum…

A: The rectangular solid has a square base. Let the dimensions of the rectangular solid be x, x and y.…

Q: Maximize xyz on the ellipsoid

A: See the details solution in below

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

A: Given sphere is

Q: There is a line through the origin that divides the region bounded by the parabola y=8x−4x2y=8x-4x2…

A:

Q: Draw the left and front vlews of the solid below. Left Front

A: Solid shapes are nothing but solids that consist of 3 dimensions, namely length, breadth, and…

Q: What is the maximum vertical distance between the y=x+2 and the parabola y=x^2 for -1 is less than…

A:

Q: Sketch the section of the surface at y = 0. 4 2 -2 -6 -4 -6 -4 4 6. -61

A:

Q: A company that manufactures dog food wishes to pack the food in closed cylindrical tins. What should…

A: Use application of derivative concept. volume of cylinder and total surface area of cylinder…

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

A: Given: The region bounded by y=2x2, x=0, x=2 and y=0.

Q: 2

A:

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

A:

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: Sketch the graph of -x + 9y² – 4z² = 36 and identify the surface. %3D

A: Given a function in terms of x, y and z. Here x and y are independent variables and z is a dependent…

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: 1 Find the points have minimum distance From the origih to the Surface xyz =1.

A: Using the lagrangian ultiplies Let For critical points,

Q: ) Find an equation of the tangent plane to the paraboloid defined by -- 4x² + 5y² at the point (,-2,…

A:

Q: Find the parabola y = ax2 + bx + c that passes through (2,1) and be tangent to the line y = 2x + 4…

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.