The exact solution of the 2q(z - px - qy) = 1 + q^2 equation and by using this solution, Find the integral surface through the curve y: 2x = y^2 + z^2,  y + 1 = 0

Q: Find the equation of the tangent plane to the surface 2= 42 + 3y+7zy at the point (0,-1,3).

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Q: Given S as a quadric with equation 4x^2 - (y-3)^2 + 4z^2 = 4 Find a generating curve for S (as a…

A: Given S as a quadric with equation 4x^2 - (y-3)^2 + 4z^2 = 4 Find a generating curve for S (as a…

Q: For a given surface z-x^2-y^2=10 Find the parametric representation of the straight line which…

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Q: Sketch the following surfaces. 1) 4x^2+9z^2=9y^2 2)y^2-x^2=z Show all work.

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Q: Sketch or describe the surfaces in R³ of the equation presented x² + y} – 2x = 0

A: The equation is x2+y2-2x=0

Q: Consider the following equation of a quadric surface 9x^2 - 81y^2 - (z^2/4)=0 (a) Find the…

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Q: - Graph the surface 1 = y² + z² — by first sketching at least three cross sections in each of the xy…

A: To Plot: Graph The Surface 1=y2+z2-x24 by plotting at least three cross section in xy and yz plane

Q: Find the point(s) on the surface z^2=xy+1 which are closest to the point (10,11,0).

A: We have to find the the point(s) on the surface z^2=xy+1 which are closest to the point (10,11,0).

Q: Find a vector equation for the curve of intersection between the surfaces y^2-x^2=9 and 2x-3y-z=12.

A: Introduction: We can determine the vector equation of the curve formed by the intersection of two…

Q: Describe the surface whose equation is given by x² + y² + z² + 6y - 2z = 0.

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Q: Find the equation of the tangent plane to the surfaceln(x3 + y3 + z3) = x2z + 1at the point (1, 1,…

A: The objective of this question is to find the equation of the tangent plane to the given surface at…

Q: Find the length of the curve whose parametric equations are x = 3t^2 and 3t^3, from t = 0 andt = y =…

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Q: Find the trace of the surface 4x^2 − y^2 +6z^2 = 2 in the yz-plane and identify the conic section.

A: Given 4x2-y2+6z2=2

Q: Q1.6 Find the point on the surface given by the equation x^2 + 5y^2 + 10z^2 = 18016 that has a…

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Q: The locus of the foot of the perpendicular from the centre of the hyperbola xy = c² on a variable…

A: Given hyperbola equation is  xy = c2 The parametric form of this hyperbola is  x = c t  and   y =…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.