Q2: A cube of edge 24mm is resting on the top of a frustum of cone of base diameter 60mm and top diameter of 40mm with axis height of 72mm. Draw the isometric view of these solids?

Q: Find, correct to four decimal places, the length of the curve of intersection of the cylinder 9x2 +…

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Q: Graph the curve 8y2 = x2 (1 − x2 ). Use a computer algebra system to find the surface area of the…

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Q: Find the points on the surface y2 36 + xz that are closest to the origin. (х, у, 2) (smaller…

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Q: (i) What are the projections of the point (2, 3, 5) on the ry-, yz- and rz-planes? (ii) Write…

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Q: Find the surface area of the cone frustum generated by revolving the line segment y = (x/2) + (1/2),…

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Q: Find the distance between the point and the plane.

A: The distance of a point from a plane in the standard equation form is equal to . The given point…

Q: 5a. Consider the right square pyramid with a horizontal plane intersecting the pyramid halfway up…

A: The horizontal plane will be parallel to the base of the pyramid.

Q: Find the area of the segment of a sphere formed by revolving the graph of       y = √(r2 − x2) , 0 ≤…

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Q: Find the points on the surface y = 4 + xz that are closest to the origin. (х, у, 2) (smaller…

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Q: and the plane - 3 X + Z Intersect along a line. Find Parametnic desenetion of this la

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Q: Use the parametric equations of an ellipse, x=4cos(theta), y=3sin(theta), 0 less than or equal to…

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Q: You are given a y=sqrt(36-x^2) curve that rotates about the x-axis. What is the area of the…

A: To find the surface area of rotation of the below curve about the x-axis. y=36−x2

Q: FIND THE AREA OF THE SURFACE FOR THE PORTION OF THE PARABOLOID Z = 49-x² - y² IN THE FIRST OCTANT

A: Formula: The surface area of the function z=fx, y over the region D is: SA=∫∫D1+zx2+zy2 dA The given…

Q: Sketch the surface given by the function. z = 9-x?-y?

A: Given, z=9-x2-y2

Q: Radiation is focused to an unhealthy area in a patient’s body using a semi-elliptic reflector,…

A: The position of the elliptical reflector is placed  such  that it contains the one of the focus and…

Q: Find the point lying on the intersection of the plane x + y +z = 0 and the sphere x2 + y2 + z? = 25…

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Q: vo ume of the solid in the litoctanit bounded by the plan 2x+3u +62=12

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Q: Find the area of the surface generated by revolving the curve y=x^3/18, 0(<=)x(<=) 2 square root 2,…

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Q: The quadric surface 2z-x²-4y² = 0 is O Hyperboloid of two sheets. O Elliptic paraboloid. O…

A: We have to solve given problem:

Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x2 +y? + 2? = 1 is T =…

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Q: Find the isogonal trojecdories of x*+y² =r² at 45",

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Q: Find the area of the surface of the part of the plane 3x + 2u + z = 6 that lies in the first octant.

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Q: Find the area of the cap cut from the top of the sphere x2 + y2 + z2 = 1 by the plane z = sqrt(2)/2.

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Q: Find, correct to four decimal places, the length of the curve of intersection of the cylinder 9x2 +…

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Q: The sphere x² + y² +z² = 100 has the center (0,0,0) and a radius of length 50. Select one: True…

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Q: Which one, y=ex, 1≤y≤2, gives the surface area of the solid formed by rotating the curve segment…

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Q: Find all points on the isometric dot plane, Ax,1 yl, with x and y integers, that are ex- actly V133…

A: a)The distance from origin to point x,y is 133. b)The distance from origin to point x,y is 217.

Q: The lateral (side) surface area of a cone of height h and base radius r should be πr√r2 + h2, the…

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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: Find the area of the ellipse cut from the plane z= 8x by the cylinder x +y = 4. Surface area = (Type…

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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: Find the surface area of the part of the plane 3x + 2y + 4z = 24 that lies in the first octant…

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Q: Compute the surface area of the ellipse that lies on the plane z = 11 – 3x + 2y and inside the…

A: The surface area of the surface given by z=f(x,y) where (x,y) is a point from the region D in the…

Q: Find the area of the surface. The surface cut from the “nose” of the paraboloid x = 1 - y2 - z2 by…

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Q: Find a formula for the distance from the point P(x, y, z) to thea. xy-plane. b. yz-plane. c.…

A: Distance FormulaDistance between two points x1,y1,z1 and x2,y2,z2d=x2−x12+y2−y12+z2−z12

Q: Find the area of the ellipse cut from the plane z= 3x by the cylinder x + +y? =4

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Q: Please help me with this problem

A: Parametric equation:

Q: Compute the surface area of the surface generated by revolving one arch of the cycloid…

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Q: Find the area of the cap cut from the top of the sphere x2 + y2 + z2 = 1 by the plane z = √2/2.

A: Given equation of sphere is    x2+y2+z2=1     And the equation of plane is  z=22=12 But we know that…

Q: 2 Find the area of the ellipse cut from the plane z = 3x by the cylinder x² + y² = 16. Surface area…

A: Given plane z=3x and the cylinder x2+y2=16. The objective is to find the area of the ellipse cut…

Q: Sketch the solid described by the given inequalities.   0 <= theta <= pie/2, r <= z <=2

A: r≤z≤2,   0≤θ≤π2 We need to sketch the solid.

Q: Find the area of surface that is generated by revolving the portion of the curve x = /9 – y? , -2 <…

A: We will find out the surface area of revolution.

Q: The lateral (side) surface area of a cone of height h and base radius r should be pai rsqrt(r2 +…

A: Obtain the lateral surface area as follows.

Q: The surface that is linear with the three variables, x, y, and z is called cylinder plane sphere O…

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Q: Find the point lying on the intersection of the plane x + + z = 0 and the sphere x2 + y2 + z2 = 25…

A: According to the given information, it is required to find a point lying on the intersection of the…

Q: 3) Which type of quadric surface listed in Table 2 below is 4x² + y² + 4z² – 4y – 24z + 36 = 0?

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Q: Find the point lying on the intersection of the plane  x + (.5)y + (.25)z = 0  and the sphere  x2…

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Q: use Cylindrical coordinates to the Vaume of the Solid bovnded by the parabolo ld z=16-x²-y? %3D

A: Introduction: A point with rectangular coordinates left(x,y,z right) in three-dimensional space R3…

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.