Calaulate the volume between 2= 12x°+ay2 Vax? 2. and 2 = 6- 2x- 2y?

Q: *® x'+yt+ 2" =4 r=2 coso , %3D Find the volume

A: We have r = 2cosθ and x² + y² + z² = 4

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

A:

Q: Find the volume of the solid generated by revolving the shaded region abouti хаxis Q 3x+ 5y = 15 5

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Q: Suppose that r = 12 cm and h = 15 cm in the right circular cylinder. Find the exact and approximate…

A: In right circular cylinder   radius(r)=12 cm and height(h)=15 cm (a)  For lateral surface area…

Q: The side of a cube decreases at a rate of 8 m/sec. Find the rate at which the volume changes, when…

A: Given data: The side of a cube is decreases at the rate of 8 m/s. The objective is to find the rate…

Q: What is the volume of this equation using the shell method? 2(pi)y((6/y+y^3)-(3/2(sqrt3))dy from the…

A: The volume for the given interval over the interval [1, sqrt3] can be computed as follows.

Q: (d) Estimate the hydrostatic force on the bottom of the pool. X Ib

A: Answer is mentioned below

Q: volume solid= T1 da.dy.dz of 30 2पट 5 1. r.das.do.dz

A: Given, Volume of solid=∫∫∫v1·dx·dy·dz=∫03∫02π∫051·r·dr·dθ·dz

Q: A circular swimming pool has a diameter of 20 m, the sides are 4 m high, and the depth of the water…

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Q: find The volume of Ihe solid generated by revolving each vegion enclosed by he triangle wilh…

A:

Q: The surface area of a sphere increases at a rate of 64 m2/sec. Then the rate at which the radius…

A: Given rate of increase in the surface of sphere=64m2/sec And radius of sphere=3m Now we have to find…

Q: 13 1 y = 1/2x² + ²x² 6x 1 √2 <x< 1 Curved segment rotated about the ox-axis.Calculate the area of…

A: Given that y=12x3+16x ,12≤x≤1

Q: A ring that weighs 80 grams is made of gold and silver. By measuring the displacement of the ring in…

A: Let ring contains x grams of gold. Density of gold = 19.3/cm3. So, the volume of gold ring =…

Q: D. Calculate volume enclosed by (z = 8-x² - y²) and (z = x² + y²), (Use order dy dz dx). وكنت طول

A: Given

Q: F. Determine the specific gravity of the substance having a volume of 9.85 ft x 13.12 ft x 59 ft if…

A:

Q: A rectangular pontoon is 7 m long and 3 m wide. The welghl pontoon is 30 tons. Determine the…

A:

Q: Find the volume generated by revolving the curve y = cos(2x) about the x-axis, 0 < < 4

A: Given:       y=cos(2x) , 0≤x≤π4

Q: The Kinehc of a body with mass m energy 8 velo city 22K V IS k = mv? Show that %3D %3D Əvz

A: Topic-derivative

Q: The surface area of a sphere increases at a rate of 59 m?/sec. Then the rate at which the radius…

A: We have to find rate of change of radius

Q: A fluid has density 1000 kg/m³ and flows with velocity v = xi + yj + zk, where position is measured…

A: Given density 1000 kg/m3   velocity v= x i^+y j^+z k^   Given Paraboloid the x = 36-y 2 - z ²…

Q: The side of a cube decreases at a rate of 8 m/sec. Find the volume changes, when the side is 6 m. O…

A: Please refer the image.

Q: 4. Determine the surface area of the solid obtained by rotating y = v9 – x², -2 <x<2 about the x –…

A: Let's find.

Q: The side of a cube decreases at a rate of 7 m/sec. Find the rate at which the volume changes, when…

A:

Q: An oil storage tank can be described as the volume generated by revolving the area bounded by =D0,…

A: Graph the curves to find the area bounded by them: Volume of area revolved about x-axis is given…

Q: The end plates (isosceles triangles) of the trough shown to the right were designed to withstand a…

A: Given: The end plates of the trough were designed to withstand a fluid force of 5400 lb. Assuming…

Q: Let Vis the volume of the solid of revolution expressed by the equation V = 4n fx²e²dx. Find the…

A:

Q: A trapezoidal plate with height h and bases a and 2a is submerged vertically in water as shown.…

A: Explanation of the solution is given below....

Q: The side of a cube decreases at a rate of 7 m/sec. Find the rate at which the volume changes, when…

A: Let the side of the cube be a m Then, given dadt=-7m/sec    (- sign indicates side is decreasing) To…

Q: A circular swimming pool has a diameter of 24m, the sides are 5m high, and the depth of the water is…

A: Question is solved.

Q: (b) Find the volume of the solid generated when R is rotated about the x-axis.

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Q: (d) A sphere of radius 0.4 m and having negligible weight is floating in a large freshwater lake.…

A: Given: The sphere of radius 0.4 m. The density of water is 1000 kg/m3. Calculation: Suppose the…

Q: The volume of the solid given by tl

A: Given,             z=8-3x2+y2            z=x2+y22-2

Q: Use cylindrical coordinates to find the volume of the solid. Solid inside both x2 + y2 + z2 = 36 and…

A:

Q: Use cylindrical coordinates to find the volume of the solid. Solid inside both x2 + y2 + z² = 64 and…

A:

Q: A closed cylindrical tank of maximum volume is to be constructed. With only 381.7 m^2 of material,…

A:

Q: The volume of the solid generated by revolving the curve x = 4, about the y-axis between y= 0 and y…

A:

Q: A cylindrical tank of radius 5 ft and height 9 ft is two-thirds filled with a liquid of weight…

A: Solution

Q: Find the volume of the ellipsoid x² + y² + 10z² = 49.

A:

Q: %3D Jo 12+t+2dt2

A:

Q: Find volume if area enclosed is rotated about y= -2.

A: To find the volume if the area enclosed by the below curves is rotated about y = -2.

Q: Sketch the hypocycloid x2/3 + y2/3 = 1 and find the volume of the solid obtained by revolving it…

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Q: A parabolic arc y = Vã,1< x<2 revolves around x-axis. What is the volume of the solid of revolution?…

A:

Q: The surface area of a sphere increases at a rate of 52 m2/sec. Then the rate at which the radius…

A: Let A is the surface area of Sphere.

Q: What is the volume of the solid formed when the region bounded by the curve y =√16x², x = -3 and x -…

A: Given curve is y=16-x2, x=-3, x=3 is rotated about the x axis. find the volume of the solid Formula:…

Q: Find the volume of the solid of revolution when the curve y = 2r? - 2 is revolved around the x-axis…

A:

Q: The surface area of a sphere increases at a rate of 82 m² / sec. Then the rate at which the radius…

A: Use rate of change

Q: Find the volume of the solid generated by revolving the shaded region about the given axis. About…

A: By using volume of a solid formula, we calculate the required volume.

Q: Use cylindrical coordinates to find the volume of the solid. Solid inside both x² + y² + z² = 16 and…

A:

Q: Revolving a circle of radius a about a tangent line will generate a solid whose volume will be equal…

A:

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.