A plate in the form Ot an isoceles triangle uith base' 10 tt ancl altitude 4 ft iS submerged vertically in water Surtace it water has ueight clensity p=62.J1blft And the fluid fore F asaint the plate

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Q: Find div F and curl F if F(r, y, z) = 10e i- 2 cos yj+ sin2 zk. %3D

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Q: Disseuss po sibility af existence of Saludion for ucx)=sinlox+25 x² k(4,t)ult)dt マラスラの sin(2-) Find…

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Q: 4 1 Find the area of the region cut from the first quadrant by the curve r = 2(2- sin 20) ² A= (Type…

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Q: Tank 2 250m pipe Tank 1 system nino

A: Note:-  Euler's Method for a function f(x, y)=0 yn+1=yn+h fxn, yn; n=0, 1, 2, ...Here, xn+1=xn+h…

Q: 19. Find. thedivergen ce. and.cur..4the fellowiny vecter. field: a.. F = Xej+. y.e... b. Ês ĕsiny i…

A: We need to find the divergence and curl of the following vector fields. a. F→=xeyj+yezk=(0,xey,yez)…

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Q: Ĉ the given curve is rotated around the y-axis Find the area of the resulting surface y = I 9 2 "² I…

A: The given curve is:y=14x2-12ln x ;           4≤x≤5

Q: + Bsin z Differentiate @ wi th xespect to x - - S"d (use dy A sinz + B cose

A: Given that: y=Acosx+Bsinx

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Q: QUESTION 6 I X+y+Z If fxyz.w) = then f, equal x +y +z Ox+y O 1

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Q: 42 er

A: Given query is to perform dilation of scale factor 0.5

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Q: 11. A plate in the form of a parabolic segment of base 12 m and height of 4 m is submerged in water…

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Q: Complete the table: Give all answers to at least 2 decimal place accuracy. (Assume acceleration and…

A: we know that   r''(t) = r'(t) - r'(t-1) and r'(t) = r(t) - r (t-1)

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Q: He knöws that for he needs for each slanted area. If he wants the slanted areas to extend 9 yards…

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Q: Check the deviation theorem for the function v(x, y, z) = r²sin0 î + 4r²cos0 Ô + r?tan0 @

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Q: Let F= . •ff, curl F S S is the hemisphere x² + y² + z² = 1, z ≥ 0, oriented upwards. Use Stokes'…

A: Given: F→=x2eyz, xexz, z2exy, x2+y2+z2=1, z≥0 To find: ∫∫ScurlF→.dS

Q: 27 12 Q Y B. de

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A: Given,Below the line y=260The water level is 36 m Below the the top of the dam.We have to find the…

Q: (5,1,2) V= (4,-3.1) is ON -bas in RB V to U Given Qud Find the projection W of Determine the engle a…

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Q: find work done Let F = ) and let c be unit circle centered on(2,0) note:r? not constant

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Q: 4) A spherical tank is full water with the spout at the Lísdest point on the tank

A: Given, a tank has a radius=4 ft                           spout length=1 ft

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.