Suppose the divergence of the electric field in some spherical region is found to be V E = 5kr³. Find the total charge contained in a sphere of radius R, centered at the origin.

Q: Evaluate the iterated ntegral by Lonverting to polor coordinates. 2. zy dx dy 34

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Q: The area bounded by the parabolas (x − 2)^2 − 9py=0 and y^2=9p(x−2) is to be revolved around x = 2.…

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Q: Prove that fe, r*dx + rydy = 0 where Co is the line segments from (0, 1) to (0,0) by using…

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Q: The standard parametrization of the circle of radius 1 centered at the point (1, 0) in the xy-plane…

A: using the formula to determine surface area revolving to y axis S=2π∫abx(t)(dxdt2+dydt2)dt

Q: Find the center of mass for the region bounded by y = 4 - x² that is in the first quadrant

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Q: Compute the line integral (х — y) dx + xe x dy, where C is the closed curve consisting of two line…

A: line integration

Q: Set up a triple integral in spherical coordinates to c

A: Given, the solid bounded above by the cone x2+y2=z2and bounded below by the sphere…

Q: The plane figure below is a square of side length 2 with a quarter circle of radius 1 taken out of…

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Q: 3. For what value of K the velocity field in plane polar coordinates given by v, = tion of…

A: 3. The given values are,vr=K36r2-1cosθ and vθ=k36r2+1sinθ

Q: has a scalar potartial in the region Ro {iy = ).X} IR

A: Since you have posted multiple questions and we can answer one question. So, answered first…

Q: Use Green's Theorem to evaluate the line integral f(e*c - 2y)dx+(5x+ev* dy, where C is the 15. 2cos:…

A: We need to find integral.

Q: Fi for oec ind volume of the solid of revolution by rolahng about the -ais each regton boundad b the…

A: To calculate the volume of the given solid of revolution

Q: The volume of the solid generated by the curve y = e, between z = 2 and z = 6 about the z- azis is

A: Given: The curve is y=e-x   To determine: The volume of the solid generated by the curve y=e-x…

Q: 4. Illustrate and find the center of mass and moment of inertia with respect to x and y for the…

A: y = f(x) =4-x2   only in First quadrant…

Q: Find the center of mass of the lamina bounded by the graphs of the equations x = 64-y² and x = 0 for…

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Q: Find the line integral with respect to arc length (5x + 3y)ds, where C is the line segment in the…

A: Given integral∫C5x+3ydswhere C is the line segment in x-y plane with the end points P(5,0) and…

Q: Calculate the area under y = x2 over [0, 1] using Eq. (11) with the parametrizations (t3, t6) and…

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Q: Evaluate the cylindrical coordinate integral: L L dzr dr de O 647 O 87 O 167 O 1287

A: To solve the integral

Q: Show that the volume of a spherical block can be approximated by ∆V ≈ ρ2 sin ϕ ∆ρ ∆ϕ ∆θ.

A: Suppose x,y,z is a point at fixed distance from the origin in the 3D-space.

Q: Suppose that a semicircular wire has the equation y= V25- x and that its mass density is 8 = b- y.…

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Q: . Calculate the flux integral fF.n ds, where C is the positively oriented circle of radius 1…

A: Given function is, Fx,y=x,2y The formula for calculating the flux of the integral ∮F·nds is,…

Q: Suppose f(x, y, z) = x² + y² + z? and W is the solid cylinder with height 9 and base radius 5 that…

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Q: Use Green's theorem in order to compute the line integral (2sin z + 3y²) dx + (sin(4®) + 2x³) dy…

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Q: Calculate the area of the region bounded by: r = 3 cos(0),r = 3 sin(0) and the rays 0 = 0 and 0 =

A: r=3cos(θ)r=3sin(θ)θ=0  and θ=π4Area of the polar…

Q: Set up an integral to compute the arc length L of the curve C: r (t) = (t, 4t, V2t) %3D from the…

A: It can be found by integrating between limits of t= 0 to 1

Q: Find the line integral with respect to arc length|| (9x + 8y)ds, where C is the line segment in the…

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Q: Use Polar coordinate to evalute ff gdA, 8 where R is the region Bounded by the life line yet, the…

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Q: Given i = x²& + xy ŷ + yz 2 check the fundamental theorem of divergence over a cube whose each side…

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Q: Evaluate the cylindrical coordinate integral. бл 8 LL dzr dr de 4л 8

A: = ∫4π6π ∫48(9r-8r)rdrdz =∫4π6π(8-4)dz = 4(2π) = 8π

Q: Adobe Scan Mar 10, 2021.pdf Page 4 of 5 Q Q Search © Find, He volume revolution for, fa)='4-a, xE…

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Q: Find the moment of inertia about a diameter of a thin spherical shell of radius a and constant…

A: Let the diameter lie on the z-axis and let f(x,y,z) = x2+y2+z2=a2; z≥o  be the upper hemisphere…

Q: Use the separated solutions to solve the Laplace equation. in the region 0 0 given the boundary…

A: The Laplace Equation Uxx+Uyy=0with(a) U(0,y)=U(1,y)=0(b) U=0 as y tends ∞c) U(x,0)=sin5(πx)

Q: Sketch the region enclosed by the given curves. y = 3D 4 cos(5x), у %3D4 —4 cos(5х), 0 < x < T/5

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Q: Set up an integral to compute the arc length L of the curve C: r(t) = (, 4t, v2t) %3D from the point…

A: I am going to setup an integral to compute the arc length of the given curve using the required…

Q: 8. Set S be the bondary of the cube with side length 1 in Oc tant 1. Is in 6 pieces) Use Stokes…

A: (1) Over the surface ABCD ∫sx dy dz +z dz dx=∫01dz∫01xdy…

Q: Evaluate the line integral Jxy + z)ds where c the arc of circle x + y = 4, z= 0 from (2, 0, 0) to…

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Q: Consider a thin plate of constant density d lying in the regionbounded by the graphs of y = √x and x…

A: Given Data The density of a thin plate is d. The first equation is y=√x. The second equation is…

Q: at Va:-x dz dy.dx

A: To convert the integral  ∫-aa∫-a2-x2a2-x2∫aa+a2-x2-y2zdzdydx to spherical and cylindrical…

Q: Use Green's Theorem to calculate the circulation of F =2yi +xyj  around the unit circle, oriented…

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Q: Find the area of the surface generated by eY + e -Y revolving the curve x = in the interval 2 In 5…

A: solution:-given curve x=ey+e-y2 in the interval 0≤y≤ln5revolving about the y-axisarea of a surface…

Q: Evaluate the triple integral ryz dV, where T is the solid “tetrahedron" with vertices (0,0,0), (0,…

A: Identify the limits of integration from the region. The base of the tetrahedron is in the xy-plane.…

Q: Q1/ Find the volume of the solid generated by revolving the shaded region about the x- axis for the…

A: To find:- Volume of solid  generated by revolving the shaded region about x axis by disc method…

Q: Use green's theorem to calculate the integral Fdr, F(x, y) = (e* + a²y , e" – xy² + sen(y) + 2)…

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Q: Sketch the region enclosed by the curves and find its area. 1 y = 2 V1- NOTE: Enter the exact…

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Q: Compute the area A under the parametrized curve c(t) = (e',5t) for 0 <t < 1. %3D (Give an exact…

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Q: The center of mass of a lamina of total mass 5 has coordinates (2, 1). What are the lamina’s x- and…

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Q: Find the line integral with respect to arc length (2x + 7y)ds, where C is the line segment in the…

A: Given end points of line segment are  P=8,0 and Q=0,3

Q: please answer the (a) (b) (c)  parts

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Q: 5. Using Divergence Theorem, calculate the integral // ry dx + yz?dy + za*dz where S is the upper…

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.