a)Calculate the integral [D zdV on the D region bounded by the 6 = x2 + y2 paraboloid from the bottom and the sphere x2 + y2 + z2 = 6 from the top. b)N; In the 1st eighth region, 9 + y2 = 4, x2 + y2 = 9 cylinders and the region formed by z = 0, z = 1, x = 0, x = y planes, Mn ( x2 + y2)dv =?

Q: Let f(z) = E-oo Qn (2 – zo)" in the annulus 0 < |z – z0| < R. Give the definition of zo being a…

A: Consider the given information.

Q: 22 Use a triple integral to find the volume of the given solid. The solid enclosed by the evlinder…

A: According to question,Given Cylinder and planes,x2 + z2 = 4y = -1y+z = 4

Q: The solid E in the first octant of 3-space shown in is bounded by the cylinder z = 1– x² and the…

A: Let's find.

Q: Let D be the solid region in space bounded below by p = 1 and above by cosp = Then the region D is…

A:

Q: A) Evaluate the triple integral ydV, E = 0, where E is the solid region bounded by the cylinder 4 =…

A: Given

Q: 5. Find the volume of the tetrahedron bounded by the coordinate planes and the plane 3x + 6y + 4z -…

A:

Q: 2. Evaluate the double integral / 1OxydA, where D is the triangular region with vertices (0,0),…

A: ∬D10xy dA where D is a triangular region with vertices 0,0,1,2, and 0,3.

Q: Calculate the double integral Sle (x² + 2y) dA, where R is the triangular region with vertices 8/3…

A:

Q: Evaluate the double integral 8xy dA, where D is the triangular region with vertices (0, 0), (1, 2),…

A:

Q: Let G be the solid in the first octant bounded by the ellipsoid 9x2 + 4y2 + z2 = 36, the parabolic…

A: We have the ellipsoid as 9x2+4y2+z2=36 and the parabolic cylinder as 2x+y2=4. It is bounded by the…

Q: In Exercises 11-16, a graph of a planar region R is given. Give the iterated integrals, with both…

A: The region R is given. The given triangular region is bounded by the lines as shown in the…

Q: 2) Calculate the integral the regions descri bed. over / 2x- 5xy- 3y² dA. On a y = (x-1) /3 , y= -2x…

A: Bounding lines y=x3         → 3y-x=0y=(x-1)3→3y-x =-1y=-2x    →y+2x=0y=1-2x  →y+2x=1

Q: Evaluate the integral ∭U(x4+2x2y2+y4)dxdydz, where the region U is bounded by the surface x2+y2≤1…

A:

Q: The surface integral xyzdS, where S is the portion of the cylinder y+z = a² (a >0), in the first…

A: We will use basic knowledge from Integral calculus, in particular, surface integral calculation.…

Q: Evaluate the triple integral. xyz dV, where G is the solid in the first octant that is bounded by…

A:

Q: Consider the region formed by the graphs of y = e^x , y =0 , x = 2 and x = 4. Which integral…

A: We sketch the region using a graphing calculator The shaded region is rotating about the y-axis The…

Q: A) Evaluate the triple integral ydV, E a2 + y?, and the planes z = 0, where E is the solid region…

A: Since you have asked multiple questions, we will solve first question for you. If you want other…

Q: Given that c is the boundary of a region bounded by y=4-2,y= -x+2, X =1 and y=0 with positive onient…

A:

Q: 3. A) Evaluate the triple integral xdV, where E is the solid region bounded by the cylinder 4 = y =…

A: 3.A) The given integral is      ∫∫∫E x dV , E is the solid bounded by x2+y2=4, z=0, y=3z, x=0 and in…

Q: 1. Find the volume of the solid in the first octant bounded above by the sphere a? + y? + (z – 5)² =…

A:

Q: 1. Find the surface area of the region S in the plane z = 3x + 2y such that 0 <x < 10 and 0 < y <…

A: We have to find the surface area of the region S in the plane z = 3x + 2y such that 0&lt;=x&lt;=10…

Q: What is the region of the solid generated by the graphs of a = y – 4y and a = -y ?

A:

Q: Evaluate the double integral || 8xy dA, where D is the triangular region with vertices (0, 0), (1,…

A: Given data: The first vertex is O=(0, 0). The second vertex is B=(1, 2). The third vertex is A=(0,…

Q: 7.3 5. Use the shell method to set up and evaluate the integral that gives the volume of the solid…

A:

Q: 12. Consider the solid Q bounded by the surface of equation z = x*+ y° and the plans z = 4, yv3 = x,…

A:

Q: Evaluate the triple integral zdV E over the solid region E enclosed by the two surfaces z = 2/x² +…

A: Given a region E bounded by z = 2x2+y2 to z=x2+y2  ∴ ∫∫E∫zdv=∫R∫∫2x2+y2x2+y2   zdzdA…

Q: 2. Calculate the double integral 2ry dA, where R is the triangular region with vertices (0,0), R (1,…

A:

Q: Prove that the volume of the sphere x2 + y² + z² = a² is V = na³ using triple integrals.

A: The formula to calculate the volume in spherical coordinate system is given below: V=∫ϕ∫θ∫ρρ2sinϕ dρ…

Q: Consider the solid whose base is the region bounded by 4x? + 9y? = 36. Y 3 -3 -2 -1 -1 2 3 2 -3 1.

A:

Q: 2. Set up the triple integral f[Sp I+y+zdV, where D is the tetrahedron with vertices at (0,0,0),…

A:

Q: Evaluate the triple integral zdV where E is the solid bounded by the cylinder y² + z² = 64 and the…

A: Here, to evaluate: ∫∫∫Ez dV where E is the solid bounded by the cylinder y2+z2=64 and the planes…

Q: 6. Use a triple integral to find the volume of a solid enclosed by the elliptic paraboloids z = 2x²…

A:

Q: Find the volume of the solid bounded by the sphere x² + y² + =? = 6 and the paraboloid := x² +y² .…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: If the region that lies inside the cardioid r = 1+ cos 0 and outside the cirele r = 1 is the base of…

A:

Q: 3. A) Evaluate the triple integral xdV, E where E is the solid region bounded by the cylinder 4 = x2…

A: To evaluate the integral:

Q: Evaluate the triple integral II. x* dV, where T' is the solid tetrahedron h vertices (0, 0, 0),…

A:

Q: Set up an integral for the surface area of the part of the paraboloid z = 1 - x2 - y2 that lies…

A:

Q: 18. Set up an integral to compute the volume under the hyperbolic paraboloid z = over the disk D =…

A:

Q: Let D be the solid region bounded above by z = -5x² +y? and below by z =-5. Then the projection of D…

A:

Q: Let D be the tetrahedron in the first octant bounded by the coordinate planes and the plane 6x + 3y…

A: The volume of the region D can be calculated by the following formula. Volume=∭DdV

Q: Set up a triple integral to find the volume of the solid that lies in the first octant bounded…

A: The triple integral is written as  ∫x=ax=b∫y=p(x)y=q(x)∫z=f(x,y)z=g(x,y)F(x,y,z) dz dy dx Change of…

Q: Let D be the solid region bounded above by z = -3/x² + y² and below by z = -3. Then the projection…

A: Given Region D is bounded  above by cone  Z=-x2+y2and bounded the  below by  plane z=-3

Q: Evaluate the double integral. 8xy dA, D is the triangular region with vertices (0, 0), (1, 2), and…

A:

Q: . Set up the triple integral fSSp r+y+zdV, where D is the tetrahedron with vertices at (0,0,0),…

A: The equation of tetrahedron with intercepts (a,0,0), (0,b,0) and (0,0,c) is given by: Given…

Q: 1) Evaluate the triple integral SS, f(x,y,z)dv : B) f(x,y,z) = 3y² – 2z , Q is the tetrahedron…

A: given f(x,y,z) = 3y2-2z, Q=3x+2y-z=6 The region bounded by the equation Q is a tetrahedron cutting…

Q: What is the volume of br^3 of the region bounded by the z=9-x^2-y^2 paraboloid, the xy plane, and…

A: Triple integral is used to integrate the function of three variable over the three-dimensional…

Q: 1. Find the surface area of the cone z = √x² + y² that lies between the plane y = x and the cylinder…

A:

Q: Evaluate the triple integral zdV, where E is bounded by the cylinder y² + 2² = 4 and the planes z =…

A: Given problem:- Evaluate the ∫∫∫E z dV, where E is bounded by the cylinder y2+z2=4 and the planes z…

Q: Let D be the solid region in the first octant bonded above by z-3 and below by 2= 2++y. Then the…

A: Here we will have to project the 3-dimensional solid regions on a 2-dimensional plane. Hence, we…

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.