The volume of the parallelepiped is Volume = |a x b||c|| sin | = |(a × %3D b). c| True False

Q: Find the volume of the solid generated when R is revolved about the given line. -E,y-1, and x- | , a…

A:

Q: Find the volume of the 'ice-cream' that is bounded by x² + y2 + z² = 79 and the upper cone z? = 3x2…

A: We will use the triple integral to find out the volume, also we will use the cylindrical coordinate…

Q: The measurements x1 = 10m, x2 = 8m, and x3 = 6m %3D represent the sides of a rectangular…

A:

Q: B) Show that V=367 is the volume of a sphere of radius 3 by using spherical coordinates.

A:

Q: Find the mass of the lamina described by the inequalities, given that its density is p(x, y) = xy. x…

A:

Q: Evaluate the double integral V1 + 4x² + 4y²dA, where D is the region inside the circle x + y? = 25…

A: We have to find area of the region bounded by the circle given in the first quadrant of the plane.

Q: Find the volume of the region bounded above by the sphere r = 2a cos0, and below by the cone = a…

A: Given :             r =2a cosθϕ=α0 < α <π2  To Find : Volume of the bounded region

Q: FR,y-I, and x= | , a bout

A: Given that,

Q: Find the mass of a thin wire in the shape of the quarter circle a² + y² = 9 in the first quadrant,…

A:

Q: Q3-Find the volume common by the plane x+y=a? & x*+z=a? ?

A:

Q: Reduce the surface integral ( S A.ds) of a cube of sides parallel to the three perpendicular axes,…

A: Here we can use divergence theorem to reduce the given surface integral. Divergence theorem states…

Q: Let m be the least possible surface area of a closed circular cylindrical can whose volume is equal…

A:

Q: The volume of the tetrahedron bounded by the coordinate planes and the plane x+y+z=4 is

A: Given

Q: b) Find the volume of the solid which is in the first octant and bounded between the spheres p = 1…

A: To find- Find the volume of the solid which is in the first octant and bounded between the spheres ρ…

Q: Describe a region whose volume is equal to: (а) 27 | p² sin o dp dộ dô Jo (b) /4 2 rdr de dz -2 J7/3…

A:

Q: The volume of the solid region, in the first octant, that lies below below the surface, z = above…

A:

Q: Suppose that a thin metal wire in the shape of a semicircle occupies the curve c, where c is the top…

A: Given a thin metal wire in the shape of a semicircle occupies the curve C, where C is the top half…

Q: 1. The hy per bola x²-y² = a² revolves about its transverse axis. Find the volume of a segment of…

A:

Q: The volume of the solid bound by the two surfaces is z = 8- 3(x² +y?), z= (x² + y?)² - 2.

A:

Q: 2. Find the volume of the region enclosed by the paraboloid z = x2 + y? and the plane z 2x.

A: Given paraboloid, z=x2+y2and the planez=2x To find the volume of region enclosed by the paraboloid…

Q: Show by integration that the volume of a sphere of radius r is V=4/3 πr³

A:

Q: In cylindrical coordinates, the integral r dz dr do represents the volume of a solid... in between…

A: Given ∫02π∫12∫01rdzdrdθ

Q: Find the mass of the lamina described by the inequalities, given that its density is p(x, y) = xy.…

A: The limits of x is from 0 to 4 And of y is from 0 to 16-x2

Q: ind the mass of the lamina described by the inequalities, given that its density is p(x, y) = ху. 0<…

A:

Q: (d) Consider the parallelepiped P in R³ whose adjacent sides are (0, 4, 0), (3, 0, 0) and (-1, 1,…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Let a sphere of radius r be cut by a plane, thereby forming a segment of height h. Show that the…

A: Sphere was cut at height h, radius of the circle at intersection of 2 cuts is r2-h2. Similarly…

Q: The volume of the solid E bounded by the cylinder x +y = 4, and the planes z = 1 and z = 2 in the…

A: The Given volume of the solid can be found using the triple integral and converting the rectangular…

Q: Show that the volume of the region bonded by the cone z = Vx² +y2 and the paraboloid z =x² +y is…

A:

Q: 5. Find the volume under the paraboloid = -a? – y?, and above the cone z = - p² + y?.

A:

Q: Interpret the volume below the surface z = x +y?, above the plane z = 0, and inside the cylinder x'…

A: The given problem is to find the volume of the region below the surface paraboloid z=x2+y2 above the…

Q: Find the volume of the 'ice-cream' that is bounded by x2 + y2 + z2 = 3 and the upper cone z? = 4x2 +…

A: Let's find.

Q: Find the area of the upper portion of the cylinder x² + z? = 1 that lies between the planes x = ±1/2…

A:

Q: If a plane region R located in the first quadrant is revolved about the x-axis, then the measure of…

A: False.

Q: ind the volume of the solid generated by revolving the region bounded by the graphs of the equations…

A: please refer to the image below.

Q: Evaluate SI, cos (2) dA ,where D is the region bounded by (x, y) D = {- sxs V24 ,0 < y< x²} V8n

A:

Q: Find the volume bounded by the paraboloid z = 1+ 3x? + 3y? and the plane z = 16 in the first octant.

A:

Q: Chapter 6, Review Exercises, Question 011 Find the volume of the solid whose base is the region…

A: We have to find the volume of the solid whose base is bounded by the two curves y2=x and y1=1x.…

Q: The volume of the parallelepiped is Volume = |a x b||c|| sin o| = |(a x b)- c| %3D %3D True False

A: We have to check either the volume of parallelepiped is volume=a×bcsinϕ=a×b·c or not.

Q: Find the mass of the lamina described by the inequalities, given that its density is p(x, y) = xy.…

A:

Q: Find the volume of the solid bounded by a lune with an area of 36t. The given angle is 25°. C D Q..…

A: To Find: the volume of spherical wedge bounded by lune with an area of 36π, and an angle of 25°.

Q: O Find the volume of solid in the first octant bounded by the co- ordinate planes, the planes x-3,…

A: We will find out the required volume of the solid in the first octant.

Q: 4) Calculate the volume of the solid E bounded by the parabolic cylinders 2 = y? – 5 et z = 4 – x².

A:

Q: A volume is described as follows: 1. the base is the region bounded by æ = - y? + 10y + 95 and æ =…

A:

Q: (3) Find the mass of the lamina described by the inequalities, given that its density p(x, y) = xy.

A: Given,             ρ(x, y)=xy and  x≥0, 3≤y≤3+9-x2

Q: Find the mass of the lamina described by the inequalities, given that its density is P(x, y) = xy.…

A:

Q: If we have a half-circle of radius r centered at 0, prove thatthe volume of the sphere resulting…

A:

Q: Let a sphere of radius r be cut by a plane, thereby forming a segment of height h. Show that the…

A:

Q: By rotating the line y = r about the x-axis, for x in the interval [0, h], and applying the surface…

A:

Q: A thin metal rod is oriented along the x-axis over the interval TT T If the density of. the rod is…

A: We will use integration to solve this

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.