Consider the IVP y'-1+y', y(0)=0 on the region D= {(t, y): rS100, y|s1}. Then, the interval in which the unique solution to the IVP is guaranteed to exist is a) |ts100 b) ts100 c) |t|50.5 d) ts0.5

Q: Verify Green's Theorem by evaluating both integrals dk + x° dy = /. / dA ду for the given path. C:…

A:

Q: Determine a region of the xy-plane for which the DE (y- x) y' = y+ xwill have a unique solution…

A: Consider a differential equation y'=F(x,y), y(x0)=y0. Then there exist a unique solution to this…

Q: 8. Evaluate the double integral S Sp y³dA where A is the triangular region with vertices (0, 2),…

A:

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

A: Given

Q: A region R is bounded by the graphs of  y=0.8 (x)^1/2 and y=0.8x.  Find the moments Mx and My of R…

A: Given,

Q: The double integral 2xy³dA over the rectangular region R {(x, y) E R“, 0 < xS 4 and – 1 S y< 0} is…

A: The double integral ∬Rfx, ydA can be written as ∬Rfx, ydxdy. We have given the rectangular region as…

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: 39.) The solid bounded by the cylinder x+y² = 9 and the planes z= 0 and z = 3 - x. 40

A:

Q: Sketch the region of integration and evaluate the integral∫∫∫R xy dV where R is the solid…

A: Given, ∫∫∫RxydV Where R is the solid tetrahedron with vertices (2,0,0),(3,3,0),(3,3,3)and (0,3,0)

Q: Use Green's Theorem to evaluate the line integral Icov for the given path. (y-x) dx + (2x - y) dy C:…

A:

Q: A flux is given by F = x²y³ i – xy j. Verify the Green's theorem for the region bounded by the…

A:

Q: State the double integral f S (x² – y²) dæ dy where R is R the region in bounded by |æ| + |y| < 9…

A:

Q: Integrate f(x, y, z) = x over the region in the first octant (x 2 0, y 2 0, z 2 0) above z = y2 and…

A: Given that,

Q: 16. By inspection, a simply-connected and continuous region R A. has no holes and is closed. B. has…

A: Introduction: The application of connected regions is very significant in different fields of…

Q: Evaluate the integral. SSS_* √x² + z² av E where E is the region of integration bounded by the…

A: To solve this put x=rcos(theta) And z=rsin(theta)

Q: Evaluate the triple integral∭E xy dV where E is the solid tetrahedon with vertices…

A: Given Data : Triple Integral ∬∫ExydV and E is the solid tetrahedron with vertices 0,0,0,…

Q: Use Green's Theorem to evaluate the line integral Scox (y - x) dx + (2x - y) dy for the given path.…

A: The given integral is                                    ∫Cy-xdx+(2x-y)dy for the given path.…

Q: integrate ƒ over the given region. ƒ(x, y) = x2 + y2 over the triangular region with vertices (0,…

A: Given: f(x,y)=x2+y2 over the triangular region with vertices (0,0), (1,0),(0,1)

Q: Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

A:

Q: y + x -0,x-1 and y=0,y-1-xto T.of u- dydx in terms of (u)and (v) given that: Region bounded R: x…

A: Evaluate, ∬Ry+x-4x-2y2-412dydx                        …1 Region R: x=0, x=1 and y=0, y=1-x u=2y+2x2…

Q: 1. Compute fSSp(z+1)°dV where E is the region lying inside the sphere x² +y² + 22 = 1 of radius 1…

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: Calculate the double integral S SR (x2 + 2y) dA, where Ris the triangular region with vertices…

A:

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

A:

Q: Let R be the region in the half plane x 2 0 bounded by the curves y = -5x +5 y = x - 1 x = 0 Compute…

A:

Q: Use Green's Theorem to evaluate the line integral (y - x) dx + (2x - y) dy for the given path. C:…

A:

Q: Prove that: 1- Cos (2) dxdy (¹) where R the region bounded by x+y=1,x=0.y=0

A: Given integral I=∫∫Rcosx-yx+ydxdy Where R is bounded by x+y=1x=0y=0

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: 10- Evaluate JJI where E is the region that lies inside the cylinder Vx2 + y?dV E x? + y? = = 16 and…

A: Here we use polar coordinate and Jacobian .

Q: Integrate f(x, y, z) = x over the region in the first octant bounded above by z = 8 - 2x 2 - y2 and…

A: Given that, z=8-2x2-y2        ...(1)z=y2              ...(2)

Q: Use Green's Theorem to evaluate the line integral (y – x) dx + (2x - y) dy for the given path. C:…

A: Use greens theorem

Q: 5. Evaluate the double integral Sſpx² + xy dxdy where D is the regiom bounded by y = x², x – axis…

A: We have to evaluate the double integral ∫∫Dx2+xy dxdy  , where D is the region  We first sketch the…

Q: Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

A: Line integration by using Greens theorem

Q: Let I = S+0)dpdød0. Then the region of integration of I is presented by:

A:

Q: The centroid of the region bounded by sin x < y< cosx, and 0<x<7/4 is, TV2-4 b) 1 1 a) 4(42 +1) 4(v2…

A:

Q: Use Green's Theorem to evaluate the line integral $. (x2-y2)dx + (2y -x)dy where C consists of the…

A: We will plot the region bounded by two given curves and find the integral using Greens theorem

Q: SSR (r + y)2 dA, where R is the region bounded by the limaçon r = 2 + cos 0

A:

Q: Use Green's theorem to evaluate the integral: 6(-x²y)dx + xy°dy where C is the boundary of the…

A: Let C be a positively oriented, piecewise smooth, simple, closed curve and let D be the region…

Q: A region R is bounded by the graphs of y=0.5 Vx and y=0.5x. Find the moments Mx and My of R about…

A:

Q: You are rotating the region bounded by y 2 = x, y = 1, and x = 0 about the line x = 1. Set up the…

A: The graph formed After rotation it will look like Take the elementary element as

Q: 3. Determine the valume of the solid ebtained by rotating the region bounded by y=x² and x =y2 about…

A:

Q: Evaluate the triple integral III xy dV where E is the solid tetrahedon with vertices (0, 0, 0),…

A: The given integral is, ∫∫∫E xydV Here E is the solid tetrahedron with vertices O0,0,0, A10,0,0,…

Q: Exercise 6. Evaluate the integral ffn ldA, where D is the region bounded by the lines y = 2x + 5, y…

A: Let us considre the given integral I=∫R∫f(x,y)dxdy Transform the variable to x=f(u,v)y=g(u,v) The…

Q: Let R be the region in the half plane x 20 bounded by the curves y = -5x + 5 y = x2 – 1 x = 0…

A:

Q: Use Green's Theorem to evaluate the line integral S (y-x) dx + (2x - y) dy for the given path. X C:…

A: Green's theorem: ∫CMdx+Ndy=∫∫R∂N∂x-∂M∂ydA   Given: I=∫Cy-xdx+2x-ydy and C: y=x and y=x2-2x It means…

Q: Use Green's Theorem to evaluate the line integral Jo for the given path. C: boundary of the region…

A:

Q: 3, Let R be the of: y: sinx region endlosed bu the grophs n enclosed by and 1 x70 . Groph R and…

A:

Q: State the double integral f S (x2 – y²) dx dy where R is the region in bounded by Jæ| + |y| < 11…

A:

Q: 10. The solid bounded by y = 4, y – x = 1, z = x², and z = = 4.

A:

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.