3. Let S = {(y, z) | 2y - 4z >16, 6y + 4z > 24, y > 0, z > 0} a. Sketch the set S (Show working for points)  b. Describe its boundary points  Determine with explanation the following c. Is the set S open or closed?  d. Is the set S bounded, convex and compact?

Q: ercise 6.67. Let E be a subset of R having at least two points. Pro- owing are equivalent:

A:

Q: Which of the following sets are well-ordered. Justify youranswer carefully.A.{x:xEZ, X…

A: A set of numbers is well ordered when each of its nonempty subsets has a minimum element.

Q: Define the partially ordered set (N",<) as follows: x < y if Xi < Yi for all 1<i<n. For example, (2,…

A:

Q: Q1:A) Let X = R and r be the usual topology on R.If Y-[4,6). 1) Determine the open ,closed ,open and…

A: Given that, X=Rand τ is usual topology on R Given that Y=[4,6). 1) 4,5 Is open in the given topology…

Q: Let A = the set of straight lines in the xy-plane. Let a L b mean “line a is parallel to line 6”.…

A:

Q: Show that the sets [0,1] and (0, 1) are equinumerous 7.

A:

Q: 3. Properties of Affine Sets. Suppose C c R" is an affine set. (a) Consider K points x1,. ...., Xk E…

A:

Q: (E, Q4: state and prove L is a normed space ? e a ne. Vila a convex set.

A:

Q: Consider the set C = {x : Ax < b}, A e Rm×n and be R". Describe the set7 of feasible directions d at…

A: Given: The set C=x:Ax≤b, A∈ℝm×n and b∈ℝm   To describe: The set of feasible directions d at a point…

Q: 5. Prove that the property of a space having an isolated point is a topological property. 6. For any…

A: Sol

Q: If c eR and S is a set, define cS be a convex set and suppose c > 0 and d > 0. Prove that cS + dS =…

A:

Q: Determine the dimension of the span of each set. 6 3 12 - A = span ({0}) 2 - -1 4 20 10 40 dim (A) =…

A: Here sets A,B and C are given. We find dim(A),dim(B) and dim(C).

Q: d) Suppose X = {1,2, 3} and Y = {5,6}. The number of elements of the set P(X× Y) =

A: Elements in X = 3. Elements in Y = 2 Elements in X × Y = 3 × 2 = 6

Q: Exercise 2.29. Pick several different subsets of R, and for each one, find its interior and boundary…

A: Suppose X,I is a topological space and A⊆X. Interior of A, Int(A) is defined as the union of all…

Q: 1. Determine whether the vectes (,2,3), (3,3,1), 3,1,2) in R?. indefendnt are

A:

Q: Q. Let A = {(x, y), y = x, x E Z,y e R}, Then A is a. connected and pathwise connected space. b.…

A: d. neither connected nor pathwise connected space.

Q: Solve number 1

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Q: F and Hare sets of real numbers defined as follows. F = {ww≤ 4} H = {w|w>5} Write FUH and FnH using…

A: We can find the union and intersection of sets in the below steps.

Q: Express the characteristics of the following sets of points, in terms of: closed or open, connected…

A: The set of points {z∈C: |arg (z)|&lt;(π/2)} is:   Closed: The set includes all complex numbers…

Q: 11. Identity the vertex of each graph. Determine if it is a maximum or a minimum. (a) b) ₁ c) f AVA…

A: To solve the following problem of finding the vertex and categorizing them as maximum or minimum.

Q: Find an eguaton for the set of all points (a sy, z) equiditant fom point (1,0,2) and

A:

Q: Suppose that you have two sets, and you know that both sets are convex. Proven that the intersection…

A: convex set is a set of points such that, given any two points x,y in that set, the straight line…

Q: 3. Use the definition of convex sets to answer the following: Show that if the sets S and T are…

A:

Q: Show that the set given in the image below is non convex. Please prove the result mathematically…

A: A set is said to be convex if for any two points in the set the line segment joining those points is…

Q: Let R = Zg, and let N = R³. Determine whether or not X = {(4, 5, 4), (4, 5, 2), (2, 2, 3)} is a free…

A: It is given that,  R = ℤ8  and  N = R3. We have to determine that whether the set,  X = 4, 5, 4, 4,…

Q: 1) Describe and shade the portion of the x-y plane which is the domain and represent the domain and…

A: The domain of a function is the range of values that can be input in the function as the value of…

Q: QUESTION 6. L Consider the following relation R on the set A = {1,2,3,4,5} R = {(1, 1), (2, 2),…

A:

Q: If minimum observation is 46.8 and maximum observation is 192.4, number of classes is 6, then the…

A:

Q: Prove that the boundary points of an open interval (a, b) CR are the points a and b.

A: A point a∈ℝ is said to be boundary point of a set A⊂ℝ, if Ba,r∩A≠∅ and Ba,r∩Ac≠∅ for every…

Q: 5 7. Let X,Y be two sets. Denote F(X,Y) the set of all funtions from X to Y. Let A, B C X such that…

A:

Q: erify that (u,,u2} is an orthogonal set, and then find the orthogonal projection of y onto Span…

A:

Q: Describe the set {TER²: doo (r,(0, 0)) = 1}.

A: To Describe: the set {x∈ℝ2: d∞(x,(0,0))=1}.

Q: Let ℓ be a line and let H be one of the half-planes bounded by ℓ. Prove that H ∪ ℓ is a convex set.

A: To prove that H ∪ ℓ is a convex set, we need to show that for any two points P and Q in H ∪ ℓ, the…

Q: A and B be two sets, each one of them having a minimum. Assume that A n B is not ty. Then An B has a…

A:

Q: pls explain to me step by step and pls write clearly. thanks

A: To verify that the contraction mapping condition is NOT satisfied using the given functions f(t) and…

Q: c) given an arbitrary convex function wcx) :R"→tR, prove fhat is a convex set.

A:

Q: 2. Let a,, az,.., a, be numbers. Show that there is a single number r such that foxo: (-a,) + (z –…

A: Solving

Q: Suppose Ak,., A2 , A1 and B are points on R" Prove that if {A1 , A2, .. Ak} is an independent linear…

A: proof :- A1,A2,...Ak are linear independent set ⇒c1A1+c2A2,...ckAk=0  where c1=c2=...=ck=0…

Q: Q. Let A = {(x, y), y = x2, x E Z, y E R}, Then A is a. connected and pathwise connected space. b.…

A: Neither connect nor path connect

Q: 3. Determine if the set Q n (0,1) is open, closed or neither. What is the boundary of the set? Also…

A: 1. Q ∩ (0,1) is neither open nor closed. 2. For the set Q ∩ (0,1), the boundary includes the points…

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.