What is the size of the space stretched by the set {x, x+x², x³, 1, x²}? a) 1 B) 4 C) 0 D) 34 E) 2

Q: Q. Assume that (R, T) is the usual Euclidean topological space. D= {(x, y) E R?, y = x² +3} C R.Then…

A: Solution: Here the subset of ℝ2 is D=x,y∈ℝ2,  y=x2+3 Now, The set D contains points x,y which…

Q: Let (R, d) be usual metric space, then Ris ot separable True False

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Q: Let (R. d) be discrete metric space, then Ris separ able O True O False

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Q: Determine las primeras derivadas parciales de la función en el punto (1,2) f(a, t) = V3x + 4t…

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Q: For the metric space (R, d) with d the usual Euclidean metric, which sets are in the topology T…

A: Wr Know that,"Let X = (-∞, ∞) and C consists of all intervals of the form (a,b).The arbitary union…

Q: Let AABC have incircle C(O,r), and let the points of tangency of C(0,r) with BC, AC, AB be D, E and…

A: Tangent is a line that just touches the figure.  Angle bisectors are those line segments that…

Q: 3. Conduct a formal proof to prove that the diagonals of an isosceles trapezoid are congruent.

A: Given: Consider the isosceles trapezoid ABCD shown below: AB=CD To prove: AC≅BD

Q: The quadrilateral ABCD is inseribed in the eircle centered at the point o. B(2y)°

A: Given that the quadrilateral ABCD is inscribed in the circle centred at the point O.

Q: What is the image of the vertical strip  {zϵC:−1<Re(z)<1} under e^z

A: A  conformal map is a one-one and onto analytic map. So, Re(z)=1 to a point. Here f1 is defined by,…

Q: 45. Prove: If the diagonals of a trapezoid are congru- ent, then it is an isosceles trapezoid.

A: Prove:- if the diagonals of a trapezoid are congruent, then it is an isosceless trapeziod Now given…

Q: A Find THE PERIMETER OF RHOMBUS ABCD WITH DIA GONALS AC AND BD INTERSECT AT poiNTE IF BD= 24 AND AC=…

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Q: 2. Use a paragraph, flow chart, or two-column proof to prove the angle congruency. Given: 2CXY =…

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Q: A(-3, 2), В(5, — 4), С(7, 7)

A: Consider the given points,  Now, prove that C is on the perpendicular bisector of segment…

Q: The dimension of the set W = {(2t – s, s, t) : s, t e R} of R is equal to: %3D

A: The dimension of the set W={(2t-s,s,t) : s,t ∈ R} of R3 x=2t-s y=s z=t (t,s) ∈ R   This can be…

Q: 1 Show that IS the separable me tre space (R, d), where el(x, y) = be-y/

A: Here we use basic real analysis

Q: In the convex quadrilaterial ABCD the diagonals are perpendicular on one another, and they are equal…

A: A convex quadilateral ABCD. Diagonals AC and BD are perpendicular to each other and equal in length.…

Q: Show that the closed interval [0, 1] and the unit circle S' = {(x, y)|x² + y² = 1} cannot be…

A: Suppose there exist a homeomorphism f:[0, ∞)-----&gt;R then restriction of f f|[0,∞)\{0} : [0,…

Q: A space has the line element, ds? = v*du? +u*dv² . Determine whether this space is flat or curved.

A: It is given that the line element ds2=v2du2+u2dv2. it is required to determine that whether this…

Q: D is the mid point of the side ВС of ДАВС;B ВЕ is perpendicular from В to the external bisector of…

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Q: What information is needed to prove that MN_ is a perpendicular bisector to AB_?

A: Using perpendicular bisector Thereom,

Q: Q2: In Euclidean metric space (R², 1. 1), is the set A = {(x, y): xy < 1} compact? giving the…

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Q: A. Let H be the set of all points (x, y) in R? such that x2 + 3y2 = 12. Show that H is a closed…

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Q: Convert the 2-column proof to a flowchart proof. Given: BD bisects ZADC and ZABC Prove: AABD = ACBD…

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Q: 3. Find the closure and interior of the set A = {(x, y): xy = 1} as a subset of R? (equipped with…

A: Closure and interior

Q: Is the set S= {I E R² | e21+2=2 >1} convex? %3D

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Q: we diveagena theosem to eveluate ty3j + XzK. dA ahose sethe boundary Of cube defined by

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Q: Write a complete proof to prove that the base angles of an Isosceles trapezold are congruent. Gven:…

A: Given, TIME is an isosceles trapezoid with IT ≅ ME

Q: Let (X, d) be a metric space and B = S(xo,r) be the open ball with centre at xo E X and radius r> 0.…

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Q: Let (C[a,b] .d) be the discrete metric space. Then Cla,b] is bounded. * False True

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Q: Let X be an uncountable set and let T = {U C X :U = Ø or U¢ is finite} %3D Then is topological space…

A: let X be an uncountable set and T=U⊑X : U=∅ or Uc is finite i.e cofinite topology on X. Then the…

Q: If U is homeomorphic to V and U is compact, then * O Vis compact V is complete V is connected O V is…

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Q: 2. Explain why there does not exist a measure Space (X,S, M) with the pro porty %3D

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Q: A prism with bases that are not aligned one directly above the other and lateral faces that are all…

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Q: Sydsaeter,Peter Hammond,Atle Selerstad Ar. 33 / 310| - 371% +| E O 2. Determine which of the…

A: See the attachment

Q: Define on R, the metric d defined by d(x, y) = |1+1리 1+ |y| Then (R, d) is not complete. True False

A: Given

Q: 1) Prove that T = { diag ( eia eip, eilxip)) | a,B E [0,27()} ís maximal torus in sul 3).

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Q: Prove that of all triangles having two given sides of lengths a and b, the one whose sides form a…

A: It is given that the length of two sides of a triangle is a and b, respectively. It is known that…

Q: Use Theorem 11.4.1 to show that the area of an equilateral triangle with sides of length s is given…

A: Consider the given:  Let the length of side of Equilateral triangle is “s”.

Q: Use Resolution to prove the following theorem schema: A (B C), BEA → B

A: if you find my answer helpful please put thumbs up. thank you. the required solution is given below…

Q: The volume of an isometric drawing can be found by counting the number of blocks in the drawing. O…

A: Given: isometric drawing in geometry

Q: uwhich regin [ind lies in first quadrant bounded afea in

A: We need to find area of the region lies in quadrant 1 bounded by v=3√u ,u axis and line v=u-2

Q: Prove that if c is a constructible number, then so is √|c|. (Hint:Consider the following semicircle…

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Q: What objects are topologically equivalent to a scissor (assume that the scissors' screwed parts are…

A: We are given a shape and asked to find a few topologically equivalent shapes.

Q: For normal linear spaces X, Y, prove that BL (X, Y) is complete if Y is complete.

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Q: 2. Does d(x, y)= (x-y)? define a metric on the set of all real numbers?

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Q: Derive the frenet frame, curvature and torison of the binormal indicatrix of hypocycloid?

A: We need to Derive the fernet frame, curvature and torsion o the binormal indicatrix of hypocycloid.

Q: Points must be collinear in order to use the segment addition postulate. O True O False

A: solution = point must be collinear in segment addition postulate .this addition apply on line…

Q: Give the definition of a separable metric space (S, d). Show that the metric space (IR, d), where…

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Q: Let AABC have incircle C(O,r), and let the points of tangency of C(O,r) with BC , AC, AB be D, E and…

A: Given a triangle ABC, in which a circle is inscribed with center at O and radius r as shown in the…