Blank 1 is movement of a side of a preimage parallel to that side with respect to one other fixed image.

Q: get an 6Usc Thesrmn to show that -x gra) = 2 has a unique haed %3D point on

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

Q: a. Show that Ø, R E T. (by definition of Topology)

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Q: If A = x a, – zy a,, evaluate § A · dī around the path L defined by 0 < x < 2,0 < y < 1 as shown in…

A: Stroke's theorem:         It is also known as Generalized stroke's theorem. It states that the…

Q: the basis of P2 cons tive to B.

A: Introduction: For some n, consider V to be a subspace of Rn. A basis for V is a collection of…

Q: 2- If ihe Velume is equal to Zevo, then the all yectors line in The Some plane. a.T b. F

A: Concept: Volume of an object is in 3 dimentional plane. If any of the dimentions is equal to zero,…

Q: If L is a line through 0 and if ŷ is the orthogonal projection of y onto L, then || ŷ|| gives the…

A: To state whether the given statement is true or false :  By definition, we know that, if L is a line…

Q: If the conditions of the fixed point theorem are not satisfied, then there exist no unique fixed…

A: I will use the condition of fixed point theorem to answer this question.

Q: 5) Let à = psin(4)ū, + p² Ug Evaluate f Ã. dl given that L is the contour of the following figure.

A: Let A→=ρsinϕu→ρ+ρ2u→ϕ we have to evaluate ∮A→.dl→

Q: is absolutely and uniformly conyergent for all vlues of x an t in the circle 121 <B-¹

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Q: Show that S {x€R* |2,• 24. • O} is/isn't %3D convex

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Q: det(A) Show that det(AB-') = %3D det(B)

A: Consider, Let A and B be the two n×n matrix, Now Consider, detAB-1 We know that the theorem, Let A…

Q: Find the set of ordered pairs (T0, Yo) for which Picard's Theorem guarantees that the IVP y ry %3D y…

A: Given,            y'=xyx+y, y(x0)=y0

Q: I Find for each of the following. keving your anwer in terms of the parameter . 2r, y- 2

A: We have to find dydx for the following...

Q: (4b) Is Tâ onto? How do we know?

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Q: The final result of a glide reflection is called a preimage. O True O False

A: The new figure created by a transformation(translation and reflection) is called the image. The…

Q: Question 12 Given u=21+31 and V51+2), ting the projection of u onto v.

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Q: Show the following se ts Convex ? are for ast sh} k k-1 PCt)=a,+aztr...a t

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Q: If the conditions of the fixed point theorem are not satisfied, then there exist no unique fixed…

A: The ciric theorem states that, Let X be a complete metric space, and let f : X → X be such that,…

Q: QUESTION 9 Suppose metric space X is not path-wise connected then X is not connected. True False

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Q: Show that the intervals S [1,3] and T =[2,8] are equinumerous by finding a. bijection between them.

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Q: Sketch the set of points satisfying: |z - 1 + 2i| = |z + 3 + i|

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Q: ome 9/ for Find The domain Dp and Rag Re De fallowing fandinse,

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Q: 1. In the figure, E is the midpoint of (NS)¯and LSzZN. Which postulate justifies that APES = A MEN?…

A: Introduction: When two parallel lines are intersected by a transversal, the pair of angles formed on…

Q: (c) A line in R² not through the origin ax + by sC #0 then &H. :, t is not a ad Umecepsang but…

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Q: Question # 01. Consder z= {acbos a-b =0; S2 Interpet that eguivale nce relation. ~ 18 is

A: That's easy, just show that this relation is reflexive, symmetric and transitive.

Q: P(5,3) Sinh (폼+북) x +1oydy (6xdx +10ydy 5 C0,0)

A: To show: The line integral is independent of the path. Given integral:…

Q: Let ā = (- 4, - 5) and b (- 5, 0). Find the projection of b onto ä. Round your answer to at least 3…

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Q: 1. Prove that given a line € and a point P not on e, there exists a line through P perpendicular to…

A: Explanation of the answer is as follows

Q: Find image of a and preimage of b T(v1, v2, v3) = (4v2 – v1, 4v1 + 5v2) v = (2, -3, -1) , w =…

A: Given, T(v1, v2 , v3 ) = (4v2 – v1 , 4v1 + 5v2) v = (2, -3, -1) , w = (3, 9)

Q: Let linear tiansformation I(4)=(2,32and Tls0) =(3B,2) Cheek whether T? exists or noti2 Find T. E=R…

A: The objective is to check whether inverse of T exists or not and find it.

Q: (a, b) is measurable. ulgn O ihi O

A: I will use the definition of measurable set.

Q: IfL is a line through 0 and if ŷ is the orthogonal projection of y onto L, then || §|| gives the…

A: Given statement is

Q: Which of the following DEs are first order linear DEs?

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Q: graph'the Sorution to the follow imy inginequratityon animber line nur (x-2) (x+5) z O

A: Solving the problem by doing the graph.

Q: Let Á = ry?a, + x³yzay, Evaluate A. dl along the path y = x2 from a(0,0,2) to b(3,9,2) Select one: O…

A: We will find out the required value.

Q: Convert the following problenm to the dual fom Ond set the talaleau up minimize Where 42=0 2>こ○…

A: Given the LPP          Minimize C=12x+4y+17z          subject to 3x-5y+12z≥17…

Q: In a reflection across line L, any point P on line L maps to P' where ______________. Any point A…

A: Rule of reflection- distance of image and object from mirror ( line of reflection ) is always equal.…

Q: 4. Select the sequence of transformations that maps triangle LAP onto triangle L'A'P'. Ay P'

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Q: 50 6 7 -> OURSTUDYBEGINS |- Find the dipeerential giren y:(It t)'

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Q: Let A = psin ø a,+p a,. Evaluate PA dl given that L is the path shown in the figure. Verify your…

A: It is given that, A=ρsinϕ aρ+ρ3 aϕ   According to stokes, theorem (also called Curl theorem),…

Q: - Consider noncoplanar points A, B, C, and D. Using three points at a time (such as A, B, and C),…

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Q: Which of the following transformations results in a congruent preimage and image for a figure?

A: Given query is to find which transformation given congruent preimage and image for a figure.

Q: IShow that the intervals S =[-2,4] and T =[1,5] are equinumerous by finding bijection between them.…

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Q: Show that F. dr is independent of its path, given that

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Q: Show that (t) =| 2 3t is the fundar

A: Given that,            y'=A(t)y                          ...(1) where                A(t)=-1t1-6t23t

Q: Prove that any ball (open or closed or half open) in R³ is path connected.

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Q: is a cycle (closed walk) of length 2. O True O False

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Q: Questlon 1 of 10 Two or more points are if they lie on the same line. O A. complementary O B.…

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