Let W = Span{u} where u = . Let y = find the distance from y to W a) v20 b) 2 c) V3 d) None of these O b o d

Q: Show that the volume V of a parallelepiped having u, v, and w as adjacent edges is V = ∣u ∙ (v ×…

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Q: Let C be the positively oriented circle r? + y? =1. Use Green's Theorem to evaluate the line…

A: Just I have used the Green's theorem to change the line integral into double integral and then by…

Q: GIVEN: AB||CD & E BC||DE & C is the midpoint of AE PROVE: ДАВС3 ДСDE

A: According to bartleby guidelines we have to answer only first question please upload the question…

Q: Let C be the positively oriented circle x? + y? = 1. Use Green's Theorem to evaluate the line…

A: Compare the integral ∫C19ydx+20xdy with ∫CMdx+Ndy to obtain M=19yN=20x Consider…

Q: If UV bisects XY at point W, which statements must be true? Select all the true statements. (A UW E…

A: Given that U̅̅V̅̅  bisects X̅̅Y̅̅at point W U̅̅V̅̅ bisects X̅̅Y̅̅ means U̅̅V̅̅ divide line XY in two…

Q: Evaluate o y*dz – x*dy, where C is the boundary of the region between the circles z? + y? = 9 and…

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Q: Given R,(AXYZ) = Ax'Y'Z', do AX'Y'Z' and DAXYZ have equal perimeters? Explain. Z' A is a rigid…

A: This is the reflection of ∆XYZ on the line "n" to get the ∆X'Y'Z'.

Q: O is the midpoint of PC. P is located at (11,12) and O is located at (4,6). What is the location of…

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Q: Let d : R? x R? – R, defined as d (x, y) = |21| wher e x = (x1, 2), y = (y1, 42), then d is metric…

A: The objective is to find the correct options.

Q: Evaluate ſſ, Vy² – x² dA where boundary of R is the parallelogram bounded by the four lines

A: In this question, we evaluate the double integral by using the change of variable. The region is…

Q: Let r < R. Revolving a circle of radius r, (x – R)² + y² = r², around the y-axis gives a donut…

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Q: Use Green's Theorem to evaluate (V1+r) dr+2ry dy, where C is the triangle with vertices (0, 0),…

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Q: In RST, U is the Centroid. If SQ=6, find SU and UQ W R

A: Given query is to find SQ and UQ.

Q: In Exercises 23 to 25, complete a paragraph proof. 23. Given: Tangent AB to ©0 at point B mZA = mZB…

A: Given: AB¯ is tangent to the circle with center O at point B. m∠A=m∠B To prove: mBD^=2·mBC^

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

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

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: |(p-q)(r-s) bc-ad

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Q: WX || ZY and Zs Z and Y are supplementary WXYZ is a parallelogram Given: Prove: W Y

A: It is given that,  WX ¯|| ZY¯  and ∠Z and ∠Y are supplementary To prove :- WXYZ is a parallelogram

Q: Consider the set A = {(u, v) E R? : u² + v² < 3} %3D Then, the area of the surface o : A R3 defined…

A: Introduction: Let us suppose that a surface is σ(u, v), then the area of this surface is given by,…

Q: Find the measure of an angle between 0 and 2 π that is coterminal with m(0) = 7 T A 4 B D TT 4 5 f 4…

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Q: Evaluate ry dr +r dy, where C is the positively oriented triangle enclosed by the lines y = I=0 and…

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Q: Find a formula for the distance from the point P(x, y, z) to the (a) xy-plane (b) yz-plane (c)…

A: Distance between two points x1, y1, z1 and x2, y2, z2 is given by x2-x12+y2-y12+z2-z12.

Q: You are given that WY XZ. What additional piece of information allows you to prove that AWYZ AXZY? W…

A: Given Data: Given congruent sides: WY≅XZ The figure of triangle XYZ and triangle WYZ is shown in the…

Q: Let C be the positively oriented circle x? + y? = 1. Use Green's Theorem to evaluate the line…

A: Given : C is a positively oriented circle x2+y2=1 We have to evaluate the line integral…

Q: What additional point is on plane RST? O R

A: Topic:- geometry

Q: Use Stoke 's Theorem to evaluate [ . dr, where v = y²i + xyj + xzk, and c is the bounding curve of…

A: We have to solve the given problem by using stokes theorem.

Q: If ABCD EFGH, are all corresponding parts congruent? Explain. H. D E F A ..... Because ABCD EFGH,…

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Q: Let W= Span(u) where u = find the distance from y to W V13 b) V3 13

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Q: Evaluate the line integral ſe ry²ds, where C is three quarters of the circle a² +y? = 1, oriented…

A: C is the three quarters of the circle x2+y2=1, oriented counterclockwise. The parametric equation of…

Q: 20. A uniform wire is bent into the form of a triangle with sides a, b, Prove that the distances of…

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Q: Based on the trapezoid shown in the standard (x, y) coordinate plane above, what is the midpoint of…

A: From the graph, it is clear that B is at (-1,2) and D is at (5,-2) Now, the midpoint formula gives…

Q: E If O is the midpoint of El and JM, what postulate or theorem proves that AEMO = AIJO? M O ssS…

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Q: Verify Green's theorem Where C is the boundary of the triangle formed by x=3 , y=0 , x2= 3y

A: Verify Green's theorem Where C is the boundary of the triangle formed by x=3 , y=0 , x2= 3y

Q: Given: AD L FB at A. AE LAC at A. 32 Prove: m 1 = mZ3 1IF a Prove that angle DAR and Angle FAC are…

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Q: Let W = Span{u} where u -2. Let y = |1, find the distance from y to W L3]

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Q: _Show that the following are metric on R": d,(x,y) max, isn Ixi - vil : d,(x,y) E X-Yil.

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Q: F(x,y, z) = xi+ yj, and S is hemisphere z = V1– a² – y?

A: In this question, we find the flux across the surface by using a surface integral. flux=∫∫sF.Nds

Q: Verify that (S, d) is a metric space. 10.2 Prove that d(x, y) < d'(x, y)s/2 d(x, y) for all points'…

A: To prove dx,y≤d'x,y≤2dx,y for all points x,y∈ℝ×ℝ where d is the usual metric and d' is the…

Q: . Let F(x, y, z) = (x³, y³, z³). Use Gauss's theorem to find ffsF dS if S is the sphere x? + y? + 22…

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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: Find the envelope of the plane 1, C + u + a + и b + u mere u is the parameter.

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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: (|F.dS, F = xz+ y° z,S is the hemisphere x² + y² +z? =36, z > 0.

A: Find double integration F•ds

Q: 4. JK, KL, and LJ are all tangent to cirele O1 JA = 13, AL = 12, and CK = 9. Find the perimeter of…

A: Triangles

Q: Calculate both sides of Green's Theorem when F = [-x²y, xy²] and y positively oriented circle x? +…

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Q: the dis fance from Pla.y,z) to the origion o d and fe clis fance from Pto ACo.003) is de .writeian…

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Q: The volume of the parallelepiped that has u, v, was adjacent edges u = 3i +j+ 2k , v = 4i + 5j + k,…

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Q: Show that the sphere of radius 5, X(u, v) = (u, v, v25 – u? – v²) is regular.

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Q: Use Gauss's D.T. to evaluate SSA.ds where Ã=x'i+y°§+7f qud S is the , surdace of the sphere x+j+z²=…

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.