7. In ABCD, AC and BD divide each other in half at E. (a) Prove that ZDBC ZBDA. (b) Prove that ADBC ABDA.

Q: Verify that cos kx is a rolulion Also, stafe what kind of DE is the DE above :

A: This question is about solving differential equations.

Q: 1. Let U2 = 2. fui, 4.} is an orthonmal basa fo IR Show that

A: The set of vectors v1,v2,…,vn of a vector space V are said to be an orthonormal set of vectors if…

Q: Show that for A symmetric inf. = Amin(A).

A:

Q: Given 21 = Z3 Prove jk 13 2.

A: Given,  ∠1≅∠3 To prove  j∥k

Q: (b) En=1 m

A:

Q: If acosα+bcosβ+csinγ=0 and asinα+bsinβ+ccosγ=0, then prove that…

A: Given: acosα+bcosβ+csinγ=0 and asinα+bsinβ+ccosγ=0

Q: 2. Show that c(x, t) = solves 1 ac(x, t) 2 ax ac(x, 1) ar

A:

Q: 12, GIVEN: JKI KT, ET 1 KT, KV TL, IL EV. PROVE: AJKL AETV. T.

A:

Q: now tha 4.31) and that cov(y-ΣΣ) Σ- as in 4.32). – E,. x) = ΣΣΣ as in (4.32). %3D

A: E(y-∑yx∑xxx) = E(y)-∑yx∑xxE(x) = μy-∑yx∑xx μx AS E(y) = μy E(x)=μx ∑yx is the covariance marix…

Q: Suppose RC 1. prove that if B has a sup b, then A(U(B))

A: Given:- Suppose B⊂A and to be proved if B has a Sup b, then λ(ϑ(B))∩ϑ(B)=b

Q: 1. Identify which theorem will prove that ZEDC = ZDEC= ZECD if DE EC = CD. A,

A: Given problem:-

Q: Show that the series 3. + + 4 To t (-1) Lonverges absolutely.

A:

Q: Find the reductión Bormula Bor d x In (a+bshmx)"

A:

Q: alue of the pur C: |z| = (:-1)(z-

A:

Q: Prove that on average, permutations of length n have H, cycles, where Hn i=1

A:

Q: 4) For A = ajax + azāy + azaz , B = b,ax + b2ay + bzaz, show that A.B cos 0 = A.AVB.B

A:

Q: 4. In the diagram below, Ĝl is parallel to NT, and IN intersects GT at A. Prove: AGIA~ATNA

A: Given :GI is parallel to NT

Q: (8.20 ds: Find the tayLor seri's expen sian of In Cxri) about XozO

A:

Q: 7, Prove the fallo aing theorem 18 (of sizes Such that A and B ere madrices siers addition is…

A:

Q: (- For all asb,C EZ,prove the folloNing (i)ala,1la, andal0; (ii)0la if and only if a=0; (iit)alb ond…

A:

Q: See picture below.

A: Consider a function f(x) such that:

Q: Prove that on average, permutations of length n have H, cycles, where Σ Hn i=1

A: We will take an arbitrary set containing n elements and observe the required permutations.

Q: Prove that, IXI<a Rf and If -aL X Z a

A:

Q: *10. Suppose AB = CD, AB 1 BC, and CD I BC. (a) Why must AC BD? (What congruence criterion…

A:

Q: 0, 2 is defined by A natural cubic spline S on 5. So()12x - 0 if 1 (1) S(r)2b(x1)c(x - 1)2d(x - 1)…

A: 5.Note that, the natural cubic spline must satisfy the conditions

Q: Q: Prove that tim x"- a" %3D

A: we have to find the limit of the expression

Q: Is there a km. lenRit 3 Why 3 kM. X4-2x If there is a konft prove 9t by using the (E-8) defnti9on of…

A:

Q: 1. Do not use a theorem to find the ff. Z if yz? + z = 5xy – 1. %3D

A: In the multivariable function, if we have to find the partial derivative of one variable with…

Q: Given: HT || SF, LH = LS and HT SF Prove: AHOT ASTF

A:

Q: 12) Show that D- ldi-dal between is shortest distance a x+ by + e2 of i ancd ax +by +Cz = dz?

A:

Q: Use the diagram to prove that ACAS ATAS. A T. Given: CS = ST and mzCAS mzTAS= 90 Prove: ACAS= ATAS

A: Given : CS ≅ STm∠CAS = m∠TAS = 90°

Q: cos (o,+ O>)+ ì s:in (8,+Ə.)) Prove this kW- Mon 183O

A:

Q: QUESTION 2 Ustng De Molure's Theorem, evaluate 12 3 -itl ard leave four angwer in the form Z=a+ ib

A: Topic:- complex number

Q: In ALMN, LN is extended through point N to point 0, mZMNO = (5x – 13)°- mZNLM = (x – 4)°, and m/LMN…

A: Solution-

Q: 2- (a) Using [X, P] = ih, show that [X, PJ = 2ih& and [&, Þ³1= 2ihP. (b) Show that [, p2 = 2in(in +…

A:

Q: Prove the following: 7. Given: PS bisects ZRST, 2SP = 3SQ, 2ST = 3SR T. Prove: ASTP~ASRQ

A: topic - similar triangles

Q: Use the given information to state the third congruence that is needed to prove AMN0=A RST by the…

A: The AAS rule states If two angles and a non-included side of one triangle are equal to two angles…

Q: AB is tangent te OC at point A. mod

A: Given : AB is tangent to the circle at the point A. ∠ABC = 37°

Q: Prove the following: %3D

A:

Q: A.o/ prove haT cosh(zi42e)=Coshzcoshai+sinh2,Suhze

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: 2

A:

Q: Question 2: Show that the set S = {rVT + V2:rE Q) is dense in IR. Explain and show your work.

A:

Q: 2.2 Find upper bound of zp (z- 3i)3 + 1 where C is the circle |z - 3i = 4. 2.3 Use the Cauchy…

A:

Q: By using Caushy Rieman prove that (2) and (3) (2) 4ca) = e (3) .w prove Thot()-

A: (a)

Q: Let flx)= a cose + 3 Sinse with (o,f to)), (,2) and (T, 2 ). Use Muller's method to find a quachatic…

A:

Q: Suppose that fo sf,:X-gy and g,-3 YoZ Prove that (Hint : First use ce) to show that gfe g,, and then…

A:

Q: 4- Prove Sca) < ela) and Conclude if ea is la-ea small Compared to lal then: ela) S(a) lal

A: