4 Let A, B, and C be three points and prove that the area of the iangle AABC is given by 1 Area =V|AB|P|AĊ|? – |AB · AT|?.

Q: het c denate the tine segment nd z=1. Show that zp

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Q: Use calculus to find the area A of the triangle with the given vertices. (0, 0), (3, 2), (1,6) A =

A: Given, The vertices of the triangle are (0, 0), (3, 2), (1,6)Equation of the line joining (0,0) and…

Q: 21) Find the area of a triangle fosmed from the twovectors a = L'+2j-k-.

A: Given, a ⇀=i+2j-kb⇀ =2i-j+4k

Q: ?, R(A)IN(A*)

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Q: Let a < c < b and s(x) be a cubic spline with a single node c. Suppose s(x) = 0 on [a, c] Show that…

A: Cubic Interpolation Polynomial : Let  for  be the points satisfying the function . The cubic spline…

Q: (d) Determine all possible points P that lie on the line passing through B and D, so that the area…

A:

Q: B is the midpoint of AC BD 1 AC Given: B Prove: AADC is isosceles A

A: Given The B is the midpoint of AC¯  and BD¯⊥AC¯ .

Q: A B What other information is needed to prove AABCY ACDA by the HL Theorem?

A: Given : ∆ABC≅∆CDA

Q: AABC has inradius r, altitudes of length ha, hb, hc, and exradii ra, b, c. 1 1 1 + r (a) Prove that…

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Q: State and prove Green's identity in an enclosed Region Q

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Q: (c) Compute the distance in AU between the points (x,0) = (1.24,0) and (1.24, 7)

A: Given: The coordinate transformation, x=Rsinhχsinθcosϕ y=Rsinhχsinθsinϕ z=Rcoshχcosθ The plane…

Q: 6. Let ABCD be a trapezoid with bases BC and AD. A line passing through the vertex C and parallel to…

A: Given, ABCD be a  trapezoid with bases BC and AD.

Q: 2. Prove that there are no rectangles in S2. More precisely, prove that if A, B, C, D E S² form a…

A: Given: ∠A=∠B=∠C=∠D=π2

Q: 1) Prove that A is uniform pentagon and B is a half of a circle, also determine the areas of A & B.…

A: Here I am attaching image so that you understand each and every step. solutiongiven data (Let…

Q: Find the values of a, b, c, d, e, f, g and h such that ax, S(x) = { 6(x – 2)³ + c(x – 2)² + d(x – 2)…

A: GivenS(x)=ax3,0≤x≤2b(x-2)3+c(x-2)2+d(x-2)+e,2≤x≤3f(x-3)3+g(x-3)+h,3≤x≤4such that S(x) is a natural…

Q: 3) Prove that A is uniform pentagon and B is a half of a circle, also determine the areas of A & B.…

A: Here I am attaching image so that you understand each and every step.

Q: Consider the region D in t

A: Given, the curves                 y=2x, y=4x, y2=x, and y2=3x To find ∬Dx2x4dA

Q: OVESTON Prove that A is inveitine if at0 and at b l Gind The pivos 9 A %3D a a

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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: 10. Given: YX = ZX WX bisects YXZ Prove: AWYX AWZX Statements Reasons

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Q: Let X = R, and d be the diserete metrie, and A= {1,2) Show that if A is compact or not

A: Given set A={1,2}

Q: 5. In AABC let the bisector of ZB meet the circle containing A, B, C in a point E distinct from B.…

A:

Q: where C is the circle |z = 3i| =4. 2.3 Use the Cauchy integral formulae to evaluate 22 1 (9 – 22)(2…

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Q: A natural cubic spline S on [0,2] is defined by |So(x) = 1 + 2x – x³, S(x) = if 0<x< 1, |Si(x) = 2 +…

A: Given Sx=S0x=1+2x-x3if 0≤x&lt;1S1x=2+bx-1+cx-12+dx-13if 1≤x≤2

Q: (a) (b) To ang bis2duo inu to odmunl 2ovig tar 19dmun leor n onnobor 2. Show that each region is…

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Q: T If the area inside both the cardioid r = 6 + 6 sin and the circle r = 6 is A + B- then what is 4 A…

A: In this question, the area between two polar graphs is to be calculated. Given, The area inside both…

Q: Complete the two-column proof. Given: ZB = ZR, ZBPC = ZRCP Prove: ABPC =ARCP R Statements Reasons I

A: Answer and explanation is given below...

Q: Write proofs in two-column form.

A: Given that K lies inside the triangle △ABC. We have to prove  m∠K&gt;m∠C   From the given triangle.…

Q: (a) Let r = ri+ yj + zk and let r = ||r||. Prove that - (1) a

A:

Q: 17 Given: AFJH is isosceles, with base JH. K and G are midpoints. FK 2x + 3, GH = 5x – 9, JH = 4x K…

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Q: 3) Prove that A is uniform pentagon and B is a half of a circle, also determine the areas of A & B.…

A: It is asked to prove the given pentagon A is uniform and B is half of a circle.

Q: 19. Given: OABCD; BE | MD: M is the midpoint of AB. Prove: DE = BC %3D E D. A M В

A: We have the given figure as, Here, □ABCD is a parallelogram and in figure BE∥MD. M is the mid point…

Q: Os Find the Taylor seaies af the gien funkon Point as conter and deteamina the with the vadius af…

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Q: In the figure alongside, P and Q are centres of two intersecting circles. If ACB//PQ, prove that 2PQ…

A: Given In the figure ,P and Q  are centers of two intersecting circles , If ACB || PQ .

Q: In AMPQ, QR IMP. If MQ = 10, RP = 4, and MR = 8, find the area of AMPQ.

A: Given that In ∆MPQ, QR is perpendicular to MP and also we have MQ=10,RP=4 and MR=8.Our Aim is to…

Q: paragraph proof please

A:

Q: 共9. L is a Uxb matrx, so the rank of Lis at most: Al I B) 2 c) 3 D)4 E) one

A: L is a 4×6 matrix.

Q: Draw the region of z that satisfies the following cases. a) z-2i| 2

A: We need to find the equation of curve for the given problems in two-dimensional real plane and then…

Q: Exercise 1 AD bisects BE AB || DE AABC = ADEC Given: Prove: A E

A: As per guidelines we can solve the first question only. If you need more answer please repost it.…

Q: Let A:e? e be gioen ACX,の2-10 2=10, prove thet A Find the spectrom of A. is compact Jun

A: Given linear operator A:l2→l2 is defined by: Ax1,x2,…,xn,…=0,x12,x222,…,xn2n,…. (a). We Know that…

Q: AABC has inradius r, altitudes of length ha, hb, hc, and exradii ra, b, c. 1 1 1 1 + ra r (b) Prove…

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Q: 6. In AABC, points X, Y and Z are on sides CB, AC and AB, respectively, so that cevians AX, BY and…

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Q: 17. If MZACB = 36, find the area of the shaded sector. %3D 5 in. A. 7.9 in2 B. 25 in2 C. 70.7 in2 D.…

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Q: 12 In the diagram below, GI is parallel to NT. and IN intersects GT at A. A G Prove: AGIA~ ATNA

A: Consider the given triangles, In this diagram GI∥NT and IN intersects GT in A.

Q: Let AABC be a triangle. Fix the points X, Y, and Z on AB, AC, and BC, respectively (as in the…

A: The given triangle is                     The given condition is BXXA=AYYC=CZZB=4 Then  BXXA=4BX=4…

Q: 8. Given: ON bisects LJOH, LJ = LH Prove: JN = HN JNH

A: here, in given ∆OJN and ∆OHN ∠JON=∠HON                                      ∵ ON bisect ∠JOH∠J=∠H…

Q: 29. Find a formula for the area of the triangle whose vertices a 0, V1 , and v2 in R².

A: Given that  Vertices of the triangle is 0,v1,V2  To find the area of the triangle

Q: QR I RS and UV 1 TÚ. Construct a proof that ZQRS = ZTUV.

A: First, we sketch the situation roughly  We have to prove:

Q: Show that a triangle with vertices (x,Y;), (x2,y2), and (x;,y;) has area + x,y3 + X3Y, – X,Y3 – X,Y,…

A: