1. Prove the HL Theorem. Hint: Construct RY that is congruent to AL. Prove that AROYALEA by LL Theorem. Use the CPCTC, Transivite Property, and LA or HA Theorem to prove AJOY = ALEA Given: LVLOE R is the midpoint of LV and OE. Prove: LOVE R [2) E

Q: 1.D Determine the following a.) (xty) SinckyDdA JR

A:

Q: by computing that the given funetions inde pendent on Show the are linearly indieated intorvale…

A:

Q: If C is the unit circle x² + y? = 1 oriented counterclockwise and F (x, y) = xi +y j, what is the…

A:

Q: 3. By using convoluti on theorem, ind the inverse Laplace +ransror of the following function eyplan…

A: We have to solve given problem:

Q: ALMN, S is the centroid. If SQ=22 find LS.

A: Here we have been given the measurement of SQ = 22 and S is the centroid.

Q: Find x. 150° 8x + 12/ E

A:

Q: If C is the unit circle x² + y² = 1 oriented counterclockwise and F(x, y) = x F. dR? -T 2π TT î 1 C…

A:

Q: 1. Given: m |l n, 2l = 23 Prove: a | b 21 3 Proof:

A:

Q: Let R be the annulus defined by {1 ≤ x² + y² ≤ 4} and let C₁ and C₂ be the circles of ratius 2 and 1…

A:

Q: Let Ē = Calculate F. dr where r is the Straight line seg ment connecting (1,1) to (2,2)

A:

Q: Let C denote the positively oriented circle |zi| = 2. Evaluate the integrals: a) z + 2z (z-1)³ dz

A: The given problem is to evaluate the given complex counter integral over the given counter C:|z-i|=2

Q: Can you show all the step please!

A: Step 1: Step 2: Step 3: Step 4:

Q: e. Find points on the graph of xy°z² = 16 that are closest to the origin.

A: Let P be point (x0,y0,z0) Then, distance between P and origin is given by

Q: Given the funchisns fyl= 3y-y cnd 8y)=-y; 9. Sketch the frunckons cnd label then nteuseckon points

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: 18) Evaluate 1 dz z(e: – 1) where I is the positively oriented unit circle, i.e., unit circle in…

A:

Q: 2. Which of the following tunctions ic/are homogeneour ? a. x + x² y + x3 b. X+ リ C. Inx - Iny - e…

A:

Q: 7 Prove : id Is perpendicular line to ra duic at its outer end point ,then t ang ent to the cirde is

A:

Q: interior to a Ex: let to be any Simple closed Contour C, when flaxed ?? de no dz = 2πT ( Hw a) and…

A: Cauchy integral formula for higher order derivative is :-fn(z0)=n!2πi∫cf(z)(z-z0)n+1dzwhere c is a…

Q: 2. Given: AB = AD; AACB and AACD are right triangles. Prove: AACB = AACD A B. D. 3. Given: KM 1 JL…

A:

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: fIntegrate the functon. fexng) the functrom. fixng). aver.the... 2. 1 -xーye 2. reginm.(.disk.).…

A: The solution is given in the next steps.

Q: Prove that a torus at R³ is equivalent to the Cartesian product of two circles at R² 3 that is,…

A: Given Information:Torus: where  and  .Circle:  where .To show:The Torus at  is equivalent to the…

Q: 3. a) Compute: f (Rez-32) dz where I is a directed line segment from z=0 to z=i. b) Let C be the…

A:

Q: Ql1. Find the dereiatine folling funchion. FG)= 3. (2t -1) It 45 using the Fundamental Theorem of…

A: To find the derivative using fundamental theorem of calculus

Q: Select all of the statements that are sufficient to conclude that APQR is congruent to AXYZ. PQ =…

A: We have to find triangles PQR and XYZ will be congruent under which conditions.

Q: 2 Use Green's Theorem to evaluate Jx*ydx-xy dy, where C is the circle 2+ y? – 2601 with…

A: Let be the vector field and C be the boundary of the region D. The Green's theorem states that .

Q: 1 x = + 6 2y What is the length br of the portion of the graph of the between the points with y = 1,…

A:

Q: Let C be the circle |z −1| < 2 taken in the positive sense.

A:

Q: (C) is a circle of center O and radius 6cm. [AB] is a diameter of (C). P is a point on (C) such that…

A: Let us drawn the diagram with the data given. The diagram looks as follows:

Q: Let F =. Use Stokes' Theorem to evaluate where [[cur J curl F.dS,

A: Given,                  To evaluate :                where S consists of the top and the four sides…

Q: Shew that if f is Lip. then P is Cont. on X. Nale- In fact f is uni formly Conhnaue

A:

Q: 19. Given: Prove: 21 and 22 are right Zs H is the midpoint of FK FG HJ || FG F H K HJ 1 G

A: