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

Q: Find the onthogonal trg ectories of y(sy +c) = I.

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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: 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: GIVEN: AB = DE M is the midpoint of BE, AM = KM, DM = KM. PROVE: AABM = ADEM. A GIVEN: KM is the 1…

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Q: By making an appropriate change of variables, evaluate the double integral I = - || ( + y)e v°dzdy…

A: Jacobian of the transformation x=g(u,v) and y=h(u,v) is  ∂(x,y)∂(u,v)=∂x∂u∂x∂v∂y∂u∂y∂v Suppose that…

Q: Let a = ci + jand b = 2i + 10j. Find c so that a and b are orthogona C = i

A: Given: a=ci+j b=2i+10j.

Q: By making an appropriate change of variables, evaluate the double integral (z + y)e* v*dzdy R. where…

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Q: Prove the following: Given: AC1 BD,D is the midpoint of AC Prove: AABD = ACBD A

A: Provides figure is  AC¯ ⊥ BD¯ D is the midpoint of AC¯.   To prove: ∆ABD≅∆CBD

Q: Describe your plan for proving the following.

A: Given CD¯⊥AB¯D is the midpoint of AB¯

Q: 14. Given: nLw, nil; AB DE;Cs the midpoint of AE and BD Prove:A4BC 2 AEDC

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Q: Assume a to be a nonzero real no.. Determine the area of the portion of surface xy = az in the fir…

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Q: Consider the area of the part of the plane z=ax+by+c that projects onto some region D in the…

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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: GIVEN: S = XH, SR I RW, HWI RW, ST = HT. PROVE: T is the midpoint of RW. T

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Q: 7. Given that BOC is a diameter and that ADC = 90°, prove that AC bisects BCD. %3D -E 10.4…

A: Join A and O. Note that, OA is perpendicular to DE

Q: garded as a subset of R. 9.E. y ing theargme ang ), prove that the interval J = { (x, y) : 0 < x <…

A: 9.F  We have given J=(x,y):0≤x≤1,0≤y≤1   to prove the compact in R2 we have to show that J is closed…

Q: PN bisects MQ ZM and 2Q are right angles ΔΡOR ΔΝMR Given: Prove: R

A: Given:         PN→ bisect MQ→.∠M and  ∠Q are right angles.

Q: Which parts must be congruent to prove APQR = A PSR by SAS? %3D P R OZQ = LS and QR = SR

A: If two triangles are congruent, then they have congruent corresponding angles and congruent…

Q: AB DC AB = DC C is the midpoint of BE AC | DE Given: Prove: A D E

A: Given, AB∥DCAB≅DC C is the midpoint of BE

Q: 7. Given: TA bisects ME at R, ME bisects TA at R, and TM = AE. R. Prove: ATRM = AARE

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Q: (a) Let r = where C is the unit circle oriented counterclockwise, and Vr2 + y?. Calculate fF Tds…

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Q: 20. Given: PQ = RQ, PS = RS Prove: QS bisects ZPQR. R

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Q: In right ARST (not shown) with right ZS, RV bisects ZSRT 6, ST = 6V3, and so that V lies on side ST.…

A: It is given that, ∆RST is right at ∠S and RV→  bisects ∠SRT so that V lies on  ST→ RS=6, ST=63 and…

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: 22. Compute the contour integral (Баллов: 2) Sof (2) dz, z E C, if f (z) = and path is semicircle z…

A: Topic:- application of integration

Q: Evaluate TI Vx + y2 dv, where E is the region that lies inside the cylinder x2 + y? = 1 and between…

A: In this question, we have to evaluate the triple integral by using cylindrical coordinates.

Q: GIVEN: X1 = X2, HK bisects RHN, HR = HN. PROVE: HK I RN.

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Q: Given: RS E TU ZSRT LUTR U Prove: ARST ATUR

A: Guven : RS ≅ TU∠SRT ≅ ∠UTR

Q: A Compute the following contour integrals and give reasoning. 2z dz where C is the positively…

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Q: Find b∈R such that ∫∫Ssin (b) ydS = 8, where S is the part of y^2 + z^2 = 4 that is between x = 0…

A: To find the value of b satisfying the given integral.

Q: Use the surface area formula SA = /I. V1 + f% + f; dA to prove that the surface area of the sphere…

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Q: 6. Compute the contour integral (a) / COS Z -dz where C is the positively oriented circle |z – 1| =…

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Q: b. Given: AE bisects DC ZC = ZD B Prove: AABD EAEBC PE D.

A: we prove it in 2nd part by using ASA identity.

Q: Consider the area of the part of the plane z = ax + by+C that projects onto some region D in the…

A: If the area of the region D on xy-plane is k. That is, ∫∫DdA=k. If the area of the some region of…

Q: 10. Using Stoke's theorem, evaluate y dx+ xz dy+x² dz where C is the boundary of the triangle cut…

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Q: Prove that dr-V3Ta? where こis the intersection of the plates: x²+ and and F=ly,Z,x)

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Q: i) Use the residue theorem to evaluate 2z+6 dz, where c is the circle |z – i| = 2. z²+4

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Q: Given:ZAPT LEPT, and P is the midpoint of AE Prove: AATE is isosceles A E

A: Given: ∠APT≅∠EPT, P is the mid point of AE

Q: Use Green's Theorem to calculate (422 – 3yx)dr + (3xy+ y² + 6)dy where C is the circumference (x –…

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Q: In ARST. U lies on TS with TU:US = TM intersects RS in V. Find the ratio RV:RS. 2:3. M is the…

A: Given that, U lies on TS with TU:US=2:3.  That is, if TU=2x, then US=3x. Also, TM intersect RS in V.…

Q: Evaluate ffp(4xy + 1) dA, where R is the region in the upper half-plane bounded by the circles a? +…

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Q: 2. Let C be an open (upper) semicircle of radius R with its center at the origin, and consider J…

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Q: 20. GIVEN: KG = JG, JR 1 KG, KL 1 JG R is the midpoint of KG, L is the midpoint of JG. R PROVE: AKOR…

A: Proving using ASA congruence rule.

Q: GIVEN: RS 1 SL, RT 1 LT, RS = RT. PROVE: 1. ARLS = ARLT. 2. WL bisects SWT.

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Q: moves along iine ield x, y, z) = z?i + + 4 s' Theorem to finc

A: The work done is the line integral o the force along the given path C, W=∫CF.dr Apply Stokes…

Q: What part is needed to prove the triangels are congruent by SAS? К С L. Your answer: ZK= ZC ZL= ZB…

A: Given:

Q: In the figure below, the segments JK and JL are tangent to the clrcle centered at O. Glven that…

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Q: Given: APQR has a right 2Q. M is the midpoint of PR. Prove: MP = MQ = MR

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