Given: YX - XZ, WX bisects ZYXZ prove: AWYX = AWZX

Q: If R is the disc with center at the origin and radius 5 then the numerical value of Lxds R xdA is…

A: We have to find the numerical value of  ∫RxdAwhere R is the disc with centre at origin and radius 5.

Q: Calculate the area of the given quadrilateral starting at A and going counter - clockwise using the…

A: Use the formula and substitute the values then simplify.

Q: Given line YZ tangent to OJ at point Y and mzWYZ = 119, what is the measure of arc WXY %3D Y W X.

A: Measurement of arc is the angle subtended by arc at the center of circle.

Q: (7) Let D be the solid above the cone z = r and below the sphere of radius 2, and let fla, 4, 7) =…

A: To convert the cartesian coordinates into cylindrical coordinates put  And the integral will be…

Q: Given: ZWZX ZYZX; ZW = ZY Prove: ZX is a perpendicular bisector of WY

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Q: ST=8, WX =5, and the perimeter of ASRT = 15 AWZX ASRT perimeter of AWZX = ?. %3D %3D %3D 72

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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: ind the valume of the portion of the Solid. Sphere x+y2,+2-10 that les between the Surfaces

A: We need to find the volume of the portion of the solid sphere x2+y2+z2 = 10 that lies between the…

Q: 2. Find the contour integral f,zdz for (a) y is the triangle ABC oriented counterclockwise, where A…

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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: By using polar coordinate, evaluate Sl, x² + y² dA, if R is the region in between circle x² + y² = 1…

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Q: Calculate the line integral ∫Cy2ds, where C is a part of the circle x=acost, y=asint, 0≤t≤π/2.

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Q: What is the image of the vertical strip  {zϵC:−1<Re(z)<1} under e^z

A: A  conformal map is a one-one and onto analytic map. So, Re(z)=1 to a point. Here f1 is defined by,…

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: Evaluate the integral eiz dz, (22 + 1)2 where C is the circle |2 + il = oriented anticlockwise.

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Q: 2. Given: WX = YZ; ZWXZ = ZYZX Prove: WXYZ is a parallelogram

A: Parallelogram

Q: In isosceles trapezoid WXYZ with bases ZY and WX, ZY = 8, YX = 10, and WX = 20. Find height h (the…

A: Given  The  WXYZ  is isosceles trapezoid  with bases ZY and WX .  Here ZY =8  , YX =10  and WX =20

Q: 11. Evaluate 2 dA, where D is the shaded part inside the semicircle of radius 2 in Figure 26. 2…

A: To Find:  D is the shaded part inside the semicircle of radius 2 From the figure, the restrictions…

Q: Evaluate the line integral 3xy® ds, where C is the right half of the circle x? + y? = 36.

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Q: Use Green's theorem to evaluate O -x²ydx + x°dy, where C is the circle x? + y? = 4 with a…

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Q: Use Green's Theorem to evaluate the integral (3x² – y)dx + 3xdy where C is the circle a? + y? = 1…

A: As we know from the Green's theorem; ∫CMdx+Ndy=∫∫D∂N∂x-∂M∂ydA   Given; I=∫C3x2-ydx+3xdy So, M=3x2-y…

Q: WY bisects ZXWZ and ZXYZ. Complete the proof that AWXY E AWZY. Y. W

A: Given that WY bisects ∠XWZ and ∠XYZ. We know that when a line bisects an angle, it means it divide…

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: Find a baxs for d (R', e'), the spece of R? to R>. 2 ee lineer tren sformations from

A: a linear transformation L : R2 -&gt; R3 such that  S = {[ 1 -1 2] , [3 1 -1]} is a basis for range…

Q: Given: XZ is al bisector of WY Prove: AWYZ is isosceles.

A: Given,  A ∆WYZ with perpendicular bisector of WY  is   XZ.  We have to prove  ∆WYZ is isosceles.

Q: 4. (45pt) Compute the following contour integrals and give reasoning. 2z dz (a) Jc 7(z+4) where C is…

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Q: ATWX is isosceles, with base WX RY | WX RWXY is an isosceles trapezoid Given: Prove:

A: We have, △TWX is isosceles, with base WX and a line RY↔ such that RY∥WX Since, RY∥WX therefore…

Q: Given: AMNP, PM = 8, %3D mZP= 90°, mZN=58° Find: Perimeter of AMNP

A: We use the formula of the perimeter of the triangle= Sum of all sides.

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

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Q: Use the distance formula to show that T (x,y) = (-y,x) is an isometry.

A: We have to prove that T(x, y) = (-y, x) is an isometric.

Q: Find the mZR in trapezoid QRST where QT||RS below.

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

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Q: In the Fgure belcw, mL2=41? Find m ZI Im %3D

A: Topic:- right angle

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: 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: 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: 3. Please give clear explanations

A: The parametrization of a surface S is given by       G(u, v)=(u, v, uv) where D is u2+v2≤1.

Q: Use De moivrés theorem to ealculate the sauare Toot Of It,

A:

Q: Find the volume of the parallelepiped shown having    u = 3i − 5j + k ,            v = 2j − 2k and w…

A: Givenu=3i−5j+kv=2j−2kw=3i+j+k

Q: Use Green's Theorem to evaluate (1in z – 2y) dz + (x – ycos y) dy, where C is the circle (x – 4)² +…

A: Given: C is the circle x-42+y-42=9. ∮Cxsinx-2ydx+x-ycosydy. To find: Using Green's theorem, value…

Q: 13-Evaluate JSS zdV E where E lies between the spheres x2 + y? + z² = 1and x2 + y? + z? = 4 in the…

A: To find- Evaluate ∭Ez dV where E lies between the spheres x2 + y2 + z2 = 1 and x2 + y2 + z2 = 4 in…

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

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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: (b) Prove the volume of a parallelepiped with a vertex at the origin and edges ü,v, and w is given…

A: In the question we have to prove the formula.

Q: Given: KM = KN Ray KO bisects ZMKN Prove: Ray LO bisects ZMLN M

A: GivenKM=KNtherefore ∆MKN is as isocsales triangle.and KO bisect ∠MLN We know in iso-scales triangle…

Q: Compute 5xy ds, where S is the surface of the tetrahedron with sides z = 0, y = 0, x + z = 1, and x…

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Q: If the region R is bounded by the inside of the circle, x?+ y? = 9 then : %3D dA=2π (e' ). VxZ +y?…

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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: Consider a Möbius strip cut along the dashed blue lines as shown below. What is the resulting…

A: When a mobius strip cut along these lines we get ,