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

Q: In AMNP, T is the centroid. If MR=30 find MT. N R T M S

A: We are given that T is the centroid and MR=30. We know that the centroid divides each median in a…

Q: . Let T be the triangular lamina in Figure 21. O Show that the horizontal cut at height y has length…

A:

Q: Use the Stoke's therorem to evaluate F. dr, where F = xzi - yj + z²yk and o is open surface of the…

A: We  have  to evaluate ,Where +Then, Curl+Now, Then, let

Q: The diagonals of an isosceles trapezoid ABΓΔ (ΑΒ // ΓΔ) intersect at O. If E, Z, H, Θ are the means…

A: Given an isosceles trapezoid ABΓ∆ . Its diagonals intersect at O. Given that the mid - points of OA…

Q: Given: AP and BP are tangent A to ©Q at A and B C is the midpoint of AB PĆ bisects ZAPB Prove: В

A: given: AP¯ and BP¯ are tangents to the circle having centre Q at A and B. C is the mid point of AB⏜.…

Q: SSg z(x² + y²)do where S is the portion of the sphere x2 + y2 + z2 = 9 in the first octant that is…

A: Surface integral of a function f(x,y,z) Along the surface S given by z= g(x,y)…

Q: s given that PORSIS a rectangle. If PQ = x and QR=y, express in tems of x and y a) RP b) PT where…

A: Since PQRS is rectangle ,so every angle is of 90°.To find a) and b) We use Pythagoras

Q: Consider the sphere x² + y² + z² = 36 and the cylinder (x-3)2 + y² = 9, for z 20. Find the surface…

A: The given problem is to find the surface area of cylinder inside the sphere. Given sphere x2+y2+z2 =…

Q: 5- ABCD is a trapezoid whose diagonals AC and BD intersect at the point E. If AB=2/3 DC, prove that…

A:

Q: (Q.)AUSE T.cx)-1 ad Tilx)= X, t fnd TECK) nd 万(x) (b) Find the raats of Ti(K) nd Tiw using the…

A: a) Given that, T0x=1 and T1x=x. Note that, the powers of x as function of Tnx for x2=12T0+T2 and…

Q: B) Evaluate S Ln z dz around the circle | z| = 2 %3D

A:

Q: Find the point (xo, Yo, 2o) closest to the origin in R³ that is both on the planes 3x + y+ z = 5 and…

A: We need to find a point (x0, y0, z0) closest to the origin in R3 that is both on the planes 3x+y+z=5…

Q: Let f (z) = 33O = Q A = 10and B= 10 + 10iet C be the contour composed of the line segments OAand…

A: The given problem is to evaluate the complex integral of the given function over the given semi…

Q: The center of mass of quarter circle given by is the point P = ( Hint: Use symmetry. " ). 2 - x², y…

A:

Q: GIVEN: V is the midpoint of XZ. XY ZW PROVE: YV = WY V. Y

A:

Q: WX || ZY and Zs Z and Y are supplementary WXYZ is a parallelogram Given: Prove: W Y

A: It is given that,  WX ¯|| ZY¯  and ∠Z and ∠Y are supplementary To prove :- WXYZ is a parallelogram

Q: Verify Stoke's Theorem. F=, C'is the boundary of the paraboloid z = x² + y² lying pelow z = 1 plane.…

A: To verify Stoke's theorem for the below function. F=y,−xz,xz2

Q: A trapezoid has bases with lengths x + 3 and 3x — 1 and a median oflength 1 1 . Find the value of x.

A: Consider the given trapezoid: where, AB=x+3 and CD=3x−1,Median, XY=11From Formula,XY=AB+CD2

Q: Lafy gaun Rncugence theorem for ダ(コ-y)で 14-2 4-ay or me" reatangelas and gn the fuufacel ef me…

A:

Q: Prove that the locus of the foot of the perpendicular drawn x2 +² a? = 1 to any of its tangent om…

A:

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: (a) Let R > 5 and let CR be the closed, anticlockwise contour obtained by joining the line segment…

A:

Q: Use Stoke's th corem to eval uate S F.dr = SS curl F. û ds, wher F=iyajz+ fx and s is the surface of…

A: We have to evaluate the integral using stoke's theorem.

Q: Given F = (yz,x+y+=,xz), determine curl F .

A: Curl F ( -1, y-z ,1-z)

Q: Consider a sphere E with center at the origin and radius equal to 1, following the Beltrami-Klein…

A: Substitute the parametric coordinates of the line in the equation of sphere and solve to get the…

Q: BC//EF Dis the midpoint of BF prove ED congruent CD

A: BC//EF Dis the midpoint of BF prove ED congruent CD

Q: ubegral Fa dx un ntegral as the areg of Q Assuming r>o,compute the tems ing the of r by interpret…

A: The given integrand indicates the circle: x2+y2=r2, with a radius of r units. Limit of the integral…

Q: Given: S is the midpoint of RT, PR = PT prove: ΔPRS ΔΡΤS

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

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

A:

Q: Let S be the sphere of radius 1 centered at (2, 3, 4). Find the distance from S to the plane x + y +…

A: