13. Given: RS I plane Y; ZTRS = LVRS Prove: ARTV is isosceles. R T V Y

Q: 135 5. y = x³, y = x + 6, and 2y + 2 = 0 (Answer: S. U. u.) 4

A: Let's find.

Q: Does the sphere x + y + ? = 25 have symmetry with %3D respect to a) the xy-plane? b) the line e: (x,…

A: we have the sphere x2+y2+z2=25  here the radius is 5

Q: The prism is bisected by the xz-plane. If P = (5, 2, 4), what is the area of the rectangle formed by…

A:

Q: 口 38 Which one of the following equations describes the tangent plane to the curve, f(x, y) =…

A:

Q: Calculate , z² dS if S is the prism whose base is the triangle in the limited xy plane by the x axis…

A: Here given figure is Since prism has 5 surfaces (1)-OAB (2) OADE (3) CDE (4) OBCD (5) ABCE

Q: 8 D Q Q 2x cm 10 cm x сm A 10 cm The above diagram shows a square ABCD of side 10 cm. The points P…

A:

Q: 3. (.J 6) For two vectors u = [1,0,0]" and v = [1,1, 1]", find a third vector with unit length such…

A: Given: Lt us consider the given, u→=1,0,0v→=1,1,1

Q: Evaluate SF.nds.... F(x,y,z)=(2z - y)i + xj - 2xk, and S: a sphere of radius 1 centered at the…

A: Evaluate ∬SF⋅n dSF(x,y,z)=(2z−y)i+xj−2xk, andS:a  sphere of radius 1 centered at the origin, and n…

Q: over the trianguar region whise verhces am (,9) , u,0) and (o,1) . are

A: Given that

Q: 20. MB is a perpendicular bisector of JK. Find the value of x. Work: 9x 18 3x K B

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: Consider the unit sphere S(x, y, z) = x² + y² + z² = 1. Assume that the temperature at a point (x,…

A: Consider the unit sphere Sx,y,z=x2+y2+z2=1. Assume that the temperature at a point x, y, z is given…

Q: a) Evaluate ff, (2x – z) dS, where S is part of the plane 3x + 2y +z = 1 that lies above the…

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: {(z, y, z) | 0< 2, Y, z< 1} is cut along the planes a = y, y= z, and z=z. How many pieces are there?…

A: Given:    C = { (x ,y , z) | 0≤ x ,y , z≤1 }      x = y  , y = z and z = x

Q: D ut he the plane 23 x=8 O Find arector in the plane X= 8 slone 3/5. Give avectar with unit per…

A: Use vector equation

Q: The sphere x² + y² +z² = 100 has the center (0,0,0) and a radius of length 50. Select one: True…

A:

Q: Describe the intersection of the horizontal plane z = h and thehyperboloid −x 2− 4y 2 + 4z 2 = 1.…

A: Put z=h in given equation -x2-4y2+4h2=1⇒x2+4y2-4h2=-1

Q: Please answer only the last 2 parts shown in the red box.

A:

Q: Let -{) -() -E) --() by and 7 1 b2 ba Find conditions on bi, b2, by such that E span{at, a, .

A: NOTE: Refresh your page if you can't see any equations. . write all basis vectors in the matrix…

Q: . Evaluate || (2- 1) do, where S is the part of the cone z = Vr + y² which lies under the plane z =…

A:

Q: Let S be the part of the paraboloid z= z +y that lies below the plane z= 3. Evaluate s atz4g°41 dS.…

A: We are given that S is the part of the paraboloid z=x2+y2 that lies below the plane z=3. Now, we…

Q: 4 Assuming that the curve ris thex + y +z = 0 intersection of the plane and the sphere , then the…

A: As per the question we are given a closed curve Γ , defined as the intersection of the plane x+y+z =…

Q: r = 14,0 = I 4 Description of locus in (x, y, z) space: Line made by the intersection of the…

A: Given the Polar coordinates      r=14 and θ=π4 Find the Cartesian coordinate y.

Q: 3. Let R= {(x, y) : x² + y² 0, y > 0}. Evaluate // Vz? + y² dA x2 +y? dA R

A: using polar coordinates x=rcos(θ)y=rsin(θ)x2+y2=r2,dA=r drdθ

Q: in R?, Hi= Sp{ (1,-,0)} %3D Hy= Sp {12900} (2,3, a) Hi + Hq=? b) H, +Hg=? c) H, tth tHg=?

A:

Q: Given two lives (zt+l, st-s,lot) f (34, 2++3, z++1) loca ted in Side th plane ? (zt+l, 5t-5,lot ) f…

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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: 3. Evaluate ox?y dx + xy? dy using Green's y 2 Theorem, where C is positively oriented by line y =x…

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Q: es v3x + z – 5 = 0 and 2x + 2/3z + 10 = 0. ond

A:

Q: 10) Consider the oriented curve C, which is the intersection, in the first octant of the surfaces…

A: Given that Surface 1: y-22=x-2 Surface 2: y+z=4 Fx,y,z=-x, y+z, z2 Find the value of ∫CF·dr