3x+1 I den hify Hie seament bisector of Then find xy

Q: Q2:- Evaluate / x + ydA where Ris the trapezoidal region with vertices given by R 5 5 (0,0), (5, 0).…

A: To find - Evaluate ∬Rx + y dA where R is the trapezoidal region with vertices given by…

Q: In AEFG, L is the centroid. If LJ=25 find EL. F H J E K Answer: Submi

A:

Q: Find the condition for the points (a, 0). (h, k){0,b) when ab = 0 to be collinear.

A: Find the condition for the given points to be collinear.

Q: Fin He ara at tHe surface af the portion oF Hae Plane 2= 5-2X -9y

A:

Q: distance Q.2A) ((q,x+ 92y+ 93z = M, ,41x + 92y+932 = M2)) |M, – M2| Prove the between to planes…

A: Let the point (x1,y1,z1) is on plane 1 and the point (x2,y2,z2) is on plane 2. As we already know…

Q: Consider the quadric ax2 + y2 + 4z2 + x + 6y−4z = −a−10 where a is a parameter. Find all the values…

A:

Q: 6. Given a rule x2 + y2 = 9, its image rule x2 + y2 – 2x + 6y + 1 = 0 under a translation, state a…

A:

Q: 2. || F. dš where F = 3x i+ 2z3+ (1- y²) k and S is the portion of z = 2 – 3y + x? Evaluate %3D that…

A:

Q: EX Find the reglon in the z-plane represented bye

A: Given

Q: %3D by the paraboloid z 4-x2-12 =4-x- c.m. R. x +y = 4

A: Given, Solid of constant density δ bounded by R: x2+y2≤4 in plane z=0 and paraboloid z=4-x2-y2 To…

Q: Evaluate S. F·dr, if S'is the portion of the paraboloid z = 4 – x² – y² for which z 2 0 and F(x, y,…

A:

Q: F(x, y, x) = i + 3xj + 2yk And G(x, y, x) = xi - yj + zk. Find the Curl(FxG).

A:

Q: Consider uxx + auxy – 2uyy + ux + 2uy = 0 Find all values of a so that the PDE is Hyperbolic.

A:

Q: Use Lagrange's multiplier(s) to find the maximum and minimum for f(x, y, z) = x² + 2x + 2y2 + 3z2 on…

A:

Q: show. that theAine in.which.the planes.X+.2y-22=-5 nod5X-2y.z=.0...jntersec.is..pavalle.to.theine.…

A:

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: 45. Find the distance from the plane x + 2y + 6z = 1 to the plane x + 2y + 6z = 10.

A:

Q: Find a parameterization for the quarter sphere x² + y² + z² = a² where z > 0 and x > 0.

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Q: Frned the poind al on 2x+y + 2' =4 n hreh bangend plana アaralle l lo tk plane x-2y +62 =5. is

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Q: (a) C in the xy-plane, oriented counterclockwise when viewed from above. SaF. dr = (b) C in the…

A: Given,

Q: (b) Give an example of a parametrisation of the unit circle, C = {(x, y) E R² | x² + y² = 1}, that…

A: The parameterization of a circle  that generates the clockwise orientation of C is given by: x=r…

Q: Consider AB in the coordinate plane below. 10 4. 2. A -10-9 -8-7 l0 1 -1 -5-4-3 -2-1 2. 4. 10 -2 -3…

A: Given: AB¯

Q: 9. Find the angle between the two planes 2x + 3y + z = 3 and x + 3y + 2z = -3

A: Given,           2x+3y+z=3    and   x+3y+2z=-3We know that,           Suppose the two equation be…

Q: Q8) The planes 3x+6z=1 and .2x+2y-z=3 are orthogonal F O

A:

Q: Find /| F-dS if F(x, y, z) = 2xi+2yj+2zk and S is the part of the paraboloid z = = 8-x?-y? lying…

A:

Q: JJs where S is the sphere x² + y2 + z2 = 1.

A: Given S is the sphere                         x2+y2+z2=1 To evaluate:             ∫∫S3x+3y+z2dS…

Q: Sketch the bifurcation diagram for y = (A– 4t)y (where A is a parameter, as usual). 2

A: To find- Sketch the bifurcation diagram for y' = λ - 4t2y (where λ is a parameter, as usual)

Q: Find the maximum value of f(r, y) = 10ry(4 – 8z - 4y) over the triangle with vertices (0, 0), (,0)…

A:

Q: 9. Suppose that a : R³ → R³ by perpendicular projection onto the plane 3x – 2y + z = 0. Find ↑

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Q: Find i x w if ||T|| = 3, ||w|| = 4, 0 = and ī, w both lie in the xz-plane (as shown). 3 %3D

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Q: lo. find a point in the plane x+2y+3z=13 nearest to the point (1,1) usung the methed of Lagrange's…

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Q: 7. C is the hexagon in the xy-plane with vertices (5, –5), (5,5), (0, 10), (–5, 5), (-5, –5), and…

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Q: Find the harmonic conjugate of u where u(x,y)=x^2 - y^2 -2xy-2x+3y

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Q: If UW = 4t- 16 and UY = t + 14, find UY in rhombus VWXY.

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Q: Find %3D as if F(x, y, z) = 2xi+2yj+2zk and S is the part of the paraboloid z = 4-x-y lying above…

A:

Q: b- Let X₁, X2,... X (a) Find a comp (b) Find the UM

A: Solution:   (a):

Q: Find the eguation f Plane that Passes through P(12-1,3) and s Parallel to the Plane 3X++6? ans. 3X+y…

A:

Q: 3.2. let f(x) = 2, x+4 xez, * 1 - 1 1/2/20 -74x45 -*>$ Approximate the foldoy using Trapezoid mule…

A: In order to approximate the integral: ∫abydx, the trapezoidal rule uses the formula:…

Q: 2. Let u(x, y) = 2+ 3.x – y + x² – y? – 4.xy. Show that u(x, y) is harmonic and find the harmonic…

A:

Q: Complex Analysis

A: For given function, First we will show the function is harmonic function as shown below :From the…

Q: Evaluate 6. F.dī by Stoke's Theorem where F = y?i+x³j– (x + z)k and c is the boundary of the…

A: We have to use stoke's theorem .

Q: SSx x dA; R is the portion of the disk x + ys 16 in the second quadrart

A: I use polar conversion method

Q: Y A B C Given: XC bisect YB at A; A is the midpoint of YB Prove: AXYA = ACBA

A: We have to prove that given Triangle are congurent.

Q: c. Let P(x, y) = y² + sin¬1 x² and Q(x, y) = 2xy + 4x. Suppose that C is the parallelogram with…

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Q: 2. Show that AB CD + AC DB + AD BC = 0, given the points are collinear.

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Q: a) Evaluate //(-ri-yj+2: k) n dS, where a is the portion of the paraboloid : = 3r - 3y between the…

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Q: Use Gramer's Rule to Find K,y and Z -y-22 = -8 %3D + 32 = 2 %3D 7X +y+Z = 0

A: As per our guidelines we are supposed to answer only one question at a time. So submit the other…

Q: : The trace of the surface S x² Z = + 9. 4 in the plane z = 4 ||

A:

Q: Given F(x.y.z) (x+y+Zi +(x-yj+(xz-2)k what is CurlF at the point (1,-1,3)? You should write your…

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Q: 2) The double integnal | 3x ekdy, whetzeT is the tniang le of VErtices 6,0),c2,0) ond (eti-2),…

A: The double integral is an integral with respect to two different variables the integral of a…

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.