2. Let D be the half-disc in the xy-plane given by x +y <9. 2. Calculate e-?+v}dA Select one: a. (1-e-9) b. 글(1-e-9) (1-e-10) d. Non of them e. (1-e-11).

Q: Find the distance between the planes 5x − 3y + z = 2 and 5x − 3y + z = −3

A:

Q: Calculate gij for the distance between (x;) = (1, 1, – 1) and (yi) = (0,1,2) in %3D T-2 1] barred…

A: A point in three dimensional coordinate system is given by xi=1,1,-1yi=0,1,2 Now the point in barred…

Q: .2 Use Green's Theorem to evaluate x-ydx - xy² dy , where C is the circle x +y² = 9 with…

A:

Q: Find the distance (in appropriate units) between the points P(2,−1)P(2,−1)and Q(3,4)Q(3,4)in the…

A:

Q: Find a parametrization of the line through P = (4, 9, 8) perpendicular to the yz-plane.

A: Equation of Linethe Line through P =(x0,y0,z0) in the diresction of vector v→=(a,b,c)is defined…

Q: State the equstion of the yz plane

A: We have to find equation of yz plane

Q: 2. Show that the xy plane W = (x, y,0) in Rº is generated by: (i)u = and v = (ii)u : and v = 3

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Q: 3) Prove thet the xy-plane with constant curva tue k= urve In is o circle of radious

A: We have to prove that a curve in the xy plane with constant curvature k=1r is a circle of radius r

Q: Find the trace of the plane 3x − 2y + 5z = 4 in the xy-plane.

A: The given equation of the plane is 3x-2y+5z=4. The trace of the plane in the xy-plane is the…

Q: Let D be the half-disc in the xy-plane given by x +y <9. Calculate e-(x2+v)dA

A:

Q: Use Green's theorem to evaluate $(xy + 3x²)dx + (3y – 2x)dy, along C, where Cis the triangle with…

A: Given Integral ∮(xy+3x2)dx +(3y-2x)dy along c where c is the triangle with vertices (0, 0), (0, 3)…

Q: Find the distance between the planes 5x - 3y + z = 9 and 5x 3y + z = -2.

A:

Q: Sketch the following planes in the window [0, 5] × [0, 5] × [0, 5]. The plane parallel to the…

A: First obtain the plane that parallel to the xz-plane containing the point (1, 2, 3).…

Q: show that the points AC!,l,4) B(2,2,2), coplanear (in the c(o,l,5) and D (1,0,5) are Same plane).

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Q: Find the condition for the points (a,0),(h,k),(0,b) when ais not equals to 0 to be collinear

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Q: Use Eq. (8) to find the distance from Q = (1, 1, 1) to the plane2x + y + 5z = 2.

A: Find the distance from Q=(1, 1, 1) to the plane 2x+y+5z=2 or 2x+y+5z-2=0.…

Q: A(n)________ is the collection of points in the plane the difference of whose distances from two…

A: The given statement is "A(n)________ is the collection of points in the plane the difference of…

Q: The point on the plane 2x+y+z=1 that is closest to the point (1, 2, 3) is (a, b, c). Then a+b-2c= O…

A:

Q: Find vohume fome above ZVy-xLy, below Z0(xy plane) inside xy/ 3.

A:

Q: 2. Find a unitvedctor with positive z-component porpendcular to the plane 2xt2y-2=3 Z-C

A: We will find out the required value.

Q: Which of the following is the least distance from the point (2, –1,1) to the plane x + y – z = 2?

A: Given: The plane equation is x+y-z=2and the distance from the point is 2,-1,1 To find the least…

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

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Q: Find the distance between the point (0, 0, 0) and the plane 2x + 3y + z = 12.

A:

Q: Find the point on the plane 2x + 3y + z = 7 that is nearest to​ (2,0,1).

A: NOTE: Refresh your page if you can't see any equations. . the given point is . the given plane is…

Q: Compute the angle between the two planes 2x + 3y + 7z = 2 and 4x - 2y + 2z = 4.

A:

Q: Find a parametrization for the line segment beginning at P, (-5, - 2,3) and ending at P2 0, 5/4

A: We have to use parameterization of the line.

Q: Зх + 2у + 3z %3D 6

A: Use a graphing utility to plot the graph of 3x+2y+3z=6 .

Q: The point (-2,0,8) is. A. In die xy-vlak O In the xy-plane B. In die yz-vlak O In the yz-plane C. In…

A:

Q: Consider the following. Z = 4 Sketch a graph of the plane.

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Q: Find the equations of the tanget plane and normal line to the graph of In(2?)x-을=3y3-VE at the point…

A: Equation of tangent plane f(x, y, z) = k at x0, y0, z0 is, fxx0, y0, z0x-x0+fyx0, y0, z0y-y0+fzx0,…

Q: Find the condition for the points (a, 0), (h, k), (0, b)when ais not equals to U to be collinear

A: We have to find the condition

Q: 22 Find the Directional Derivabive of Pary,z)= xg-y2'+Z at the point CI, -2, 0) in the direcbion of…

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Q: 2-g(%,y)%3D플-플 * at (VT ,1)

A:

Q: Suppose we have: u = and v = . Based on their relative positions in the xy-plane, in which…

A:

Q: d the distance between the point (2, -4, 3) and the plane 5x – 2y + z = 10

A:

Q: 5. Find a plane through the points P(1,2, 3), P2(3, 2, 1) and perpendicu- lar to the plane 4x – y+…

A:

Q: Calculate ff A.n ds If A = yi + 2xj – zk and S is a 2x + y = 6 plane surface in the first octane cut…

A:

Q: Find the shortest distance between (3,4,1 ) and the plane X+y +Z = -2

A: Using distance between plane and point formula we can calculate.

Q: +4z=8 and

A: The equation of the plane as, x+z=1orx+0y+z=1 Here, a1 =1,b1 =0,c1 =1. and x+2y+4z=8 Here, a2 =1,b2…

Q: Find b such that B = (0, b) has hyperbolic distance of u from the point A (0,0).

A: Given: B=(0,b) has  hyperbolic distance of u from the point A=(0,0) Formula used:

Q: 3. Show that every sphere through the circle x2 +y-2ax+r²=0, z=0 cuts orthogonally every sphere…

A: This is a co-ordinate geometry problem

Q: The distance from (10,-9,5) to yZ-plane is - 10 B.9 OC.5 OD. 206 OE. /106

A: We will find the distance between the point and the yz plane as following.

Q: Find the equations of the tanget plane and normal line to the graph of In(z2) x -= 3y³ – Vx at the…

A: Given graph is                                                        lnz2x-eyx=3y3-x Again…

Q: Use t = y to parametrize the part of the line of intersection of the two planes y = 2x – 4 and z =…

A:

Q: Find the shortest distance from the point (1, 0, −9) to the plane x + 2y + z = 9.

A: Given plane isx + 2y + z = 9and point (1, 0, -9)We have to find shortest distance

Q: 1. Find the Point the Plane X + 3y +27 = 6 that on %3D is nearest to the orig in.

A: To find- Find the point on the plane x + 3y + 2z = 6 that is nearest to the origin.

Q: Find the distance between the planes  5x − 3y + z = 5  and  5x − 3y + z = −9.

A: Two planes  and will always be parallel if The given planes  and  are parallel because we can see…

Q: Let S be the portion of the cylinder y = 1 − x2 with x≥0; y≥0, bounded by the planes z = 2, and z =…

A:

Q: 2 Let w = z². Find the image of the first quadrant in z-plane

A:

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.