Find the area of the polygon PQRS with its vertices at P(1, – 1), Q(6, -1), R(6, -6), and S(1, -6).

Q: Exercise 1. Find the area of the polygon in R³ with corners (3, –4) (-7, 7), (5, 5), (–5, –6) and

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Q: 27. Find the area of the parallelogram with vertices A (-3, 0), B (-1, 3), C (5, 2), and D (3, –1).

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Q: What is the coordinate for a point M such that ST is partitioned in a 1:2 ratio? ++++ -5-4-3-2-1 0 1…

A: The explanation of answer as follows

Q: Find T, N and k for the spacecurves:

A: We have to find Unit Tangent Vector T,  Unit Normal Vector N and Curvature K for given space curve…

Q: 11. If BX is the bisector of LABC. LABX = (4x + 12)' and LXBC = 24°. Sketch an image and then se for…

A: Given,          If BX→ is the bisector of ∠ABC. ∠ABX=4x+12° and ∠XBC=24°.

Q: Find 3xyd A A over the triangular region D with vertices (0, 0) (2, 0), (0, 4)

A: Given ∫∫3xy dA Over region (0,0)(2,0)(0,4)

Q: #S. A is a 3x3 triangular matrnx with all = 2, azz= 3, ag3=4, I will represent the 3x3 idontily…

A: We have to find the determinat of A-I.

Q: Find –3xyd A over the D triangular region D with vertices (0, 0) (2, 0), (0, 4)

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Q: snip

A: Given Parallelogram vertex।  A(1,1,1,1)  B(2,3,4) C(6,5,2) , D(7,7,5) Area = ∥AB ×AD∥ AB =…

Q: Find the perimeter of isosceles ACAT if M and W are midpoints. A 3x 2x + 2 M W y – 2 2y T

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Q: Find -6xyd A over the D triangular region D with vertices (0,0) (2,0), (0, 4)

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Q: Evaluate efffxv xdv,where D is the tetrahedron with vertices (0,0,0), (2,0,0), (0,2,0) and (0,0,2).

A: Given problem:- Evaluate  ∫∫∫D xdv ,where D is the tetrahedron with vertices (0,0,0), (2,0,0),…

Q: 2 Find the volume of the parallelepiped whose edges are represented by A=i-13j+ 4k, B = 31+2j-7k and…

A: Given A→=i-13j+4k,  B→=3i+2j-7k and C→=i-2j+2k

Q: Find midpoint M of P,P2, which joins P1(5, -7, 2) and P2(2, 5, 6), as shown in Figure 10.46 of…

A: Formula used : Mid-point formula Mx1+x22,y1+y22,z1+z22 Here (x1,y1,z1) and (x2,y2,z2) are the end…

Q: ZA'B'C' is the image of LABC following the reflec- tion of ZABC across line (. If mZA'B'C'= + 20 and…

A: Given: m∠A'B'C'=x5+20, m∠ABC=x2+5 We know that when we take reflection of a triangle across any line…

Q: Find the point E that partitions the directed segment CD in a ratio of 1:5, given the points C(4,-2)…

A: Given that the line segment  CD is cut by a point (x, y) in the ratio 1:5given that points C(x1, y1)…

Q: Find the values of a, b, c, d, e, f, g and h such that ax, S(x) = { 6(x – 2)³ + c(x – 2)² + d(x – 2)…

A: GivenS(x)=ax3,0≤x≤2b(x-2)3+c(x-2)2+d(x-2)+e,2≤x≤3f(x-3)3+g(x-3)+h,3≤x≤4such that S(x) is a natural…

Q: The diagonals of square MNOPMNOP intersect at Z.Z.  If MZ=2x+6MZ=2x+6 and NP=6x-10,NP=6x−10, find…

A: Geometry question

Q: Which of the following points is at a distance of 5V2 from the origin. * O (0,0) O (5,0) O (5,5) O…

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Q: 1. If C₁ is the segment from (x₁, y₁) to (x2, y2), find Ja x dy - y dx in terms of the four…

A: Using Green 's theorem line integral to double integral

Q: 2. Show that the points A(2,2,2), B(2,0,1), C(4, 1, – 1) and D(4, 3,0) are coplanar and that they…

A: The solution are next step

Q: - Show that the area of the triangle whose vertices are the [x1 yi det X2 Y2 A - points (x₁, y₁),…

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Q: The diagram shows a convex polygon. 3y 103° 2y 135° 72° What is the value of y?

A: find the value of y

Q: If BX is the bisector of <ABC Then ___=____

A: We know that if BX is the bisector of ∠ABC then ∠ABX=∠CBX

Q: The diagram shows a convex polygon. 129° 6z 77° 150° What is the value of z?

A: Sum of all the interior angle of a Pentagon =540

Q: Find the area of JEN if the coodrinates of the vertices are J(0,3) E(6,0), and N(8,3)

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Q: Evaluate O xy?dx + x5dy, where C is the rectangle with vertices (0,0), (6,0), (6,4), and (0,4)

A: Answer and explanation is given below...

Q: The triangle that has vertices at M(-4, 0), N(3, –1), and Q(2, 4) has been boxed in, as shown. Find…

A: Given the vertices of  the triangle M(-4,0) , N(3,-1) and Q(2,4). We need to find the area of…

Q: Find the area of the polygon PQRS with its vertices at P(1, – 1), Q(6, –1), R(6, -6), and S(1, -6).…

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Q: Find the areas of the triangles whose vertices are given A(-1, -1), B(3, 3), C(2, 1)

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Q: What is the area of the parellelogram ABCD if the coordinates of the vertices are A (5,0), B (8,2),…

A: Explanation and solutions is given below....

Q: 5) Identify the segment bisector of S a) x+ 12 Bx-2

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Q: Use the side-splitter theorem to solve for a in the triangle below. 2 22

A: Given triangle is : To find the value of x

Q: In a square ABCD, where does the vertex A go if a refection with respect to the diagonal BD is…

A: Let square ABCD be as the diagram given below

Q: what is the area of ABC with vertices a (4, 1), b (2,-1), and c (-2, -1)?

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Q: If the vertices of a polygon in counterclockwise order, are ( x1, y1 ) , ( x2, y2 ) , ... , ( xn, yn…

A: Here we use the formula for find the area of the triangle

Q: Find the area inside the inner loop of r = +5 12cosθ .

A: Given equation as r=5+12cosθ

Q: Find ff 3xydA over the triangular region D with vertices (0,0) (2,0), (0, 4)

A: We will solve the problem

Q: (a) Find the area of the parallelogram spanned by u -1 and i =

A: Area of parallelogram spanned by two vectors u→, v→ is the magnitude of the cross product of the…

Q: A triangular frame, AXY, is leant against a wall as shown in the diagram. ZXAY= 90° and ZCAY= 0°,…

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Q: The diagram shows a convex polygon. 97° 2z 83° 2z What is the value of z?

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Q: Find the area of the parallelogram with vertices (0,0), (4,0), (5,2) and (1,2). (1,2) (5, 2) (0,0)…

A: Here, we need to find the area of the given parallelogram.

Q: Find the value of y in polygon JKLM. A 4y° K 4y° 6y

A: Sum of All angles subtended on a straight line = 180 Sum of all angle of any quadrilateral =360 Sum…

Q: ■ Show that the area of the triangle whose vertices are the [X1 У1 points (x₁, y₁), (X2, Y2) &(X3,…

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Q: A natural cubic spline is defined by [a, (x – 1)' + b, (x – 1)² +c, (x – 1) + d, f(x) = if 0<x<1 (x…

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Q: (a) If C is the line segment connecting the point (x,, y,) to the point (x,, Y½), find the…

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Q: 29. Find a formula for the area of the triangle whose vertices a 0, V1 , and v2 in R².

A: Given that  Vertices of the triangle is 0,v1,V2  To find the area of the triangle

Q: Find the area of the parallelogram with vertices  A(−3, 5), B(−1, 8), C(3, 6), and D(1, 3).

A: We first have to find the AB and BC vectors. A(−3, 5), B(−1, 8), C(3, 6)AB=(-1 -(-3) , 8-5)…

Q: Let fa) = x -1E Zs CxJ, wrte fX) as a produt of ireduclble polynomias as Zg.

A: Answer