Ex: Find the area of the triangle with vertices P(1,-1,0), Q(2,1,-1) and R(-1,1,2). Area of the parallelogram= |PQ x PR| = 16i + 6j| = v62 + 62 = 6v2 %3D Area of a triangle= area of parallelogram = (6v2) = 3V2 %3D

Q: •ff yo y(x - y)dxdy over the parallelogram with corners (0,0), (3,3), (7,3), and (4,0) in two ways:…

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Q: Find the endpoints points of the lactus rectum for (y-3)^2=8(x+1)

A: Given problem:- Find the endpoints points of the lactus rectum for (y-3)2 =8(x+1)

Q: f (x, y) = x² + y² – 2x, D is the closed triangular region with vertices (2, 0), (0, 2), and (0, –2)

A: According to the given information, it is required to find the absolute maximum and minimum values…

Q: 33. Which of the following has an axis of symmetry of x = 8? mra. y = (x + 4)2 b. y = x2 – 8x + 16…

A: 33. Axis of symmetry of y=ax2+bx+c is x=-b2a

Q: 8. , (2x – y) dA, where R is the region in the first quadrant enclosed by the circle x? + y² = 4 and…

A: Dear bartleby student ,According to bartleby rule Answer the first question, unless the student has…

Q: 24 dA - I 3x – Y when D is the parallelogram bounded by x – 2y = 0, x – 2y = 2, - and Зх — у 3D 1,…

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Q: 7. If WXYZ is an isosceles trapezoid, and WX and YZ are the legs. XY is the base. And WX = 6x-5, YZ…

A: In isosceles triangle length of legs is equal

Q: 2. Consider any five points P1, Ps in the interior of a square S of side length 1. Show that one can…

A: To solve this problem we use the Pigeonhole principle . Pigeonhole principle : If there are m holes…

Q: Of the Sollds gene by Volving the regions Doundeu by graphs of equation given iines. y = 3x2 y = 0 X…

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Q: 2. Consider any five points P1, Ps in the interior of a square S of side length ... 1. Show that one…

A: Since you have asked multiple questions here, we will solve the first question for you. To get the…

Q: 3) Point R bisects XY. If XR=4n and YR=6n-9, what is the length of XY?

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Q: F = (-3y, 3x); R is the triangle with vertices (0, 0), (1, 0), and (0, 2).

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Q: Find b and c so that y 6x? + bx + c has vertex (2, – 3). b c = ||

A: Compare with standard equation of parabola then solve

Q: (d) [[x - y dA where R is the triangular region with vertices (3, 10), (3, 0) and (-2, 0).

A: Use double integral

Q: Determine the equation of the perpendicular bisector of KL if it's endpoints are at K O-7,5) and…

A: Given:    Points : K ( 7 , 5 )    ,   L ( 9 , 1 )

Q: (x² +2y) where D is the triangular region with vertices (0, 1), (1,2) and (4,1).

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Q: JK in the coordinate plane has endpoints with coordinates (-4,11) and (8, -1). Find all possible…

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Q: Q3. Find the distance between the points AB and BC where A is (2,1,0), B is (-1,3,1) and C is (-1,…

A: The points A2,1,0, B-1,3,1 and C-1,0,1 we have to find the distance between the points AB and BC…

Q: The coordinates of the vertex are......................... .

A: Given,

Q: Apply T (x, y) = (2x/3,2y/3) to the following pentagons: (a) vertices (3,-3), (3, 3), (0, 6), (–3,…

A: Now in T(x,y)=(2x/3,2y/3)=(x/1.5 ,y/1.5) so by apply T(x,y) we are expecting that our pentagons area…

Q: 4. Determine whether the pair lines are equal, parallel but not equal, skew, or intersecting. L1:x =…

A: Given:      L1:  x=1-4s, y=3+s ,z=8-6s      L2: x=2+3t ,y=2t ,z=-1-3t   For Parallel test:…

Q: (10x + 10y) dA, where R is the parallelogram with vertices (-1, 4), (1, -4), (4, –1), and (2, 7) ; x…

A: Assume that L1 is the line connecting (-1,4) and (1,-4) then the equation of the line connecting…

Q: Part (a) Evaluate 4e*dz, where C is the polygonal path consisting of the line segments from z = 0 to…

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Q: AHGF is equilateral. a If ZF solve for x and find mzG. H. (x + 32)° and ZH = (2x + 4)°, %3D %3D b If…

A: We use the result , Perimeter of equilateral triangle is = 3 times side of triangle

Q: How many circles touch the x-axis and the y-axis and pass through the point (2,1)? Select one: a.…

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Q: Find the point on the plane 3x + 4y + z = 8 that is nearest to (2,0,1). What are the values of x, y,…

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Q: Find the points on the cone z2 = x² + y² nearest the point P(6,8,0).

A: Here, we need to find the points on the cone z2=x2+y2 nearest the point P(6,8,0).

Q: -62-y Find dA, where R is the parallelogram enclosed by the lines -3x +y R - 6x – y = 0, - 6x – y =…

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Q: 3. Triangle DEF with vertices D(0, 6). E(3.5), and F(1, 1): 90° counterclockwise about the point…

A: Rotation is a rule of transformation. Through this transformation, one can produce a new image by…

Q: 4. Determine whether the pair lines are equal, parallel but not equal, skew, or intersecting. Lị:x =…

A: Recall: Given two lines  L1:  x1=a1+b1s  , y1=c1+d1s   , z1= e1+f1s  L2:  x2= a2+b2t  , y2=c2+d2t…

Q: The region S = (x, y (x- 2) + y² < 4 is rotated about the line x = 5.

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Q: 1. Find the value of x if R is the midpoint of OS, QR = 5x - 7, and QS = 96. %3D

A: It is given that R is the midpoint of QS and it is also given that QR=5x-7.

Q: Which figure has the GREATEST area? y. -7- P. Q. K M 3- R .-9.-7-5 -3 -1 -3 -5 9. 3- -5- O A. kite…

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Q: c. Find the distance from Po = (3,9, 6) to the plane 3.x + 4y – 5 = 0.

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Q: Hw-2 If A(X, -2,0),B(-lel,=3)_, C(-4,ile2)_and D(3,0,0)are-points-in Slace thenfind value that…

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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 Line in the plane of the points the PCO 10,0) ,Q (e,2,0) and R Coul,-d thal- passes through Q f…

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Q: 10 X- 3y dA, where R is the parallelogram enclosed by the lines x - 3y = 0, x - 3y = 5, 8x - y = 5,…

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Q: I need help w/ following integration by pullback

A: Given that R be the parallelogram with the vertices at (1,0), (3,1), (4,4), (2,3). And…

Q: (b) Find the area of the triangle whose vertices are A(0,0,0) ; B(1,1,1) and C(0,2,3). 1 (C) Find…

A: Given (b) The vertices are A0,0,0, B1,1,1, C0,2,3 c(1) y=1x2-1 c(2) y=9-x2

Q: (b) Find the area of the triangle whose vertices are A(0,0,0) ; B(1,1,1) and C(0,2,3). 1 (C) Find…

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Q: 6. trapezoid DEFG with vertices D(0,-3), E(1, 3), F(3, 3), and G(4,-3) in the y-axis ty O X D' =_ E'…

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Q: Find the shortest Distance d faumthe point to the plane X+y+Z=8.

A: Let's find.

Q: 2. Find ffR(2r – y)dA, where R is the region in the first quadrant enclosed by the circle r² + y² =…

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Q: i = 1 , where r is square with vertices at z=0 , 1+i , cs (z) dz 1+i 0 10 i0

A: Option (c) 1 is correct.

Q: Trapezoid ABCD with AB | DC; also, M and N are midpoints of AD and BC, respectively a. Given: AB =…

A: AB=7x+5, DC=4x-2 MN=5x+3

Q: V. Use the method of Lagrange multipliers to find the points on the circle x² + y? = 10 which are…

A: Solution of given problem is followed by

Q: To describe the triangular region whose vertices are (0,0), (2,2), and (-2,2) we use the following…

A: We have to describe the triangular region whose vertices are 0,0,2,2 and -2,2