Sſcos( dxdy y-x y+x D

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: Find the point(s) of intersection of the line x = 1 – t, y = t, z =1– 2t - and the paraboloid z = 8…

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Q: XZWY is a rhombus with diagonals XW and ZY intersecting at point M. Given YMX = 3p + 6, solve for…

A: diagonals of rhombus makes right angle at ntersection point

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: Find the coordinates of the point where the line F = (1+ 2t)i + tj – 2tk intersects the plane 2x – y…

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Q: A) || Jx2 + y2 dA , R is the disk x2 + y? < 9

A: We have to use polar coordinates here.

Q: Use Lagrange multipliers to find the shortest distance, d, from the point (1, 0, -2) to the plane x…

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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: Find the points on the cone z = x+y' that are closest to the point (-2,3,0) 22

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Q: Use Lagrance Multipliers, and find the point P(r, Y, z) closest to the origin on the plane 2x + y –…

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Q: find the trace of the plane in the given coordinate plane.  −x + y = 4, xz

A: Find trace of the plane in the coordinate plane -x+y=4 in xz

Q: V and Y are the midpoints of the legs, UW and XZ, of trapezoid UWXZ. If WX = 4t 8, VY = 4t 4, and UZ…

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Q: W and T are the midpoints of the legs, VX and UY, of trapezoid UVXY. If XY = -2p + 58, TW = 3p - 48,…

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Q: Apply Stoke's theorem to calculate S. (x + y – 4)dx + (2x – z)dy + (y + z)dz, where C is the…

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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,…

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Q: Evaluate fff(r +y²+y dV, "AP where 2 is the solid hemisphere (half of the sphere) enclosed by x +y…

A: Converting into spherical  coordinates

Q: W and Z are the midpoints of the legs, VX and UY, of trapezoid UVXY. If UV = p 15, WZ = p + 2, and…

A: Using mid point theorem of trepazium

Q: The line X=t, y+1=t, Z=t intersects the plane. x-2y+Z=2 at the point

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Q: Evaluate (y + Vx) dA, where R is the triangular region with vertices (0, 0), (1,0), and (0, 1). R

A: The solution starts from step 2. The information presented below will be helpful to understand the…

Q: Verify Green's theorem for Q7 [x(x? + y²)dx – y(3x² – y²)]dy Where C is the boundary of the triangle…

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Q: d counterclockwise as viewed from above. section of the plane x+z1 and the cylinder x + y? = 9.

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Q: C is the intersection curve between the paraboloid z=x²+y² and

A: Given that C is the intersection curve between the paraboloid z=x2+y2 and the cylinder x2+y2=1.

Q: Q3: Find the length of y=√x+2,1 ≤ x ≤ 7, Using ds = Y 04 1+²dy rotating

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Q: Use Lagrange multipliers to find the shortest distance, d, from the point  (1, 0, −2)  to the plane…

A: Lagrange Method:- The method of Lagrange multipliers is a strategy for finding the local maxima and…

Q: Find the coordinates of the point where the line F = (1+21)î + tĵ – 2tk intersects the plane 2x – y…

A: Let's find.

Q: 10. If ZYXW is an isosceles trapezoid with WY = 15x-2 and XZ = 9x + 10, find x. X 1 partn Z Y

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Q: e point on the plane x+y+z:

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Q: Find for the point P(x,y,z) on the plane 3x + y – z – 15 = 0 that is closest to the origin.

A: The distance of the point P(x,y,z) from the origin is: d2=x2+y2+z2 Now we have to minimize d if the…

Q: H.W: Find the point where the line y=-2t, 1+t intersects the plane 3x+2y +6z 6

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Q: Use Cartesian coordinates to evaluate JIJ y² dv D where D is the tetrahedron in the first octant…

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Q: x − 3y + 6z = 4 e 5x + y − z = 4

A: For the equation of plane a1x+b1y+c1z+d1=0, a2x+b2y+c2z+d2=0The angle between them is given…

Q: Let R be the triangle in the xy-plane with vertices (0,0),(0, 1),(1,0). Find C[n(2 – x – y) dA.

A: Given vertices of triangle now we have to find the area as shown below

Q: Find the points on the cone z 22 = x2 + y? that are closest to the point (-3,1,0)

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Q: 2. Trapezoid QRST with vertices Q(3. 1). R(5, 2). S(10, 0), and T(4, -3); 270° counterclockwise…

A: Procedure for rotating shape about a point ( not origin) 1). Subtract the point of rotation from…

Q: XZWY is a rhombus with diagonals XW and ZY intersecting at point M Given ZYMW 3p + 6, solve for the…

A: We have given a rhombus. We have to find the vaule of p from figure.  We know that diagonals of a…

Q: 2. Trapezoid QRST with vertices Q(3. 1). R(5. 2), S(10, 0), and T(4,-3); 270° counterclockwise about…

A: GIVEN Trapezoid QRST with vertices Q(3,1),R(5,2). S(10,0) and T(4,-3); 270 counterclockwise about…

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

A: When points are colllinear area should be 0Therefore, 12a01hk10b1=012ak1b1+1hkb1=0

Q: In ARST, SV bisects y ZRST. Find the coordinates of point T in terms of a. S (a, a) 2a T?, ?) V (2,…

A: Given that, Let ∠TSV=θ and ∠VSR=θ(∵SV is angle bisector)

Q: Use Lagrance Multipliers, and find the point P(r, y, 2) closest to the origin n the plane 2r +y-z-5…

A: Given,

Q: ƒ(x, y) = 4x - 8xy + 2y + 1 on the triangular plate bounded by the lines x = 0, y = 0, x + y = 1 in…

A: Given function f(x, y),f(x, y) = 4x-8xy+2y+1             ........................(1)Given conditions…

Q: ce cut from the first octant by the cylinder z = 12 – 3y, and the plane x + y = 2

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Q: Find the point on the line y = x closest to the circle of radius 1 and center (5, 2) using Lagrange…

A: First I have find the function f(x,y) and then decide the constraint.Then using Lagrange multipliers…

Q: Determine the location of a point (x, y, z) that satisfies the condition(s). xy &gt; 0, z = −3

A: Here Our Aim is to determine the location of a point (x,y,z) that satisfiesthe condition(s):→…

Q: Evaluate //R V2x(y – 2x)dA where R parallelogram on the xy-plane with vertices (0, 0), (0, 1), (2,…

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Q: Evalute ff Rx²dA, where R is the region in the first quadrant bounded by the hyperbola xy = 16 and…

A: The given integral: ∫∫Rx2dAWhere R is the region in the first quadrant bounded by the hyperbola…

Q: Evaluate dV, where E lines between the spheres a+ y + z = 9 and E 2 + y2 + z? x2 + y? + z2 = 16 in…

A: The answer is in step 2

Q: 9. f(z) = e'n/4z %3D

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Q: х2, у3D 12 — х, х 3D 0, around line y — -2

A: the function given to us is y = x2 and the line about which it revolves is y = -2 we have to use the…

Q: Let B be the ball with center at the origin and radius 1 SS $3(x² +y? + z²)dV = 16 12m 24m :5

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Q: WZ is the midsegment of the trapezoid UVXY. If XY = 6t, WZ = 10t – 2, and UV = 6t + 4, what is the…

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