7. Use Green's Theorem (and no other method) to show that the area of the triangle with vertices (0,0), (2,0), and (0, 1) is equal to 1.

Q: A natural cubic spline S on (0,2] is defined by Jsin - 1+2-r. S) = if Osr<l. |S,0) = 2+ b - 1) + cư…

A:

Q: For numbers 1-2, consider a plane bounded by the curves y=9-x² and y=x+3. 1. What is the desired…

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Q: Sketch the triangle with vertices O, P = (0,7, 3) and Q = (7,4,0) and compute its area using cross…

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Q: (15) Let D be the half-disk x² + y? 0. Compute / | (a + y) dA D

A:

Q: Evaluate the line integral S 3ydx + 6xdy where C is the straight line path from (1, 2) to (6, 5). So…

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

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Q: 47. Sketch the triangle with vertices at the origin 0, P = (3,3,0), and Q = (0, 3,3), and compute…

A: The triangle OPQ formed by the three points P (3, 3, 0), Q (0, 3, 3) and origin O (0, 0, 0) is shown…

Q: The value of the triple integral 6zdV where E is the upper half E of the sphere of x² + y? + z? = 1…

A:

Q: Q4) Using Green's theorem to evaluate: (12 marks) Sc [ (x3 – xy³)dx + (y³ – 2xy) dy] Where C is the…

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Q: Find the minimum distance from the point (8, 3, 4) to the plane x - y + z = 4. (Hint: To simplify…

A: Let ax+by+cz+d=0 is a plane  Then distance from the  a point (xo,yo,zo) is D= |axo +byo +czo…

Q: Suppose surface #1 is defined by o =45° , 0 <ps9, 0 < z< 6 and surface #2 is defined by 0 =56.3° The…

A: given:

Q: 5. Find the area and centroidal distances of the curve that lies between he equations y%3D4-x^2 and…

A: The region bounded by curves y=4-x2andy=x+2 To find the area and centroidal distances.

Q: 44. Use the cross product to find the area of the triangle with vertices P = (1, 1, 5), Q = (3, 4,…

A: If triangle T spanned by two non zero vectors u, v Then the area of the triangle is given by…

Q: 6. Let ABCD be a trapezoid with bases BC and AD. A line passing through the vertex C and parallel to…

A: Given, ABCD be a  trapezoid with bases BC and AD.

Q: If R is the region boundeb by the square a|+|y = 1 then ffR(y-2)dA is equal

A:

Q: The base of a three-dimensional figure is bound by the line y = x +2 on the interval [0, 4].…

A: Let's find.

Q: The intersection between the surface x + y + z = - 1 and the circle x2 + y2 = 1,z = 0 is

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Q: 1) Prove that A is uniform pentagon and B is a half of a circle, also determine the areas of A & B.…

A: Here I am attaching image so that you understand each and every step. solutiongiven data (Let…

Q: 3) Prove that A is uniform pentagon and B is a half of a circle, also determine the areas of A & B.…

A: Here I am attaching image so that you understand each and every step.

Q: 1. Carefully prove the theorem: The sum of the distances from any interior point P to the sides of…

A: I will solve the first one only if you want remaining solution then repost it again qith mention the…

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: (6) I. adv, where E is bounded by the planes z=0, y = 0, =0, y+= =1 and +=1, as shown in the figure…

A: Given that,

Q: Show that, in the triangular region with vertices (0,0), (1,0) and (1,1) the following double…

A: Double integral

Q: Find the points on the cone z2 = x2 + y2 that are closest to the point (2, 2, 0).

A:

Q: 2. Find the area of the plane region bounded by y = 3x + 1, x = 1, x = 3,and the x-axis. y y = 3x +…

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Q: 1. A such that the difference in distances between (x, y) and two fixed points (called is the set of…

A: A___ is the set of points (x, y) in a plane such that the difference in distances between (x, y) and…

Q: 1. Find the area of the part of the planer+ 2u + 3z = 1 that lies inside the cylinder x2 + y? = 3.

A:

Q: The base of a three-dimensional figure is bound by the circle x² + y² = 9. Vertical cross sections…

A: Given circle x2+y2=9. The objective is to find the area of each triangle.

Q: Let C be the positively oriented square with vertices (0, 0), (3, 0), (3, 3), (0, 3). Use Green's…

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Q: 4. A 5m x 5cm is cut from a corner of 20cm x 30cm. cardboard, find the centroid from the longest…

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Q: The base of a three-dimensional figure is bound by the line x = y² and the y-axis on the interval…

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Q: 10) Use Green's Theorem to eualuate S+10ny +y?)dx + l6xy+ 5a²) dy Toxy+ sa?) dy where C is the…

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Q: 23 +3 Evaluate the integral dz, where C is the circle (a) |z + 3| = 3, (b) |z| = 3, (c) |z| = 7. 22…

A:

Q: 3) Prove that A is uniform pentagon and B is a half of a circle, also determine the areas of A & B.…

A: It is asked to prove the given pentagon A is uniform and B is half of a circle.

Q: 2.5 What is the distance between two parallel hyperplanes {x E R" | a"x = b} and {x E R" | a"x =…

A:

Q: 3] By using the properties of dot and cross product, prove the following: a) (w x i). ū = 0.

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Prove that (x+) ) is the rolution on the dipporen tial equation y'+ y-e 9= C,e*+ C2x + Cg, y" - 4 y"…

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Q: can u help me with pullbacks and integration plz

A: Given that the integral,

Q: 8. Evaluate the double integral // ydrdy where T is the triangle with vertices (0,-1), (0,5), (4,…

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Q: What is the shortest distance from the surface xy+3x+z^2=12 to the origin?

A: Let (x ,y, z) any point on surface. We have to minimize function f(x,y,z) = x2 + y2 + z2 under…

Q: 13-Evaluate JJI zdV E where E lies between the spheres x2 + y? + z2 = 1and x2 + y? + z? = 4 in the…

A: The given integration is , Let, I=∫∫∫EzdV change the integral into spherical coordinates Put x=r…

Q: 6. Find the area and centroidal distances of the curve that lies between the equations y-4-x^2 and…

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Q: Findd Fhie boundled by Ahe Cureo area 2. X= 3J-y' and x+Y=3 ーレ

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Q: 8. Use Green's Theorem to evaluate px*dx+xydy where C is the triangle with vertices (0,0), (1,0),…

A: As we know from the Green's theorem: ∫CMdx+Ndy=∫∫R∂N∂x-∂M∂ydA And The expression for the equation of…

Q: Sketch the solid described by the given inequalities. Oses n/2, r szs4

A: We have given that 0≤θ≤π2 &amp; r≤z≤4

Q: 3.use Greens theorem s (1+x5 dx + 2xy dy ,where C is triangle With vertices (0,0),(1,0),(1,3)…

A: Apply greens theorem

Q: Find the points on the cone z2 = x² + y2 that are closest to the point (8, 2, 0).

A: we have given the equation of cone z2=x2+y2 and the point (8,2,0)to…

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: Prove that if 0 < x < 2r, then a circle of radius r has a chord of length x. (You can do this using…

A: According to given ,only 1st solved....Radius of circle = r