Question 1 The value of the line integral (x²ydx + 2y2dy), where n is the square with vertices (0,0), (1,0), (1,1) and (0,1), correct to ONE decimal place will be . . ...

Q: 1. The plane containing the point (1,-5,8) and orthogonal to the line given b x=-3+15t, y=14-t,…

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Q: 4. For what value of h is vz in Span {v, v2} and for what value of h is {v1, V2, V3} linearly…

A: v1=1-32, v2=-39-6 and v3=5-7h

Q: Find the shortest distance between the lines i-(i+2j+k) + 2(i-j+â)and 7= 2i - j-k + 4(2i + j+ 2k)

A: The equation of the given lines are r→=i^+2j^+k^+λi^-j^+k^r→=2i^-j^-k^+μ2i^+j^+2k^ It is known that…

Q: Let C be the positively oriented square with vertices (0, 0), (2, 0), (2, 2), (0, 2). Use Green's…

A: Introduction: According to Green's Theorem, a line integral of a vector over a closed curve C…

Q: Let L be the line passing through the point P(-1, -3, -2) with direction vector d=[-1, 1, 1]T. Find…

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Q: 1. Let F(x, y,z) = (x + y², y + z²,z + x²). Let C be the triangle with vertices (1,0,0), (0,1,0),…

A: Consider the provided question,

Q: only part b

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Q: 5. Evaluate the integra 21-dA, RZ-3y %3D where R is the parallelogram enclosed by the lines 2r-y 0,…

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Q: The area bounded by the curve y3a and the lines z 4 and a-9 above the z-azis is aquare units O 27v0…

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Q: Let C be the boundary of a rectangle with vertices (0, 0), (-1,0),(-1,5) and (0, 5). Then ve dx +…

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Q: e point of intersection of the lines [4 0] and

A: As per our guideline we are supposed to answer only one question. Here question 8. answered.

Q: Evaluate (x + y)ds where C is the straight-line segment x = 4t, y = (12-4t), z = 0 from (0,12,0) to…

A: Let  where C is straight line segment  from .We know thatwhere

Q: Evaluate ▼ (x² y + x y z²) ·dr where C is the line segment from ( 1, – 1,0) to (2,1,3 Select one: a.…

A: Given integral is

Q: The vertices of AJKL are J(-3, 4), K(3, 0), and L(-5, -4). The equation of the median JLis y = 0.…

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Q: 9. In triangle ABC, point E (5,1.5) is the circumcenter, point H (4.3, 2.3) is the incenter, and…

A: Solution:- The given triangle is  E(5,1.5) be the circumcenter of the circle. then, we have to find…

Q: 3. Evaluate the line integral (3ry² + 6y) da, where C' is the path traced by first moving from the…

A: The given problem is to evaluate the given line integral of (3xy2+6y) over the given path C which is…

Q: 4. Using two methods find the point point P = (5, 4, 4) on the plane x +y + z = 4 nearest the %3D

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Q: 2x+y 5x+6y Find [/02/53 -dA, where R is the parallelogram enclosed by the lines R 2x+y=0, 2x+y=9,…

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Q: - ARŞT is drawn on the coordinate plane. The coordinates of R are (0, 6). The coordinates of S are…

A: We need to find the third coordinate of triangle such that the area is 6 sq units.

Q: Let C be the positively oriented square with vertices (0, 0), (3, 0), (3, 3), (0, 3). Use Theorem to…

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Q: where Dx = X₁-X₂ and Dy = |Y₁ — Y2]. Assume that the two locations are independent and uniformly…

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Q: J₁ R - x + 3y = 0, x + 3y Round your answer to 4 decimal places. Find - x + 3y -dA, where R is the…

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Q: Suppose ABC- > LMN is a reflection across the line x = 0. If A(4, 4) what is the y coordinate of L?

A: Suppose ABC- > LMN is a reflection across the line x = 0. If A(4, 4) what is the y coordinate of…

Q: Find the angle between the following pair of lines: £ =2? =5] +k + 2(3 + 23 + 6k) and = 7i — 6k +…

A: A vector in the three dimensional space is represented by v=ai∧+bj∧+ck∧, where a, b and c are the…

Q: Evaluate √ zdz xdx + xydy + (x+z)dz where C is the line segment from (3, 1, 3) to (4, 2, 2).

A: First we calculate the line segment between two point and convert x,y,z variable to one variable t.…

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.