The length of the line segment described by (x,y,z)=(1,2,1) +t(-1,5,1)), where 0

Q: 19. f(x, y) = x + y+y+ 1, constrained to the triangle with vertices (0, 1), (-1,–1) and (1, +1). %3D

A: As per bartleby guidelines i can answer only one question, kinldy upload rest questions separately.…

Q: Find the line integral / ( + y) 7 +y 7 ). d 7 where C consists of the three line segments from (7,…

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Q: [E] Given that u 5zy? ,Ez, Ey and ɛ, denote the errors in æ, y and z respectively such that a = y =…

A: Using differential.

Q: Evaluate S. F dr where F(x, y, z) = e'i+ (xe + e²) j+ye²k and C is the line segment from (0, 2, 0)…

A: answer is in next step

Q: fc (y+z) dx (x+z)dy+ y2 dz, C consists of line segments from (0,0,0) to  (1,0,1)  and  (1,0,1)  to…

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Q: The figure below shows contours of g(x, y) on the region R, with 3 < x <9 and 4 < y < 10. 10 1 2 3 6…

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Q: The absolute minimum of f (x, y) = x² +y² – 2y on the semicircle region D= {(r,y) | y> 0, x² + y? <…

A: Given function is fx,y=x2+y2−2y and D=x,y|y≥0,x2+y2≤4. We have to find the absolute minimum of fx,y…

Q: An area of a region bounded by a curve y = f(x), x axis and lines x = a and y = b for (b > a) may be…

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Q: he area bounded by the curve y = 3Vz and the lines z = 5 and z = 9 above the r – aris is_ quare…

A: Find the area of bounded curve with line x=5 and x= 9 above x-axis

Q: Find the length of the curve y = x³/2 from x = 0 to x = 5. O 12.407 O None of these O 14.702 O…

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Q: Let M and m be the maximum and minimum values of Ax, y) = 5x + 4y on the region x +y < 49 . Then…

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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: The medians of ATUV are TX, UY, and VW. They meet at a single point Z. (In other words, Z is the…

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Q: The area bounded by the curve y= 3va and the lines z = 3 and T = 8 above the z- aris is square units…

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Q: of the valve matix is consistant e an linear

A: Given augmented matrix is: -412h2-6-3 Let the variables be x, y. The above augmented matrix will…

Q: If C is the line segment from (1, 3) to, (0, 0), find the value of the line integral: 3y i+ 3x j) ·…

A: Given If C is the line segment from (1, 3) to, (0, 0),

Q: 6. Let f(r, y, z) = e=² cosh y + z ar ff at the point P in the direction of :

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Q: Evaluate the line integral ∫c x3 z ds, where C is the line segment from (0,8,8) to (5,7,6).

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Q: 30. Find the shortest distance from the point P(0, 1, – 1) to the line (x, y, z) = (1, 1, 0) + t(1,…

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Q: 38. Calculate y = x, x = 0, and x = 1. || e* dA, where D is bounded by the lines y =x +1,

A: We have to find ∫∫D ex dA, where D is bounded by the lines y=x+1, y=x, x=0 and x=1

Q: The value of the integral (inage 1). where C is the closed curve 4x2 + 5y2= 7, 3x + 2y − 9z = 5.

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Q: 4. Prove that fer*dr+xydy = f, So*(y– 0)dydr where C is the triangular curve consisting of the line…

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Q: Compute Δy and dy for the given values of x and Sketch a diagram showing the line segments with…

A: Given: Now,

Q: Evaluate x*dx C + xy dy, where C is the triangular curve consisting of the line segments from (0, 0)…

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Q: Evaluate ||| Vx2 + y2 dV, where E is the region that lies inside the cylinder x2 + y? = 25 and…

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Q: || x dA, R is bounded by y = x, 2x + y = 6 and the y-axis. R

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Q: The length of the curve that results from the intersection of r = 1,0 <0 < T,0 < ¢ < 0.5n, with 0 =…

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Q: f(x, y, z) = xe z2, piecewise linear path from (0, 0, 1) to (0, 2, 0) to (1, 1, 1)

A: To Determine: calculate ∫cxez2dx Given: we have piecewise linear path from (0, 0, 1) to (0, 2, 0) to…

Q: a) Evaluate the line integral S. (2x – y) dx – (x + 3y) dy, where C is a straight line from (1,1) to…

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Q: Suppose that a thin metal wire in the shape of a semicircle occupies the curve C, where C is the top…

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Q: The length of the curve y = (2+ 2x )3/2 between x=0 and x=2 is O 41/3 O 45/2 O 43/2 O 47/3 49/6 ООО…

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Q: a) Find the length of the given curve: x = (y³/3) + 1/(4y) from y = 1 to y = 3 %3D b) Find the area…

A: a) given curve isx=y33+14y from  y=1,  y=3 find the length the curve  b) f(y)=4-y2, x=0 find the…

Q: Check the deviation theorem for the function v(x, y, z) = r²sin0 î + 4r²cos0 Ô + r?tan0 @

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Q: The distance between the two lines x = 1+t,y = -2 + 3t, z = 4 -tand x 2s, y = s, z = s is a) 1/2 b)…

A: Please see the explanation below

Q: If C is the line segment from (1, 5) to, (0,0), find the value of the line integral: So(4y? i + 4x…

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Q: Calculate (y+z)dx+ (x+ z)dy+ (x+y)dz , where C consists of line segments from (0,0,0) to (3,2,4) and…

A: We will use parametric equation of lines to find the integral

Q: Given 급 (1+ 블" -를 -용), dy * = k). What is the value of k such that y is perpendicular to the curve…

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Q: Evaluate the line integral ∫CF⋅d r where F=⟨2sinx,3cosy,xz⟩ and C is the path given by…

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Q: Evaluate (x+y)ds where C is the straight-line segment x =t, y= (2- t), z =0 from (0,2,0) to (2,0,0).…

A: We need to evaluate ∫C(x+y) ds. We are given that C is the straight line segment x=t, y=2-t, z=0…

Q: Find the distance between the skew lines defined by L1:(t) = L2: r2(s) =

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Q: Compute the length of the curve r(t) = (2t, In(t), t² ) over the interval1<t < 4. (Use symbolic…

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Q: The value of $ (2xy - x²)dx+ (x+y²)dy, where C is the enclosed curve of the region bounded by y=x²…

A: As we know from the Green's theorem: ∫CMdx+Ndy=∫∫R∂N∂x-∂M∂ydA   I=∮2xy-x2dx+x+y2dy And C: y=x2, y2=x…

Q: Compute the length of the curve r r(t) = (2t, In t, t²) over the interval 1 < t < 3 L =

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Question 15 Find the distance from S= (1,1,5) to the line L: x=1-1, y=2-t, z=31.

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Q: 11. Find the distance between the point (1,0,-1) and the line x = 5 – t, y = 3 t, z = 1 + 2 t.

A: 11) The direction ratio of the lines  = -1,3,2 The direction ration of the point (1,0,-1) and the…

Q: a) Evaluate the line integral S. (2x - y) dx – (x + 3y) dy, where C is a straight line from (1,1) to…

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Q: If y (x, y, z) = x² + y? + z² and A (x, y, zis perpendicular to Vy (x, y, zeverywhere, wh…

A: Perpendicular vector field

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.