Evaluate the line integral 3ydx + 6xdy where C is the straight line path from (1, 2) to (6, 5). Sc 3ydx + 6xdy =

Q: Evaluate the line integral 6ydx + 4xdy where C is the straight line path from (2, 3) to (5, 5). Jc…

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

A: Given that x=t,y=4-t,z=0 from (0,4,0) to (4,0,0) evaluate ∫cx+yds

Q: Evaluate the line integral 4ydx + 2xdy where C is the straight line path from (4, 2) to (8, 4).…

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Q: Determine the value(s) of k such that the lines 2y= -kx +6 and 3y-x= 2kx+3 are parrallel.

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Q: Evaluate each line each line integral. dx +(xy-x² )dy where C is the curve y = 9x from (0,0) to…

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Q: Compute yds ds where C is the line segment from (1, 2) to (4, 7).

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Q: wn is bounded by the line y = − 5x + 4, - -axis and the y-axis. y X

A: we will find the area.

Q: Integrate ƒ(x, y, z) = x - 3y2 + z over the line segment C joining the origin to the point (1, 1, 1)

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Q: The value of the line integral fydx + xydy over the straight-line path C from (0, 0) to (1, 2)…

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Q: If C is the line segment which begins at (-2, 1) and ends at (2, 4), evaluate the line integral: e+y…

A: Given, The line integral ∫Cex+yds Where C is line segment from the point -2,1 to the point 2,4 So,…

Q: Evaluate F- dr where F(, y, z) = (1.5yz cos(ryz), 1.5xzcos(ryz), 1.5xy cos(ryz)) and C (*) is the…

A: We need to evaluate the line integral between the two points.

Q: Let C be the line segment connecting the points P(−2,1,−4) and Q(5,−4,3). Evaluate ∫C(2x+4z)dy…

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Q: Sc 7ydx + 3z dy where C is the straight line path from (2, 4) to (4, 7).

A: The parametric equation of the straight line between the points (a,b), (c,d) is x-ac-a=y-bd-b=t,…

Q: Find the equ. nf line through the Pont (-2,3,4) and Parallel to Planes: 2X+3y +42=5 3X + 4Y+52=6…

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Q: If C is the line segment which begins at (-2, 1) and ends at (2, 4), evaluate the line integral: et…

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

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Q: Find a path c(t) that traces the line y = 2x + 1 from (1, 3) to (3, 7) for 0 ≤ t ≤ 1.

A: Given:

Q: Compute x²z ds where Cis the line segment from (0,6,–1) to (4,1,5).

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Q: Find K so that the line through( 1, 5 )and( K, 8) is a) parallel to 4y -3X =7 and b) perpendicular…

A: compute the equation of a line joining (1,5) and (k,8) by using below formula.

Q: Determine whether the work done along the path C is positive, negative, or zero. y O positive…

A: Consider that the sign of the work depend on the orientation of the path C. here the circulation can…

Q: Evaluate S(-x+y+z) dx + (x+y-3) dy + (x-y+z) dz where C is the line segment from (-1, 2, 3) to…

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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: Please see the explanation below

Q: Find the equations of the normal line to the surface z = 2x°y* at the point (2, 2, 256). y = 2 = -t…

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Q: By using the calculus of variations, prove that the shortest distance between two points in the y z…

A: The functionals with in the calculus of variations are of the form V[f(x)]=∫abF(x,y(x),y'(x))dx The…

Q: Find the veeton equation of a Line L going thagh the P= C-6,2) $ paeallel to the ine point %3D…

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Q: Determine whether the work done along the path C is positive, negative, or zero. y

A: The work done along the path C is

Q: The area bounded by the curve y= 4x and the lines r = 7,1 = 10 and x - aris is O 4900 square units O…

A: From the given curve bounded region is shown below:       So,   I=∫x=7x=10∫y=0y=4xdydx

Q: If ∆MNP is reflected across the line y = 2, then translated using the rule (x + y) → (x – 8, y – 1),…

A: We have been given the coordinates of the point P(7, 4) using the rule  (x + y) → (x – 8, y – 1).

Q: Evaluate S(-x+y+z)dx + (x+y-z)dy + (x-y+z) dz where C is the line segment from (-1, 2, 3) to (3,-2,…

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Q: Find the are bounded by the curve y=x²-4, the lines y=0 and x=4.

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Q: Let C be the line segment connecting 0 to ni. Then f. 1-e2z dz =

A: we have to find integration

Q: Let y = [3] and u = [2] to the line through u and the origin. Compute the distance from y

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Q: Find the per pendicualar olistace from the P (5,6) to the line -2xr+3Y+4=0.

A: Formula for perpendicular distance is as below : Given :-2x+3y+4=0Ax+By+C=0A=-2B=3C=4 Point  (m , n…

Q: The area bounded by the curve y = 4x and the lines r = 6 ,x = 12 and a – axis is 144 square units O…

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Q: Find the shortest distance from the origin to the line of intersection of the planes 2x + y − z = 1…

A: Given: The planes: 2x+y-z=1 and x-y+z=2.

Q: Show that the point (x0 , y0) closest to the origin on the line ax+ by =c has coordinates

A: Distance between x0, y0 and origin (0, 0) is, D=x0-02+y0-02D=x02+y02D2=x02+y02f=x02+y02…

Q: 13. XPOQY and AOB are straight lines. PO =0Q and 21 = L2. Prove that ZA = ZB. B. A

A: That's easy. Have a great day!!!

Q: Compute (x² + 2y + 3z +1) ds where Cis the line segment from (0, 2, 3) to (2, 5, 7).

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Q: Show that f(-ydx + xdy) where C is the line segment joining (x, y) and (x₂, y2).

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Q: show.. that. the line in.which. and. .5Xm2y.Z==.0. jntersect..is

A: Equation of the plane: - In three-dimensional space, a plane surface is represented by an equation…

Q: Let s(xy) = x²+y²_2x – 16y +10 =0 a cirdle be L (xy) = X-5y + 10=0 be a line.

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Q: Evaluate the line integral ∫Cx2yds along the segment of the line y=x from the origin up to the point…

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Q: O whion of the line: y--2x+8 Poliowing line5 ave perpendicular to this. B. ut

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Q: The area bounded by the curve y = 10z and the lines z = 9,7 = 11 and a – azis is O 1010 square units…

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Q: 5. Find the distance between the point (4, 3, 1) and the line f(t) = (2x - 1, –3y + 1, 2)

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Q: By using the calculus of variations, prove that the shortest distance between two points in the y z…

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Q: If C is the straight line from (1,1,1) to (2,1,2) find 2xlnzdx + 2y²zdy + y³dz.

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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.