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

Q: Find the distance between the planes 5x − 3y + z = 2 and 5x − 3y + z = −3

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Q: aber of linearly 1 is

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Q: Find the point at which the line f(z)= 5z + 21 intersects the line g(z) = - 2z -7 %3D -2 11 Submit…

A: To find the intersection point of the lines f(x)=5x+21 and g(x)=-2x-7.

Q: Find the parabola y= ax2+bx+c that passes through (2,1) and be tangent to the line y=2x + 4 at (1,6)

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Q: Find the equation of the line tangent to Y 3x2 + x + 1 at x = -3. у 3 —17г — 26 O y = 6x – 3 O y =…

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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: Parallel to x + 2y = 0; (1, 2) on line

A: To find the equation of line paralley to x+2y=0 and (1,2) is on the required line.

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

A: we will find the area.

Q: The antiderivative of a constant is the family of lines.

A: Let y = mwhere m = constant

Q: 1. Determine whether the lines L₁ given by z=t, y=1 with -∞ <t<∞o) and L₂ given by z=2+s, y = 3-2…

A: Introduction: If two lines are parallel then the ratio equality is true between them. And if two…

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: Find the orthogonal trajectories for the family of curves y=c1x4

A: First of all rearrange the given equation in such a way that both the variables be on one side of…

Q: Find the condition that the line ax+by =1 may be normal to the curve an-1y =xn

A: Given thatan-1y =xn Solution is as follows

Q: Find equations for the lines tangent and normal to the cissoid of Diocles y (4 – x) = 9x° at (2,6).

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

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Q: Find the shortest distance from the point (2,0, –3) to the plane x + y + z = 1.

A: This is a problem related to geometry part. Based on the concept of plane and point we will find the…

Q: Evaluate the length of the curve x = 6 – Vy – 2 , 3< y<6

A: To find the length of following curve  x = 6 - sqrt( y - 6) 3 ≤ y ≤ 6

Q: ompute the line integral ∫C [2x3y2 dx + x4y dy] where C is the path that travels first from (1, 0)…

A: The line integral is given ∫C2x3y2dx+x4y dy Consider fx,y=x4y22. ddxx4y22=12·4x3y2+22x4y…

Q: Evaluate the line integral Sc (2x² − 3y) dx + xy dy, where the curve/path C is the line 3 y = 2/2 x…

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Q: Compute the length of the curve x = 2y3 + 1/(24y) from y = 1 to y = 3.

A: Given: x=2y3+124y1≤y≤3

Q: A few years ago, there were light sabre battles. What is the distance between two light sabers given…

A: Solution of this question is

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: 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: 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: Let (21, Y1) = (7,9), m = 3. Then the equation of the tangent line is O y = 3x- 20 O y = 3r - 16 O y…

A: Equation of the tangent line = ?

Q: Evaluate S(z² + 3z)dz along the straight line from (2,0) to (2, 2) and then from (2, 2) to (0, 2).

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Q: If 2x^4 + x^2y^2 - y^8 = 3x^2 + 4,what is the value of dyldx at point (4,1)? %3D

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Q: Make the curve y=ax²+bx+ c pass through (2,1) and be tangent to the line y=2x+4 at (1,6)

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Q: Estimate 3√9 using a linear approximation at a=8.

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Q: Make the cubic y = ax3+bx2+cx+d pass through the points (0,-6), (1,-2) and be tangent to the line…

A: This is the simple question based on algebra and derivative which could be solved using the basic…

Q: 2 Show that the line y = x +3x+m for all values of m. y= mx+4 will touch or intersect the curve

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Q: Find the shortest distance from the point (0,2,3) to the plane x+2y+z=1

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Q: Find the length of the the interval -2sxs-1. y = L, V3t² – 1 dt curve in

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Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and y =…

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Q: Find the distance between line 2xy + z = 4.

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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: 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 the surfaces S1 : 4x + y° + 9z² = 108 and S2 : xyz = 36 are tangent at the point (3, 6,…

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

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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: 27 hPlans that pas Ses through the Point C60,27 and contains the like メt4-2t)ソ= 34st) Zzス+4t 7.

A: Recall: General equation of a plane :     An equation for the plane through (x0, y0,z0 ) and…

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

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Q: Find the slope of the tangent to the curve of intersection of the survace 3z =√36 – 9x² – 4y² and…

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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: Show that the line y = -10x + 20 is tangent to the curve y = x4 – 4x^3 – 5x^2 + 26x – 16.

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Q: y 1-

A: The solution is given below in the next step:

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: 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: Evaluate | xyzdx + In(xy)dy + xzdz over the straight line segment from (2, 1, 1) to (–1,1, –2)

A: We need to evaluate integral∫Cxyzdx+lnxydy+xzdz over the line segment from 2,1,1 to -1,1,-2.