Evaluate (x+y)ds where C is the straight-line segment x = 2t, y = (8 – 2t), z = 0 from (0,8 C (X+y)ds =

Q: Find a function f (x, y) that has the line y = 3x - 4 as a level curve.

A: A function is a relation which maps each value in its domain to exactly one value in its range. A…

Q: Find the length of the curve on y=2x^(3/2) from x=0 to x=1

A: Explanation of the solution is given below...

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 length of the curve y =x/2 from x = 0 to x = 3.

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Q: Find the local extreme values of ƒ(x, y) = x2y on the line x + y = 3.

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Q: Find the length of the curve 4t2 -1 dt, y = %3D 1<x<3 8. 15 104 3 3.

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Q: #4 Find y! of 3-y3+y2+5y-x²=D0.use it to find the eguation of the line that is perpendicular to the…

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Q: Find equations for two lines through the origin that are tang net to the curve x²-4x+y²+3=0 .

A: We have given equation of curve x2-4x+y2+3=0. We also know that the slope of the line will be the…

Q: Determine the coefficients a, b, c and d so that the curve y = ax³ + bx² + cx + d be tangent to the…

A: Curve y=ax3+bx2+cx+d is tangent to the line y=3x+8 at the point (-2,3). The curve y=ax3+bx2+cx+d has…

Q: Find the length of the curve x = y^4/16 +1/(2y^2) between y= -3 and y= -2.

A: we have to find the length of the curve . I have explained in details please see the explanation and…

Q: Where does the line x = 1 + t, y = 3−t, z = 2t intersect the cylinder x² + y² = 16?

A:

Q: Find the length of the curve y= 3/2x^2/3 from x = 1 to x = 8

A: Given,         The length of the curve y=32x23 from x=1 to x=8.We know that,         The length of…

Q: Find the length of the curve y = x2 from x = 0 to x = 7.

A:

Q: 2.) What is the equation of the line tangent to y(x) x- 2r3+6x-3 at r =-1?

A: Follow the steps .

Q: Find the length of the curve y = 1 - e^-x, 0 &lt;=x&lt;=1.

A: The given curve is

Q: Determine the length of the curve x = 3y2 -1 between y = 0 and y = 4 3/2

A: The given curve is x=3y32-1 We will find the arc length of the curve between y=0 and y=4

Q: Find the length of the curve y = x/2 from x =| 0 to x = 3.

A: We have to find out the length of curve.

Q: fc z2 dx+ x2 dy +y2 dz, C is the line segment from (1,0,0) to  (4,1,2)

A: Given, r(t)=z2dx+x2dy+y2dz We have the line segment from (1,0,0) to (4,1,2) We parametrize the given…

Q: Determine the coefficients a, b, c and d so that the curve y = ax* + bx³ + cx² + dx + e will pass…

A: Since we have to find value of a,b,c and d

Q: B. Find the length of the curve y= x2 from x = 0 to x = 7.

A:

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: Find the set of values of y=2x+k meets the curve y=1+2kx-x² at 2 distinct points?

A: Given: y=2x+kat 2 distinct points

Q: 2 The Range (Ry) of y = v9 – x² -

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Q: Find the length of the curve y = x3/2 from x = 0 to x = 3.

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Q: Find C so that the line y = 4x + 3 is tangent to the curve y x2 + C.

A: The given equations are y=4x+3 y=x2+c.

Q: Find c so that the line y = 4x + 3 is tangent to the curve y= x^2 + c?

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Q: The line that is normal to the curve x + 2xy - 3y = 0 at (4,4) intersects the curve at what other…

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Q: B. Find the length of the curve y = x² from x 0 tox = 4.

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Q: Find the equation of a line perpendicular to 3x – 2y = 16 that passes through the point (9, 4). - Oy…

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Q: Find the length of the curve x = y2 — 2y, 0 ≤ y ≤ 2.

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Q: The line that is normal to the curve x + 3xy - 4y² = 0 at (3,3) intersects the curve at what other…

A: Given: x2+3xy-4y2=0 at (3,3)

Q: Evaluate 2y dS where S is the portion of y +z = 4 between x = 0 and x = 3-z.

A: To evaluate ∫∫S2ydS where S is the portion of y2+z2=4 between x=0 and x=3-z

Q: An insect is moving on the surface of a hot plate, the temperature of which at the point x units to…

A: As a first step we need to find the gradient of the surface and evaluate the same for the point (1,…

Q: Q2) find the distance between two lines L1: x= 1 +4t, y=5 - 4t, z=-1+5t L2: x=2 + 8t, y=4 - 3t, z-5…

A: Method 1:

Q: The line that is normal to the curve x2 + 2xy - 3y2 = 0 at (1, 1) intersects the curve at what other…

A: Given thatx2 + 2xy – 3y2 = 0          …(1)On differentiating equation (1) with respect to x,

Q: ƒ(x, y) = 4x - 8xy + 2y + 1 on the triangular plate bounded by the lines x = 0, y = 0, x + y = 1 in…

A: Given function f(x, y),f(x, y) = 4x-8xy+2y+1             ........................(1)Given conditions…

Q: Find the equation of a line normal to the curve x^2=16y at (4,2).

A: Solve the given problem.

Q: Find the equation of the line normal to x^3 + y^3 = 6xy at (3,3)

A: Given, x3+y3=6xy

Q: In the xy-plane, the line x + y = k, where k is a constant, is tangent to the graph of y = x^2 + 3x…

A: Given line is x + y = k, where k is a constant it is tangent to the graph of y = x^2 + 3x + 1…

Q: The line 2x + 5y = 1 meets the curve x² + 5xy - 4y² + 10 = 0 at the points A and B. Find the…

A: The midpoint of the line joining the points: x1, y1 and x2, y2 is x1+x22, y1+y22. The roots of the…

Q: Evaluate (x-y+z-2)ds where C is the straight-line segment x=t, y= (1-t), z=1, from (0,1,1) to…

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Q: Determine the coefficients a, b, c and d so that the curve y = ax³ + bx² + cx + d be tangent to the…

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Q: Find the length of the curve y = (x/2)2/3 from x = 0 to x = 2.

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Q: Find the length of the curve of 8x = y² + 2y-² from y = 1 to y = 2.

A: Length

Q: 2. Find the shortest distance from the point (2,0) to the curve: (a) y = 3x – 1 (b) y = x^2 (c) x^2…

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Q: X. xy ds where C is the straight line from (2,3) to (4,0).

A: Given: The curve C is the straight line from 2,3 to 4,0, To find: The value of ∫Cxy2ds.

Q: 4. x = 9-y2 ,-2 <y S2 about y-axis vis

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Q: S. 3 z dz where C is straight line segment from i to -2 - 3i

A: We put z=x+iy And dz=dx+idy

Q: Find an equation of the line tangent to the curve y = v4x – 3 – 1 and perpendicular to the line x +…

A:

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.