I Let C be the line segment from A(0,-3) to B(-4, 1). a) Sketch the graph of C, and find parametric equations for C. b) Use the curve C to evaluate the line integral xydx + (x – y)dy. Provide detail solution. -

Q: In Exercises 23–38, find parametric equations for the given curve. 25. 4x - y2 = 5

A: For the given curve:                                     4x-y2=5   To determine:…

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A: a set of parametric equations for the line passing through the point (2, 0, 9)  that is parallel to…

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Q: Sketch the curve defined by the parametric equations x = t2, y = t + 1, -∞ < t < ∞.

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Q: 12- Find an equation of the tangent plane to the given parametric surface at the specified point.…

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Q: 25) Show that the curve with parametric equations x = tcos(t) , y = tsin(t), lz = t ies on the cone…

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Q: Show that the curve with parametric equations x = tcost, y = tsent, z = t is z cone z2 = x2 + y2 and…

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Q: Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces…

A: Given surfaces are And the given point P is

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Q: Find parametric equations for the line tangent to the curve of intersection of the surfaces at the…

A: To find a parametric equation of the line tangent to the curve of intersection of the surfaces at…

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Q: Find a parametric form for the line through the point (8, –6, –3) and perpendicular to the plane 2x…

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Q: Find the distance between the point (1, −2, 4) and the line given by the set of parametric equations…

A: The given point is M=(1, −2, 4) The direction vector of the line is =s=(2,1,2) A point on the line…

Q: 2. Find parametric equations for the line tangent to the curve of intersection of the surfaces at…

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Q: 7. Sketch the curve with parametric equations z =e, y =e', teR.

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Q: The parametric equations for the line tangent to curve of intersection of the surfaces x? + y? = 8,…

A: Given: The parametric equations for the line tangent to curve of intersection of the surfaces…

Q: Given the planes  π1 : x − 2y + 3z + 1 = 0 and π2 : 2x + y + z + 2 = 0. Let L be the line of…

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Q: A particle moves in space along a path whose parametric equations are given by bsin(wt), x2 =…

A: Image is attached with detailed solution.

Q: Find a set of parametric equations for the curve of intersection of the cylinder (x − 1)² +: 4 the…

A: We will use trigonometric identity  sin2t+cos2t=1 and parametric form of standard ellipse to find…

Q: In Exercises 23–38, find parametric equations for the given curve. 30. Line through (2, 5)…

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Q: Find the general equation of the plane through the point (1, 1, 1) that is perpendicular to the line…

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Q: Find the length of the parametric curve x = e^t + e^-t, y = 5-2t on the interval [0,3]

A: Find the length of the parametric curve x = e^t + e^-t, y = 5-2t on the interval [0,3].

Q: Find a parametric description for the curve y=4-x^2 from (-2, 0) to (2, 0) such that t=0 corresponds…

A: Given: The curve y=4-x2 from (-2,0) to (2,0)

Q: iminate the parameter in x = -t +2t and y =t-4 and then identify the parametric sketch its image in…

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Q: Find the parametric equations of the tangent line to the curve of intersection of the surfaces x² -…

A: The equation of the tangent plane to the surface f(x, y, z)=0 at x0, y0, z0 is defined as: fxx0, y0,…

Q: Find a parametric description for the curve x=y^2-9 from (0, 3) to (-5, -2) such that t=0…

A: We need to parametrize the curve x=y2-9 from 0,3 to -5,2 We need to put either x=t or y=t and see a…

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Q: Find the parametric equation of the line tangent to the curve of intersection of the cylinder…

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Q: Find the points (x, y) on the curve with the parametric equations (x3Dt3- 4t at ly=t +2 which the…

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Q: Find the length of the curve having a parametric equation of x= 2cos³0 and y=2sin²0 from 0-0 to…

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Q: Sketch the plane curve represented by the parametric equations x = 6 cos t, y = 4 sin t, π ≤ t ≤ 2π…

A: Given  x = 6 cos t, y = 4 sin t, π ≤ t ≤ 2π

Q: Let C be the curve of intersection of the spheres x 2 + y 2 + z2 = 3 and(x - 2)2 + (y - 2)2 + z2 =…

A: Let fx=x2+y2+z2-3=0 & gx=x-22+y-22+z2-3=0 At P=(1, 1, 1) ∇f=2x, 2y, 2z∇fP1, 1, 1=2, 2, 2…

Q: a) Find the are length of the parametric curve x = B(t. sint), y = B(1+ cost), in the range 0 sts,…

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Q: 2. Use parametric equations to derive the formula for the lateral surface area of a right circular…

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Q: The parametric equations for the line tangent to curve of intersection of the surfaces x? + y2 = 8 ,…

A: We have given the surfaces; And the point (2,2,8)

Q: Find parametric equations for the line tangent to the curve of intersection of the surfaces tan-1(x?…

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Q: 5. Sketch the parametric curve x = t2 – t, y = t³ – 3t and determine the location (x, y and t) where…

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: 7. Sketch the curve with parametric equations x = e-t , y = e', teR.

A: Topic = Functions

Q: # 2. Let C be the curve that is the intersection of the cylinder x²-2x+4y2 = 0 with the plane z-x…

A: The cylinder x2-2x+4y2=1 and a plane z-x=3. We have to find the parametric equations for the…

Q: 2. Find an equation of the tangent plane to the parametric surface F(u, v) = (, 2uv, uv?) at the…

A: (2) Consider the provided question,

Q: Find a set of parametric equations for the line passing through the point       (1, 0, 2) that is…

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Q: Sketch the plane curve represented by the parametric equations x = 5 cos t, y = 2 sin t, 0 ≤ t ≤ π…

A: x=5cost,  y=2sint Now,…

Q: Find the distance between the point (4, −1, 5) and the line given by the set of parametric equations…

A: The point is: P(4, −1, 5) The line is: x = 3, y = 1 + 3t, z = 1 + t The line is: <3, 1, 1> +…

Q: The position in feet, of a baseball t seconds after being thrown from third base to first base is…

A: A)                                t                        x=80 t             y=-16t2+24t+5 0…