Let C be the curve of intersection of the surfaces with equations   x2 + y  =  5   and   24x + 4y + z  =  3   Find the unit vector u, with a positive x-component, which is tangent to C at the point P  =  (4, −10, −55) .

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Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

A: Given:

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A: Let's first draw the curve -  Domain - -1 ≤ t ≤ 1 where, we can take values of t as -  t = -1, -0.5,…

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Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

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Q: Let C be the curve of intersection of the paraboloid x? + y² = z and the cylinder + (y – 1)² = 1. 4…

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Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. the…

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A: given parametrically by x = x(t), y = y(t), and z = z(t) for a ≤ t ≤ b in the vector form.

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Q: Consider the vector function r : R - R° given by r(t) = (21² + t, t + 1, 1² – 2), and let C be the…

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Q: Write an equation for the plane tangent to the surface F(x, y, z) = 0 at the point (a, b, c).

A: Given surface is Fx, y, z=0 and the point is a, b, c.

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Q: B-For the surface z² = x² + y² find the directional derivative at the point (√2, √2,-2) in the…

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Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

A: First solve the given equations for finding the values in terms of x

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Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. the…

A: The objective is to find the vector function that represents the curve of intersection of the two…

Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

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Q: a) Start by finding a single vector function that represents the intersection of the surfaces z = y?…

A: Given: The two surface equation: z = y2 and  x2 + y2 = 4

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Q: The unit vector tangent to the curve r(t) = (1,41*,3r*) is (a) (0,4/5,3/5). (b) (0,81,6t)

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Q: Find the vector equation that represents the curve of intersection of the paraboloid z = 2x² + y²…

A: Given: Let us take x = t. So, we get y=t4  and  z=2t2+t42=2t2+t8.

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Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

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Q: B- Find the length of the curve given by the position vector r=, =r'i+(1+(1/3)x')j+(1-(1/3)')k for

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Q: Sketch the curve of intersection of the surfaces, and find a vector equation for the curve in terms…

A: First, we will sketch the curve of the intersection of the surface. The equation of the surfaces are…

Q: What is the perpendicular vector to the surface f(x.y.a)-ay-3r+'y-0 at (1,-1,2)? (3,3.0) (1,1.3)…

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Q: Show that the vector-valued function r(t) = e−t cos ti + e−t sin tj + e−t k  lies on the cone z2 =…

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