Eliminate the parameter t to find a simplified Cartesian equation of the form y = mx + b for Į ¤(t) = ly(t) - 4 - t – 4 – 4t The Cartesian equation is y =

Q: r(t) = ti + (2tt2) intersect the paraboloid (2) At what points does the curve r(t) z = x² + y²?

A: We are asked to find the intersection point.

Q: Find T, N, and x for the plane curve r(t) = (9t +2) i+ (3-t°) j T(t) = (O i+ (Oi (Type exact…

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Q: + y? )dx + (x² – y²)dy , where C is the triangle with vertices (0, 0), (2, 1), and (0, 1), sitive…

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Q: Complete the parametric equations for the line where the planes - 5x – 2y + 2z = 2 and - 13x + 10y +…

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Q: d?y For the parametric system, find dy and dx When is the graph concave up or down? dx2° x = t2 – 1…

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Q: Find T, N, and x for the plane curve r(t) = -8 In(sec tji - 8tj, -<t<; T(1) = )i - Oi (Type exact…

A: Given Data The equation of plane curve is r(t)=-8ln(sec t)i-8t j.   The expression for the unit…

Q: Eliminate the parameter t to find a Cartesian equation in the form x = f(y) for: S¤(t) = ly(t) = 3t2…

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Q: Eliminate the parameter tto find a Cartesian equation in the form z = f(y) for: S z(t) = 3² ly(t) =…

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Q: Eliminate the parameter t to find a Cartesian equation in the form x = f(y) for: S¤(t) ly(t) 3t? = -…

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Q: h) Find a parametric representation of the Parabolic equation z = 9(x² + y²)

A: Parametric representation of the Parabolic equation z = 9(x² + y²) will be cartesian coordinates as…

Q: Suppose the position of a particle is given by parametric equations x(t) = t3-3 and y(t) = 2t2. (a)…

A: Solution: x(t)=t3-3  and y(t) = 2t2

Q: Eliminate the parameter t to find a simplified Cartesian equation of the form y = mx + b for S ¤(t)…

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Q: Complete the parametric equations for the line where the planes -+ 4y+ 13z = - 3x + 5y = 21 and 10…

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Q: Find T, N, and x for the plane curve r(t) = (2t + 5) i + (9-²) j T(t) = (O i- O i (Type exact…

A: Given:

Q: Suppose the position of a particle is given by parametric equations x(t) = t3-2 and y(t) = 4t2. (a)…

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Q: Eliminate the parameter t to find a simplified Cartesian equation of the form y = mx + b for Sz(t) =…

A: Explanation of the answer is as follows

Q: Eliminate the parameter t to find a Cartesian equation in the form * = f(y) for: [x(t) = −2+² ly(t)…

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Q: The position P(x, y) of a particle moving in the xy-plane is given by the equations and parameter…

A: Given data:     The given x-coordinate in parametric form is: x=t1/2. The given y-coordinate in…

Q: Rewrite the parametric equation as a Cartesian linear equation by building an x-y table. Įx(t) ly(t)…

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Q: Suppose the position of a particle is given by parametric equations x(t) = t³-2 and y(t) = 5t2. %3D…

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Q: Eliminate the parameter t to find a simplified Cartesian equation of the form y = mx + b for S¤(t) =…

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Q: Y is the midpoint of XZ.X has coordinates (3, 4), and Y has coordinates (-1, 9). Find the…

A: Coordinates of Mid point M of a line joining two points A:x1,y1&amp; B:x2,y2 are given by…

Q: Find the parametric equation of the line that passes through P(1, 0, -3) and is parallel to the line…

A: Given: We have to find the parametric equation of the line that passes through the point P(1, 0, -3)…

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A: The given differential equation is dydx=3x, y(0)=-3

Q: d'y and dx² dy 23 Find -in terms of t for each of the following parametric equations. dx a x= -3, y…

A: d. Given parametric equations: x=et  y=et-e-t To find - dydx  and d2ydx2 which  can be given as-…

Q: 3) For the parametric system, find dy d2y When is the graph concave up or down? and dx dx2 x = t2 -…

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Q: Eliminate the parameter t to find a simplified Cartesian equation of the form y = mx + b for fæ(t) =…

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Q: Eliminate the parameter t to find a simplified Cartesian equation of the form y = mx + b for Sa(t) =…

A: Cartesian Equation of a Line: The equation of a line in cartesian form is given by y=mx+c, where m…

Q: Consider the parametric equations defined by x(t) = 3t² – 3 and y(t)= 2t +1, for t> 0. d'y at t= 1.…

A: Option A is correct option.

Q: The spherical coordinate equation of (x – 4)² + y² + z? = 16 is p= 8sinØcose

A: The spherical coordinates are given by  x=ρcosθsinφy=ρsinθsinφz=ρcosφ The given equation is…

Q: Find all integer solutions to the linear Diophantine equation, 0.05x + 0.14y +0.35= 10.29. Write…

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Q: Eliminate the parameter t to find a simplified Cartesian equation of the form y = mx + b for Sa(t)…

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Q: Suppose the position of a particle is given by parametric equations x(t) = 4t and y(t) = 2t2-1. (a)…

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Q: Find an equation in rectangular coordinates for the cylindrical equation p2 + z? = 16

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Q: Eliminate the parameter t to find a Cartesian equation in the form x f(y) for: S¤(t) ly(t) 3t? 4 +…

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Q: Eliminate the parameter t to find a simplified Cartesian equation of the form y = mx + b for (x(t) =…

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Q: Find T, N, and k for the plane curve r(t) = - 3 In(sec t)i – 3t j. -7<t<5. T(1) =i- (Type exact…

A: Given: r(t)=-3lnsec t i-3t j,  -π2&lt;t&lt;π2 Formulas to obtain T, N and k are given as:…

Q: 2. Find the parametric and symmetric equations for the following lines. (a) r=i- 2j- 3k+t(i+j+k).…

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Q: Find the Eccentricity of the conic. x. y? = 1 16 %3D 64 48 Eccentricity: e = 48 48 Eccentricity: 64…

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Q: The parametric equation of the x_axis is t=1 O x=1 O x=0 O x=t

A: To find the parametric equation of x axis.

Q: (C) Find parametric equations for the line that is tangent to the curve u(t)=1²1+ sect²j+ √² +3 k at…

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Q: Find the parametric equation for the line where the planes 4x – 6y + 8z = - 36 and – 6y + z = – 15…

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Q: Find the cylindrical equation for (x-20)² + y² = 20². o a.r = 40 cos (theta) o b.r = 0 O c.r = 20…

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Q: In(t), y = Vt, t > 25 (a) Eliminate the parameter to find a Cartesian equation of the curve. (b)…

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Q: 5. Find the angle or rotation and new equation of curve 5x2 such that the transformed equation will…

A: Given To find the angle or rotation and new equation of curve 5x2-6xy+5y2-12=0 such that the…

Q: Eliminate the parameter t to find a simplified Cartesian equation of the form y = mx + b for Sa(t) =…

A: We have to eliminate the parameter t to find a simplified cartesian equation of the form y = mx+b.…

Q: 5. Find the angle or rotation and new equation of curve 5x2 - 6xy +5y2 - 12 = 0 such that the…

A: Consider the general equation Ax2+Bxy+Cy2+Dx+Ey+F=0is rewritten asA'x'2+C'y'2+D'x'+E'y'+F'=0by angle…

Q: Find the parametric equation of the line passing through P (1, 2, 3) and perpendicular to the lines…

A: Given:  r1= (2+t)i + (1+2t)kr2=(-t)i + (1-6t)j - (2t)k

Q: Find a parametric representation of the solution set of the linear equation. i. x + y = 2 3 x-y - z…

A: We have to find

Q: Find 2 for the parametric curve c(t) = (3r³, 3r² – 3) at the point t = 4. (Use symbolic notation and…

A: Consider the parametric curve  ct=3t3,3t2−3 To find : dydxt=4