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1. A) Create a table of x- and y-values for the parametric equations, x = 3t...
Consider the parametric equations below. x = 2 + 4t y = 1-t2
Consider the parametric equations below. x = 2 + 4t y = 1-t2 (a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases.(b) Eliminate the parameter to find a Cartesian equation of the curve. y = _______ Consider the parametric equations below. x = 3t - 5 y = 2t + 4 (a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the...
For the following equations : x= 2t^2 , y = 3t^2 , z= 4t^2 ; 1 <=t <=3 A) write the position vector and tangent ve...
For the following equations : x= 2t^2 , y = 3t^2 , z= 4t^2 ; 1 <=t <=3 A) write the position vector and tangent vector for the curve with the parametric equations above B) Find the length function s (t) for the curve C) write the position vector as a function of s and verify by differentiation that this position vector in terms of s is a unit tangent to the curve.
Consider the parametric curve given by x(t) = 16 sin3(t), y(t) = 13 cos(t) − 5 cos(2t) − 2 cos(3t...
Consider the parametric curve given by x(t) = 16 sin3(t), y(t) = 13 cos(t) − 5 cos(2t) − 2 cos(3t) − cos(4t), where t denotes an angle between 0 and 2π. (a) Sketch a graph of this parametric curve. (b) Write an integral representing the arc length of this curve. (c) Using Riemann sums and n = 8, estimate the arc length of this curve. (d) Write an expression for the exact area of the region enclosed by this curve.
Use a table of values to graph the plane curve defined by the following parametric equations. Fin...
Use a table of values to graph the plane curve defined by the following parametric equations. Find a rectangular equation for the curve ★17)x-t3 + 1.y=t3-1,for t in [-2, 2] 17) Give two parametric representations for the equation of the parabola. 18) 18) y=x2 + 6x + 15 Find the partial fraction decomposition for the rational expression.
Use a table of values to graph the plane curve defined by the following parametric equations. Find a rectangular equation for the curve...
3. (5 points) (a): Find parametric equations for the tangent line to the curve with the...
3. (5 points) (a): Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x=etcost, yr etsint, z=et; (1,0,1) (b): Find the unit tangent vector T, the principal unit normal N, and the curvature k for the space curve, r(t) =< 3 sint, 3 cost, 4t >.
Give parametric equations that describe a full circle of radius R, centered at the origin with...
Give parametric equations that describe a full circle of radius
R, centered at the origin with clockwise orientation, where the
parameter t varies over the interval [0,22]. Assume that the
circle starts at the point (R,0) along the x-axis.
Consider the following parametric equations, x=−t+7, y=−3t−3;
minus−5less than or equals≤tless than or equals≤5. Complete parts
(a) through (d) below.
Consider the following parametric equation.
a.Eliminate the parameter to obtain an equation in x and y.
b.Describe the curve and indicate...
Uestion 7[value16jp (a) Find parametric equations for the tangent line to the curve of intersecti...
uestion 7[value16jp (a) Find parametric equations for the tangent line to the curve of intersection of the cvlinders y -r2 and z - r2 at the point (1, -1,1) (b) Find an equation for the osculating plane of the curve ア(t) 〈cos 3t, 4t, sin 3t) at the point (-1.4T,0).
uestion 7[value16jp (a) Find parametric equations for the tangent line to the curve of intersection of the cvlinders y -r2 and z - r2 at the point (1, -1,1) (b)...
(6pts) Consider the curve given by the parametric equations x = cosh(4t) and y = 4t...
(6pts) Consider the curve given by the parametric equations x = cosh(4t) and y = 4t + 2 Find the length of the curve for 0 <t<1 M Length =
Consider the parametric equations below. - 2 y=+4 -3553 (a) Sketch the curve by using the...
Consider the parametric equations below. - 2 y=+4 -3553 (a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the 2 + 6 (b) Eliminate the parameter to find a Cartesian equation of the curve. for 1sYS 7 Need Help?
1 The parametric equations x = x2 + (x2 - *,), y = y + (72...
1 The parametric equations x = x2 + (x2 - *,), y = y + (72 - Y2) where osts i describe the line segment that joins the points P2(XqrY,) and P2(%20Yz). Use a graphing device to draw the triangle with vertices A(1, 1), B(5, 4), C(1,6). Find the parametrization, including endpoints, and sketch to check. (Enter your answers as a comma-separated list of equations. Let x and y be in terms of t.) A to B B to C...
Use a table of values to graph the plane curve defined by the following parametric equations. Find a rectangular equation for the curve ★17)x-t3 + 1.y=t3-1,for t in [-2, 2] 17) Give two parametric representations for the equation of the parabola. 18) 18) y=x2 + 6x + 15 Find the partial fraction decomposition for the rational expression.
Use a table of values to graph the plane curve defined by the following parametric equations. Find a rectangular equation for the curve...
3. (5 points) (a): Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x=etcost, yr etsint, z=et; (1,0,1) (b): Find the unit tangent vector T, the principal unit normal N, and the curvature k for the space curve, r(t) =< 3 sint, 3 cost, 4t >.
Give parametric equations that describe a full circle of radius
R, centered at the origin with clockwise orientation, where the
parameter t varies over the interval [0,22]. Assume that the
circle starts at the point (R,0) along the x-axis.
Consider the following parametric equations, x=−t+7, y=−3t−3;
minus−5less than or equals≤tless than or equals≤5. Complete parts
(a) through (d) below.
Consider the following parametric equation.
a.Eliminate the parameter to obtain an equation in x and y.
b.Describe the curve and indicate...
uestion 7[value16jp (a) Find parametric equations for the tangent line to the curve of intersection of the cvlinders y -r2 and z - r2 at the point (1, -1,1) (b) Find an equation for the osculating plane of the curve ア(t) 〈cos 3t, 4t, sin 3t) at the point (-1.4T,0).
uestion 7[value16jp (a) Find parametric equations for the tangent line to the curve of intersection of the cvlinders y -r2 and z - r2 at the point (1, -1,1) (b)...
(6pts) Consider the curve given by the parametric equations x = cosh(4t) and y = 4t + 2 Find the length of the curve for 0 <t<1 M Length =
Consider the parametric equations below. - 2 y=+4 -3553 (a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the 2 + 6 (b) Eliminate the parameter to find a Cartesian equation of the curve. for 1sYS 7 Need Help?
1 The parametric equations x = x2 + (x2 - *,), y = y + (72 - Y2) where osts i describe the line segment that joins the points P2(XqrY,) and P2(%20Yz). Use a graphing device to draw the triangle with vertices A(1, 1), B(5, 4), C(1,6). Find the parametrization, including endpoints, and sketch to check. (Enter your answers as a comma-separated list of equations. Let x and y be in terms of t.) A to B B to C...
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