A particle moves on a trajectory described by the parametric equations x(t)=2t, y(t)=8t, t≥0. What is the shape of the trajectory?

Q: Eliminate the parameter from the parametric equations to find the rectangular equation for the…

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Q: From the two parametric equations below, find dy dx x = (2 − 3t)/ (1 + t) , y =(3 + 2t)/(1 + t)

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Q: 4. If y = tx, where t is the parameter, what are the parametric equations of the curve x' +y° = 4xy?…

A: The solution is given as

Q: A cheetah can run at 105 feet per second, but only for 7 seconds, at which time the animal must stop…

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Q: Find the PARAMETRIC model that models the trajectory of the ball.

A: Solution  Given The exit velocity of baseball is 128 feet per second , in the direction of 30. above…

Q: Find dy/dx of the following set of parametric equations 1. x = 3(t-2)2 ,  y = 9t2 + 4 2. x =…

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Q: Find the distance between the skew lines with parametric equations x = 1 + t, y = 2 + 6t, z = 2t,…

A: The distance from a point P(x1,y1,z1) to a plane  is

Q: For the parametric equations: = 26e4 and y = 46et dx () dt %3D dy (ii) dt dy (ii) %3D dx

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Q: Find the distance between the skew lines with parametric equations x 2 + t, y = 1 + 6t, z = 2t, and…

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Q: Parametric Equations Parameter - V, y = V1

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Q: The parametric equation of a curve is given by x= cost, y= sint− cost, 0 ≤ t ≤ 1 . Without…

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Q: Find the exact length of the parametric curve x =1+3t², y = 4+2r°, 0<t<2.

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Q: ELIMINATE THE PARAMETER IN THE PARAMETRIC EQUATIONS: x=t +1 Y = t t-1

A: Topic - equations

Q: 8. The position of a particle moving in the xy-plane is given by the parametric equations x =…

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Q: A particle moves along the path whose parametric equation are x = t³ and y = 12t2. What is the…

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: find the slope of the parametric curve x=-6t-5, y=3t^3, at the point t=3

A: To find the slope we have to find dy/dx For that we find dx/dt and dy/dt first

Q: Two particles travel along the space curves r(t) and u(t). If the particles collide, do their paths…

A: Given that Two particles travel along the space curves r(t) and u(t) collides. That mean there exist…

Q: A curve is defined by the parametric equations x (t) = at² and d² y y (t) = bt where a and b are…

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Q: Find the distance between the skew lines with parametric equations x = 3 + t, y = 1 + 6t, z = 2t,…

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Q: Find the exact length of the curve described by the parametric equations. x = 7 + 6t², y = 9+ 4t³,…

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Q: The motion of a particle in space is defined by the parametric equation x(t) = −t2 + 3t + 1, in…

A: Given: x(t)=-t2+3t+1  in meter y(t)=2t+5 in meter

Q: Consider the parametric equations: x = 2t2, y =t³. Find at the point t = dx? 8 without eliminating…

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Q: Eliminate the parameter in the parametric equations æ(t) = /t – 1 and y(t) = -8t + 6 to find a…

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Q: The diagram shows part of the curve with parametric equations x = 2 In(r+ 2), y =+21 + 3. (1) Find…

A: The gradient of any curve y is given by its derivative dydx. The given parametric equations of the…

Q: Without eliminating the parameter t, find a Cartesian equation for the line tangent to the curve C,…

A: Let's find.

Q: Determine the relative maximum, relative minimum, and point of inflection without eliminating the…

A: The parametric equations are, x=1t3 y=t2-t   Differentiate x=1t3 with respect to t. dxdt=ddx1t3=-3t4…

Q: At which point will the plane 2x + 4y – 3z = -48 and the line given by the parametric equations x =…

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Q: Find the dy/dx of the parametric equations given: x= 2t² – t and y= t³ – 2t – 1

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Q: The diagram shows part of the curve with parametric equations x = 2 In(t + 2). y =+2t + 3. (1) Find…

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Q: The motion of a particle in space is defined by the parametric equation x(t)=-t2+3t+1,in meter and…

A: To find the position of the particle, use the formula, r→(t)=x(t),y(t), where x(t) is the…

Q: Find parametric equations for the line segment joining the points (-6, 4) and (2, 3). x=-6 + 8t, y =…

A: Parametric equation of line segment.

Q: A particle is moving on the curve defined parametrically by the system of equation x = 1- 2cos?t and…

A: Distance of particle from origin is:

Q: Find the exact length of the curve described by the parametric equations. • x = 7+3t², y = 1 + 2t³,…

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Q: Find the dx² for the plane curve with the parametric equations X = t³ – 4 and y = t2. -2 9t4 2

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Q: Find parametric equations for the line in which the planes x + 2y + z = 1 and x - y + 2z =-8…

A: x + 2y + z = 1 and x - y + 2z =-8 are the two planes.Let z=t So, the equations become:

Q: ) Suppose that the parametric equations x = 1, y = r', 12 0, model the position of a moving object…

A: Given

Q: Without eliminating the parameter t, find a Cartesian equation for the line tangent to the curve C,…

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Q: Find the length of the parametric curve x = 2t + 1, y = 3 + 2tž, 0 < t <%.

A: Find the Length of the curve

Q: Solve for the critical points of the parametric equations x = t3 -1, y = t2+t

A: To find the critical points

Q: A cartesian equation of the parametric curve x= 12t + 13 /t – 14, y = vt is OA. X = [ 3y – 2 [ 4y +…

A: We have to find the cartesian equation of the given parametric curve.

Q: Find dy/dx and dy/dx2, and find the slope and concavity (if possible) at the given value of the…

A: To find dy/dx and d2y/dx2.   Slope is given as = dy/dx.

Q: Consider the parametric equations: x = 2t2, y =43t3. Find d2ydx2at the point t=18 without…

A: Given parametric equations are x=2t2 and y=43t3. To find d2ydx2 at the point t=18 without…

Q: Verify algabraically whether the parametric equation x(t) = 10-2.5t, y(t) = 1.5t and the rectangular…

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Q: Determine dæ dy and of the parametric equations dy dæ? 1. x (t) = t2 – 4t and y (t) = 2t³ – 6t - -

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Q: determine the parametric equations of the tangent axis to the ellipse x²/9+y²/4=1 at the point T =…

A: As we know that the parametric equation of ellipse at a point acosθ,bsinθ  is given by…

Q: Eliminate the parameter in the parametric equations x(t) = –7t – 2 and y(t) = Vt – 8 to find a…

A: givenx(t)=-7t-2..................(i)y(t)=t-8..................(ii)we can rewrite 2nd equation…

Q: What is the maximum height of a particle whose path has parametric equations x = t9, y = 4 − t2?

A: The height of the particle is given by it's y position: y = 4 - t2 At the maximum height, dy/dt = 0

Q: The parametric equations of a curve are given by = 4t – 7t2 and y = t – 12t a) dy dzr Find in terms…

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Q: Eliminate the parameter to find a Cartesian equation of the curve with parametric equations x = et –…

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Q: Find the length of the curve given by the parametric equations z = 2t3/2 0 <t< 4 ' y = 3t + 1

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