The parametric equations for a plane curve are given as x = 2t² – 1, y = -4t2+ 3, 1s t<2. a. Find the rectangular equation for the curve. b. Sketch the graph of the curve and show its orientation.

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

A: Given curve :

Q: x = 3 – 4t, y = 2 – 3t

A: Solution is given below

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A: The given parametric curve is  x(t) = 3-t, y(t) =2t,   0≤t≤3 Here,  parameter is t.   We have to…

Q: Sketch the curve represented by the parametric equations    x = et − 1,                    y = e3t…

A:

Q: Sketch the curve represented by the parametric equations (indicate the orientation of the curve),…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Consider the parametric equations below. x = 4 + 5t,    y = 1 − t2   Eliminate the parameter to…

A: Calculation:Compute the Cartesian equation as follows.Rewrite x = 4 + 5t as follows t = (x – 4)/5.

Q: • Sketch the curve represented by the parametric equations (indicate the Orientation of the curve),…

A: Given,

Q: i) Eliminate the parameter for the given set of parametric equations, sketch the graph of the…

A: Given: x=6-7 e-2t &amp; y=4+3 e-2t To eliminate the parameter t &amp; to sketch the graph of…

Q: Find the exact length of the curve described by the parametric equations. x = 5 + 3t2, y = 3 + 2t,…

A:

Q: Sketch the curve represented by the parametric equations x = t + 1, y = t2 (indicate the orientation…

A: Given: x=t+1, y=t2. first we eliminate t and find equation of curve in x and y x=t+1…

Q: Graph the plane curve defined by the parametric equations:x = t2 + 1 ,  y = 3t ,  -2 ≤ t ≤ 2.

A: Consider the given parametric equations x=t2+1 and y=3t over the interval -2≤t≤2 now, make the table…

Q: Graph the plane curve defined by the parametric equations: x = t2 - 1, y = 2t, -2 ≤ t ≤ 2.

A: we have to graph the plane curve defined by the parametric equations: x=t2-1y=2t-2≤t≤2

Q: x = 1 – t², y = t – 2, –2 <t< 2

A:

Q: 8. x 2t2, y =t + 1 ||

A: We use substitution method to eliminate parameter

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A:

Q: Graph the curve given by the parametric equations below, and show its orientation. x=2 sin t, y=2…

A:

Q: Graph the curve defined by the parametric equations

A: Here given parametric equation as x=3t2,  y=2t, -2≤t≤2 Then t=y2

Q: Sketch the curve represented by the parametric equations (indicate the orientation of the curve),…

A:

Q: Sketch and describe the orientation of the curve given by the parametric equations. x = V7, y = 2t –…

A:

Q: find parametric equations for the given curve. . (x + 9) 2 + (y − 4) 2 = 49

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Q: please make curve clear and determine the direction (clockwise or counterclockwise) of the curve.…

A: Given that       x = -3t , y = t2  , -3 &lt;= t &lt;= 2  Here we have to draw the graph.

Q: Find length of the curve described by the parametric equations a = 3t2, y = 2t, 0<t< V3. A. 3/3-1 B.…

A:

Q: Sketch the curve represented by the parametric equations x = t − 3,                  y = t/(t − 3)…

A: Given: x=t-3                                                  ..1y=tt-3…

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A: Given, Circular cylinder, x2+y2=4 Parabolic cylinder, z=x2

Q: please make the curve easy to read and determine the direction (clockwise or counterclockwise) of…

A: Data given  X=-t+3   Y=-2t+1  value of t is given in a interval of [0, 5] Find out orientation of…

Q: 2a) Find the slope of the curve represented by the parametric equations, at 0 = T/6 %3D x = 5+ 3 sec…

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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…

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A: Consider the given parametric equation as x=t-2 and y=12t+1

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

A:

Q: Graph the plane curve defined by the parametric equations:x = t2 - 1 ,  y = 2t ,  -2 ≤ t ≤ 2.

A: The given curve is x = t2 - 1 ,    y = 2t ,    -2 ≤ t ≤ 2. Sketch the graph as shown below.

Q: What is the rectangular equation of the curve fro the parametric equation below? x=3t+2,…

A: Consider the parametric equation, x=3t+2y=t+40≤t≤4

Q: The parametric equations r = 3 - t, y = 2t + 4, 0 <t < 2 describes motion along a certain line…

A:

Q: The curve above is defined by which of the following sets of parametric equations? Select the…

A: Find the equation of the graph.

Q: Sketch the curve represented by the parametric equations x = 1 + 8t,                 y = 3 − 4t…

A: x=1+8t,  y=3-4t When t=0, x=1+80, y=3-40⇒x=1, y=3 When t=1, x=1+81, y=3-41⇒x=9, y=-1 Now the graph…

Q: Sketch the curve represented by the parametric equations Lindices Orientation of the curve), and…

A: Topic :- function

Q: Sketch the curve represented by the parametric equations (indicate the orientation of the curve),…

A: Given parametric equations, x=et,y=e3t+4 To find y.

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Q: Sketch the curve represented by the parametric equations x = 2t/2, y = t4+ 1 (indicate the…

A: Given parametric equation, x=2t2 and y=t4+1we have to write the corresponding rectangular equation…

Q: Allow A be the point with Cartesian coordinates (6, 9), and D be the plane curve with parametric…

A: The slope of the tangent to the curve: y=fx at x=a is f'a. The point-slope form of a line that…

Q: Sketch the curve represented by the parametric equations x = t3, y = t2/2 (indicate the orientation…

A: Given a parametric equation,   x=t3                ...(1)  y=t22              ...(2)

Q: 1. Sketch the graph of the curve represented by the parametric equations x = 4cost, y = 4sint 0sts…

A: We have to sketch the graph of the curve and find all points where the curve has a slope of 12.

Q: Consider the curve whose parametric equations are x (t) = 2t? – 4t + 2 and y (t) = 2t – 8t? + 8. At…

A:

Q: Given the parametric equation: x=2sint-3, y=2cost+5, 0 less than or equal to t less than or equal to…

A: Given x=2sint-3, y=2cost+5   , 0≤t≤2π

Q: Consider the parametric curve given by the equations z(t) - + 24t – 6 y(t) - + 24t – 2 How many…

A: The given parametric curves are  x(t) = t2+24t-6  y(t) = t2+24t-2  We have to find the distance…

Q: Sketch the curve represented by the parametric equations x = √t, y = t − 5 (indicate the orientation…

A: Given parametric equation, x=t         ...(1)y=t-5       ...(2)

Q: Sketch the curve represented by the parametric equations x = et , y = e3t + 1 (indicate the…

A: Sketch the curve represented by the parametric equations x = et , y = e3t + 1 (indicate the…

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

A:

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.