Use a graphing calculator to generate the curve over the interval for the parameter t. Then find the equivalent rectangular equation. x- 2t, y=t+1 for t in [ - 2,3] Select the correct graph from those shown on the right.

Q: Eliminate the parameter to find a cartesian equation of the curve. x = et,  y = e-4t

A: A curve is a two dimensional object with equation of the form y=f(x). This equation can sometimes be…

Q: Find T, N, and B for the curve r(t) = (10t, 10t, e') at (0,0, 1).

A: Given: we have ,

Q: Consider the following. x = t³, y = In(t) X = (a) Eliminate the parameter to find a Cartesian…

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Q: Consider the following. x = e', X = y = e-3t (a) Eliminate the parameter to find a Cartesian…

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Q: Find the equation of y, glven the derlvative and the Indicated polnt on the curve. dy = 2x- 1 xp

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Q: Eliminate the parameter to find a Cartesian equation of the curve: x = VE ,y = 1 – t and then sketch…

A: Given,x=t...............(1)andy=1-t...................(2)differentiating both the equation w.r.t.…

Q: The cartesian equation of the curve x = VE .y 1-t is :

A: The characterstics eqaution of the curve is

Q: Find the exact length of the curve. x =Vy ( - 3), 1sys 25

A: given: x=13yy-3

Q: given curve about the x-axis. 1. y = 7x, 0 < x <1

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Find the exact length of the curve. = 플Vy (y-3), 4sys 16 3

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Q: State the following curve in the form of a parameter equation a. y = 1-x², z = -2 b. y²-z²=9, x =4

A: a. According to question,Given equation,y = 1-x2 ,  z = -2

Q: (d) Find the points on the curve x'y = 60 nearest the origin.

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Q: Sketch the curve represented by the equations x = 1/ √(t + 1) and y = t/(t+1) , t &gt; −1 by…

A: The given parametric equations are: The given equations are in the form of a parameter t, whose…

Q: 1. Eliminate the parameter in the following and sketch the curve. Indicate the orientation. a) r…

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Q: Determine the parameter equation of the following curve x2 + y2= 5

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Q: Find the exact length of the curve. x = e - 9t, y = = 12e2, 0 sts 4

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Q: Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C,…

A: Consider the given equation as x=t3....(1) And y=t2....(2)

Q: Use the graphs of x = f(t) and y = g(t) to sketch the parametric curve x = f(t), y = g(t). Indicate…

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Q: Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C,…

A: Parametrization is a way to change the parameters of a expression in such a way that domain of the…

Q: a) Sketch the curve by eliminating the parameter, and indicated the direction of increasing t. i) x…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C,…

A: Find the equation in terms of x by substituting x=t in the given expression   y=t2-1=x2-1   To use…

Q: X bn t-1),y=2t-1for tin [.0ol,10]; windowi I-5-S]° by E2,20]

A: We graph the curve as

Q: a) Sketch the curve by eliminating the parameter, and indicated the direction of increasing t. i) x…

A: iGivenx=t−3    .........1y=3t−7  .........20≤t≤3Now elliminate "t" from equation 1 and 2 by…

Q: y =(+ + +)* x = 4t + 1, 4

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Q: III. Find the length of the following curves. (a) x = 2t , y = cos 4t, 0 < t <

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Q: 8. Eliminate the parameter to find a Cartesian equation of the curve: x(t) = t, and y(t) = 3t+4, t≥…

A: To eliminate the pararmeter to find a Cartesian equation of the curve: xt=t, and yt=3t+4, t≥0.To…

Q: A particle P moves on the curve r= 3i + 4t²j. The distance of P from the origin when t =1 is

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Q: The graph, when the curve y = √3 + x² from x = 0 to x = 4 is rotated about x - axis is A B C D

A: To find the graph of the solid formed by rotating the given curve about x axis, first we find the…

Q: I Discuss the properties of the curve and sketch fully: a) y = x? e-x

A: (a) Given- y=x2e-x To Find- The properties of the curve and sketch the curve.

Q: Find a rectangular-coordinate equation for the curve by eliminating the parameter. x = sin2(t), y =…

A: Given parametric equation is

Q: Use a graph to estimate the coordinates of the lowest point on the curve $x=t^{3}-3 t, y=t^{2}+t+1…

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Q: ²+2x 5. Sketch the curve: y? x-1

A: The graph of the given function is plotted below.

Q: analyze and trace the given curves y = x2 + 1 / x2

A: Explained below

Q: t the given point, find the slope of the curve or the line that is tangent to the curve, as…

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Q: Eliminate the parameter to find a Cartesian equation of the curve. x=2 sint, y=3cost, 0st<27

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Q: Find the equation of the curve at any point  P(x,y) of a curve the subtangent equals -1/x

A: Given that the subtangent equals -1x. Then we get, tan θ2=-1x⇒tan θ=2 tan θ21-tan2 θ2⇒tan…

Q: Sketch the figure of the described situation in the problem and then solve. Determine the equation…

A: Tangent and normal line: At the point of tangency, the normal line is defined as the line that is…

Q: 6x 4. У3 y = х+3

A:

Q: Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C,…

A: We have given the curve x=et ,y=e-t ,t∈ℝ.We have to find an equation in x,y whose graph contains the…

Q: Which of the following is/are points on the curve y = x4- 8x3 + 22x2 - 24x + 9 where the tangent…

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Q: Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C,…

A: The given parametric equation of curve is x=t3+1,    y=t3-1,     -2≤t≤2. This implies that, x=t3+1,…

Q: Find the coordinates of the point in the curve y = 12x – 2y + 23 that is nearest to the point P(10,…

A: Given curve: y2=12x-2y+23 The point is  P10,4 To find: The coordinates of the point on the curve…

Q: Find a rectangular-coordinate equation for the curve by eliminating the parameter. x = et, y = e-t

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Q: The given curve is rotated y = 3 - x2,

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Q: Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C,…

A: The given parametric curve is, x=2ty=8t3-1≤t≤1 From the parameter of x, x=2tt=x2

Q: a) Sketch the curve by eliminating the parameter, and indicated the direction of increasing t. i) x…

A: Since you have posted multiple questions, we solve the first part of the question, To get the…

Q: Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C,…

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Q: Find the exact length of the curve. 9 s ys 16

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Q: . Verify that the given point lies on the curve. p. Determine an equation of the line tangent to the…

A: given  point (2,1)

Q: analyze and trace the given curve y = x / (1 - x)2

A: To solve the following problem

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.