3T 2 a) When graphing the parametric equations, what are the x and y coordinates when t= b) Does the graph have a clockwise or counterclockwise orientation? C) What is the rectangular equation of this curve?

Q: -38, find parametric equations for the given curve. 3x 34. Segment joining (-3,0) and (0, 4)

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Q: In the given equation as  follws , find a set of parametric equations forthe rectangular equation…

A: Given :                 y = 2x -5 , t=0 at point (3,1)

Q: In two or more complete sentences, explain how to find the time it takes for a rocket following the…

A: We will find the time taken by the rocket to hits the ground as shown below

Q: Eliminate the parameter t to rewrite the parametric equation as a Cartesian equation. Sx(t) Lyct) =…

A:

Q: Complete the parametric equations for the line where the planes – 4

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Q: This is the problem  If a and b are fixed  numbers, find parametric equations for the curve that…

A: It is required to define the point P in a, b  and θ.

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:

Q: The parametric equation for the y-axis is:

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

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

Q: 4. The trajectory of the spaceship Excelsior during the first 5 minutes of the launch can be…

A:

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

A: x = 2+5 cost → x-25=cost    y = 3+2 sint → y-32 = sint  Square both equations and add them.…

Q: Find two different sets of parametric equations for the rectangular equation   y = x3

A: y=x3 Let x=t, then y=t3 Let x=t+1, then y=t+13

Q: 3. For each pair of parametric equations, find the rectangular-coordinate equation for the curve by…

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Q: 7) Find a rectangular equation equivalent to the given pair of parametric equations. x=2t-1 „y=t^2;…

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

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Q: The graph of the curve described by the parametric equations x = 4t −1, y = 3t + 2 is a straight…

A: For a line passing through the point (a,b) and parallel to the vector (c,d) its parametric equation…

Q: Find parametric equations for the path of a particle that moves along the circle æ² + (y – 1)² = 4…

A: As per our guidelines we are supposed to solve only one question. For the first question follow the…

Q: In two or more complete sentences, explain how to find the time it takes for a rocket following the…

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Q: Which set of parametric equations represents the curve shown in the figure?

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Q: d) Find the parametric equations for the line of intersection of the two planes.

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Q: Without using a calculator, convert the parametric equations of a curve into rectangular form. No…

A: Given that parametric equation and convert this equation into rectangular form and State the domain…

Q: A curve represented by the parametric equations a = et and y = e 24, will be Select one: О нурerbola…

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Q: Determine the length of the parametric curve given by the following parametric equations

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Q: Find two different sets of parametric equations for the rectangular equation y = x2 - 3.

A: Find two different sets of parametric equations for the rectangular equation y = x2 - 3

Q: Try to sketch by hand the curve of intersection of the circu- lar cylinder x + y² = 4 and the…

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

Q: Consider the parametric equations x = √t − 2 and y = (1/ 2)t + 1, t ≥ 2. What is implied about the…

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

Q: Suppose you have the parametric equations x = 4cos(6) y= 6sin( 6 ) %3D Eliminate the parameter and…

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Q: Which of the following sets of parametric equations correctly represents the curve above

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Q: Explain how a pair of parametric equations generates a curve in the xy-plane.

A: Our Aim is to explain the fact that how a pair of parametric equationsgenerates a curve in the…

Q: What is the rectangular equivalence to the parametric equations? x(θ)=2sinθ+1,y(θ)=3cosθ−2 , where…

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Q: The position of an object at time tis given by the parametric equations

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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: What are the direction numbers of a line given by the parametric equation:  x=6+t,y=5+4t,z=1−2t

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Q: 18. x = et, y = e2t - 1

A: Solution

Q: Sketch the curve represented by the parametric equations x = e−t ,y = e2t − 1 (indicate the…

A: The given parametric equations of curves are: x = e^(-t) y = e^(2t) - 1 The graphs of these…

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: Find two different sets of parametric equations for the rectangular equation  y = x2

A: y=x2 Let x=3t, then y=3t2=9t2 Now let x=4t, then  y=4t2=16t2

Q: This is the problem    If a and b are fixed numbers, find parametric equations for the curve that…

A: Let the coordinate of point P is (x,y). In the triangle OCD, sinθ=CDOCsinθ=yby=bsinθ Similarly,…

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

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Q: Sketch the curve for each pair of parametric equations. 2=3 cos t, y=5 sin t

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Q: 3) (i) Eliminate the parameter to find a Cartesian equation of the curve. (ii) Sketch the parametric…

A: Our objective is to eliminate the parameters to find the cartesian equation of the curve and sketch…

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

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.