For problems 1 – 3 determine the area of the region below the parametric curve given by the set of parametric equations. For each problem you may assume that each curve traces out exactly once from right to left for the given range of t. For these problems you should only use the given parametric equations to determine the answer.

Q: 3. Rotate x = t? y = t4 – 2 0 <t< 2 about the y-axis.

A: Step:-1 Surface Area Formula:- S=∫ab2π x(t)x'(t)2+y'(t)2dt; Here, a≤t≤b Given that x=t2, y=t4-2 and…

Q: - For what value(s) of t does the curve given by the parametric equations x= -² -1 and y=t* +2r² –…

A: As per our guidelines we are allowed to solve one question at a time . Kindly repost the rest…

Q: A. Sketch the two curves: 1. r1 = 3 cos 0. 2. r2 = 1+ cos 0.

A: Use polar system to sketch this curve.

Q: 2. r = 02, 0 < 0 < 3n

A: you can clearly understand if you follow the below solution

Q: Suppose parametric equations for the line segment between (5, 3) and (3, – 8) have the form: S¤(t) =…

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Q: Find two different sets of parametric equations for y = x2 + 6.

A: Our Aim is to find the two different sets of parametric equations for y=x2+6

Q: Problem 5: Find the equation of the tangent line to the curve defined by the parametric equations…

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Q: Problem 2.2 Eliminate the parameter to find a Cartesian equation of the curve and graph it. (a) x =…

A: a) x=t3-3 , y=t+2 , -3≤t≤3b) x=sint , y=1-cost , 0≤t≤2π

Q: The parametric equations for x3+y/3-4 , when 0s0<2n are:

A: See the attachment

Q: Match the parametric equations with the graphs labeled A - F. As always, you may click on the…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 1. Graph the line using parametric equations from t = 2 tot = 6. x = 10 – 2t, y = 3 – ÷t

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Q: 1.) Given the parametric equations: x=t'- 1 and y=f+t, find the 1ª and 2nd derivatives.

A: We will find the derivatives.

Q: Question #8 I need the curves as well

A: Question #8 The provided sample means are shown below: Xˉ1=12.3\bar X_1 = 12.3 (For those taking the…

Q: Suppose parametric equations for the line segment between (1, - 5) and (2, – 6) have the form: Sz(t)…

A: Given xt=a+btyt=c+dt if curve starts at (1 , -5) when t=0 and ends at (2 , -6) at t = 1 then we have…

Q: The following are the parametric equations for the motion of a charged particle: x = a(θ − sin θ),…

A: Given the equation of curvesx=a(θ−sinθ)y=a(1−cosθ)

Q: For problems 1- 3 determine the area of the region below the parametric curve given by the set of…

A: As per our honor code, we are answering only the first question. The parametric equations are…

Q: For problems 8 and 9 find the values of t that will have horizontal or vertical tangent lines for…

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Q: Question 16 Find the equation of the tangent plane to the given surface at the indicated point. x2…

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Q: In Problem,use a graphing utility to graph the curve defined by the given parametric equations.

A: Given parametric equations are x=4sint+2sin2ty=4cost+2cos2t

Q: Suppose parametric equations for the line segment between (8, - 9) and (9, 4) have the form: (t) = a…

A: The given parametric equation is x(t)=a+bt and y(t)= c+dt. When t=0, x=8,y=-9. That is,…

Q: x = 1 – t², y = t – 2, –2 <t< 2

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Q: 10. Eliminate the parameter and identify the graph of the parametric equation. x = sin t , y = -3…

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Q: 16.) p sin ф %3D 2

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Q: 2. Rotate = -8t y = 6 + t? - 3 <t<0 about the y-axis. ||

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Q: Suppose parametric equations for the line segment between (6, 7) and (4, 5) have the form: Sa(t) = a…

A: The parametric equations for the line segment between (6,7) and (4,5) have the…

Q: Question 14 Find the equation of the tangent plane to the surface y = 2x2 – (0,-1, –2) z2 at the…

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Q: Find the area enclosed by the simple closed curve given by the parametric equations, x = 2cost +…

A: *to find:- total area.

Q: Problem 5: Find the equation of the tangent line to the curve defined by the parametric equations…

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Q: 1) (a) Convert the following equations from parametric to rectangular. State the domain and range of…

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Q: Consider the parametric equations x t-Ssint and y = 1-cost. Which of the following represents dx…

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Q: Enter the appropriate value to answer the question or solve the problem. 6. Set up, but do not…

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Q: For questions 5-6 consider the parametric equations x t' and y=2-t. X = 5. When t=2, then dy %3D dx…

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Q: Suppose parametric equations for the line segment between (8, – 3) and (9, 2) have the form: S¤(t) =…

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Q: Below is the graph of a parametric equation. If it is known that y=t,what must be the equation for…

A: Observe from the graph that  limx→∞ y=∞limx→-∞ y=-∞

Q: Suppose parametric equations for the line segment between (6, 2) and (1, - 5) have the form: S (t) =…

A: Here we use the initial consultations.

Q: For problems 4 – 7 find the equation of the tangent line(s) to the given set of parametric equations…

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Q: What does the graph of the parametric equations x(t)=3−t and y(t)=(t+1)2, where t is on the interval…

A: Given data÷

Q: Eliminate the parameter t from the parametric equation x = 3 sint y = 3 cost 0 ≤t≤ 2π.

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Q: Suppose parametric equations for the line segment between (6, – 9) and ( – 1, – 5) have the form:…

A: ...............when  ...............when  .

Q: Problem 3 Find the equation of the tangent line to the curve defined by the parametric equations…

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Q: If the parametric curve starts at (- 2, – 9) when t = 0 and ends at (5, 7) att = 1, then find a, b,…

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Q: Consider the following parametric equation. x = 3(cos 0+ 0 sin Ø) y = 3(sin 0 -0 cos 0) What is the…

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Q: The parametric equations for the paths of two projectiles are given. At what rate is the distance…

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Q: find the parametric equation for each of the following a.) for the line of slope 2 passing through…

A: a) Firstly, we will find the equation of line of slope 2 passing through the point (-2,4) by using…

Q: 3. x = 4t2 – 3 Y = 3t 0<t< 5 -

A: Given: x=4t2-3, y=3t and 0≤t≤5. To Find: Length of the parametric curve given by the set of…

Q: Given the parametric curve: x = t3-6t2 y = t2-4t What are all the points that the curve passes…

A: Given: the parametric curve:

Q: Problem 28: The parametric equation of a curve is given as x = 4t – 3, y = 16t2 – 9. Compute the…

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Q: 2. x = 3cos? (t) – sin? (t) y = 6 + cos(t) <t<0 2 - |

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Q: find parametric equations for the given curve. 4x − y2 = 5

A: Given curve is:

Q: Question 5 Find the length of the curve. +- from y = 1 to y = 2 %3D 4y2 2

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.