for the Find CUrve reparametri zations alt)= (t, Cosht, o), tER. two

Q: 7) The curve C have the parametric equation: x(t) = t2 + 1 and y(t) = t³ – 1 a) Make a sketch of…

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Q: 1. Let S be the surface generated by the curve +y+4= 0 when it is revolved about the z-axis. (a)…

A: y = x2 - 4 (a) we choose x, θ as perameter = (x, - (x2 + 4) cos θ, -(x2 +4) sin θ)   (b) dr→dx= (1,…

Q: Tangents to Curves

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Q: 24. A particle moves round the polar curve r = a(1+ cos e) with constant angular velocíty w. The…

A: We have constant angular velocity = w  r = a(1+ cosθ)

Q: -8 Find the exact arc length of the curve over the interval. 3. y = 3x2 – 1 from x 0 to x =1 x= {0 +…

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Q: 1. The parametric equations: x = a cos 0,y = a sin? 0;0 ses 2n, define a curve called an asteroid

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Q: 15-18 The given curve is rotated about the y-axis. Find the area of the resulting surface. 16. x +y…

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Q: 1) a) sketch the curve. b) eliminate the parameter and find the Cartesian equation for the curve. c)…

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Q: Q11:- Consider the parametric equations x(t) = 2et and y(t) = t- Find the arc length of e2t %3D the…

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Q: Find the length of the curve y In (cos x), 0sxs- 3 The length of the curve is (Type an exact…

A: The length of any curve for x1≤x≤x2 is given by,l(Length)  = ∫x1x21+dydx2  dx   Also use ∫secx dx =…

Q: 1-4 Find the area of the surface generated by revolving the given curve about the x-axis. . 1. y =…

A: Surface area is 7✓55 π

Q: a:1 → E" and ß:I → E" be given curves. Find these derivates: d d d : dt |la(t)|| and dt dt |la

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Q: 15) (10.) Sketch the parametric curve x = 2 + 3sin(t), y = -3+ 3cos(t) for <t<. Find the slope of…

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Q: (iii) Given the curve with parametric equation x = e and y = In(2-r²) Find the equation of the…

A: Formula: The normal line of the parametric equation x=ft and y=gt at the point t=t0 is the line…

Q: Question 1 of 8 View Policies Current Attempt in Progress Find the arc length of the parametric…

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Q: 1-4 Find the area of the surface generated by revolving the given curve about the x-axis. 3. y=…

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Q: 3- The equations X= a -a sind, Y=a- a cosd,(0<0<2n Represent one arch of a cycloid .show that the…

A: To calculate the surface area of revolution about the x-axis, use the following formula:…

Q: Find the length of r(t)=[e"(cosbt), ea"(sinbt)] from t=0 to %=D1 (a and b are constants). This plane…

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Q: Given the curve with parametric equation x= e* and y= In(2-r²) Find the equation of the normal to…

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Q: 1. A curve called the folium of Descartes is defined by the parametric equations 3t ¤(t) = 3t2 y(t):…

A: Hello. Since your question has multiple parts, we will solve the first three parts for you. If you…

Q: 18. What is the length of the polar curve below? 3πt x = 8cos (0) for 0 ≤ 0 ≤ ³1

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Q: 1. Let C be the curve with parametric equations V2 - t? 3/2 8 1 Y = t + 3 where t e [0,+). V2 8 (a)…

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Q: 7- Find the length of the curve T = e", 30 - A<0<T given in polar coordinates. a)V10 sinh(37) b)2/10…

A: Given a curve : r=e3θ   ,-π≤θ≤π We need to find the length of the curve. Let's start.

Q: 17. The involute of a circle is the curve traced by a point at the end of a thread being unwound…

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Q: 11. dy/dx = -x/y, y(0) = 4 %3D

A: Given: Let's sketch the isoclines and their direction markers, then sketch a few solution curves,…

Q: 2. The graph below shows a curve called an astroid with parametric equa- tions x = cos t, y = sin t,…

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Q: Draw the isoclines with their direction markers and sketch several solution curves, including the…

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Q: 2. Consider the parametric equation r(t) = (1 – t°, t(1 – t)) where –1 <t < 1. (a) Plot this curve…

A: The solution is given as follows

Q: Question 3 (4+4pts) Let r(t) = a) Find parametric equations of the line tangent to the graph of r(t)…

A: Here I am attaching image so that you understand each and every step.

Q: 10-13 The given curve is rotated about the y-axis. Find the area of the resulting surface. 10. y = 1…

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Q: Question 3. The parametrized curve x = cos(t) – 5sin(t), %3D 101 y = -10cos(t)+ sin(t) is an…

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Q: (d) A curve is defined by the parametric equations: -21 x(t)= e' cos 2t, y(t) = e²¹ sin 2t dy…

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Q: 3. As cars travel on gravel roads, the roads erode and take on a "washboard" look due to the…

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Q: Arc length calculations Find the length of the following twoand three-dimensional curve.r(t) = ⟨3t -…

A: Given curve is the arc length in the interval the arc length in the interval [a, b] is given as…

Q: Question 9. A circular helix in ryz-space has the following parametric equations, where ER. I(0) = 4…

A: Given : x(θ)=4 cosθy(θ)=4sinθz(θ)=3θ

Q: 1. Given the parametrized curve (helix) a(9) = (a cos , a sin, b), seR, a(s) C C wodd where c² = a²…

A: For your demand i solve your question no c and d

Q: 17. The parametric curve given by the equations T = t3 – 3t, y = t² +t+ 1, is shown in the figure…

A: According to question,Given function,x = t3 - 3t,y = t2 + t +1

Q: (a) Find the exact length of the curve (i) r = 1+ sin 0, (ii) r = 2(1+ sin 8), 0<0< 27, 0<0< 2n.…

A: We have to find arc length of give curve after that we have to find relationship between their…

Q: 6. Trace the curve r? = 4cos*etan?e. %3D

A: The equation r2=4 cos4 θ tan2 θ can be resolved to get two equations:  r=±2 (cos2 θ)(tan θ)=±2(cos…

Q: Questions Find the exact arc length of the curve over the specified interval: (i) y=3x -1 from x=1/3…

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Q: (a) æ = sin t, y = csc t, 0 1. Thus, the curve is the portion of the hyperbola y = 1/x with y > 1.…

A: Given x=sin ty=csc t0&lt;t&lt;π2

Q: QUESTION 14 Which one of the following points lies on the curve r= sin 0-5. (5, 0) o (5, 2n) o (-5,…

A: In this we find that point which lies on the given curve.

Q: Find the lengths of the curves 1. The cardioid r = 1 + cos u 2. The curve r = a sin^2 (u/2), 0&lt;=…

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Q: 1. Given the parametric curve x = 3t2 – 1, y = 2t³ + 1. (a) Find the equation of the tangent to the…

A: Please refer the attached image for complete solution.

Q: 1. the area of the curve r^2 =a^2 cos 2 θ

A: Formula: The area of polar curve r=f(θ) is given by, A=12∫αβr2 dθ Given: r2=a2cos2θ

Q: 2. (a) Find the exact length of the curve (i) r = 1+sin 0, 0<0< 27, (ii) r = 2(1+ sin 0), 0 <0< 27.…

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Q: Consider the curve C given in parametric equations as 3t2et C:, = 4arctan(t) 4 arctan(t) (a) Find…

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Q: Questions Find the exact arc length of the curve over the specified interval: (i) y= 3x/2 –1 from x…

A: The given problem is to find the arc length of the given functions  over the given specified…

Q: Can you please answer this question and show all of the steps and say the correct letter

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Q: CHAPTER 1. CURVES 22 Exercise 1.3.1 Find the length of the arc in one period of the cycloid x = t –…

A: To find- Find the length of the arc in one period of the cycloid x = t - sint, y = 1 - cost. The…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.