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Q: Find the speed at the given value of t. r(t) = (sin(3t), cos(6t), cos(7t)), t = %3D (플) = 프2

A: Given:

Q: Find the length of the astroid x = cos3 t, y = sin3 t, 0 ≤ t ≤ 2π.

A:

Q: Calculate the length of the side XY given the following data for 29°: Sin 29° = 0.485 Cos 29° =…

A: Solve for xy

Q: The functions 7(t) = (cos t, sin t) and R(t) = (cos(t²), sin(t²)) generate the same set of (x, y, z)…

A:

Q: Find the Re(z) and Im(z) z=sin(e^i3)+sinh(5∠30)

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Q: FIND THE EQUATION Of THE TANGEN+ L INE TO C, 3JE AT THE POINT ン

A: Question - A Given curve: r=-3sin2θ The point is 322,322 The equation of a tangent line in a…

Q: find the speed at the given value of t. r(t) = (sin 3t, cos 4t, cos 5t), t =

A: Given: rt=sin3t, cos4t, cos5t To find the speed at the given value of t=π2. Solution: Speed is the…

Q: : Find the length of the cardioid r = 1 + cos 0 0 < 0 <T

A:

Q: Find the velocity, acceleration, and speed of a particle with the given position function. r(t) = (4…

A: Given position function isrt=4 cos t , 6t , 4 sin tWe have to find velocity , speed &amp;…

Q: The position of a particle moving along a coordinate line is given by: s(t) = 10 cos a) What is the…

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

Q: Find the z-values of cos i = e²

A: Given

Q: Find the length of the cardioid r= 4 – 4 cos 0. The length of the cardioid is

A:

Q: Graph the limaçon. Cardioids r = -1 + sin u

A: Given- r=-1+sinu To Draw- The graph of the above equation of the limaçon.

Q: Eliminate the parameter t from the following. Sa(t) = 2 sin t + 5 ly(t) = 5 cost – 6

A: Rewriting the given equations:

Q: Find the length of one arch of the cycloid 2(t – sin(t)), y = 2(1 – cos(t). х

A:

Q: A) S sin edo b)S sec edo )Side Ssec?eddo E)S cos ede

A: We have to find the integral

Q: az az Use the chain rule to find and as at sin(8) = r = st, 0 = s + t4 az %3D ds az %3D at Submit…

A:

Q: Find the value of dʻy/dx at the point defined by the given value of t. x = 5 sin t, y = 5 cos t, t=…

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Q: Find the angle at which the cardioid r = a(1 - cos u) crosses the ray u = pai/2.

A: Given:

Q: Graph the limaçon. Oval limaçons   r = -2 + sin u

A: A Cardioid is a curve traced out by a point on the circumference of a circle rolling around another…

Q: Show that cos(e-²) dz . 2πί - sin(1). 22 Here C = {z E C||2| = 1} (the unit circle).

A: prove is following...

Q: If Wallis is used to integrate sin rcos zda, what must be the value of a? A. 00 B.1 C.O D.

A: In wallis integration, to find the value of alpha

Q: Find the length of one arch of the cycloid a = 9(t – sin(t)), y = 9(1 – cos(t)). %3D

A:

Q: Find the area inside the oval limaçon r = 6 + sin 0.

A:

Q: Q1: Find the length of the cardioid r= 1 + cos 0 0 < 0 <T

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Describe the motion of a particle with position (x, y) as t varies in the given interval. x = 3…

A:

Q: Ut=a?Uxx , 00 U(0,t)=0, U(1,t)+aU(1,t)=1 , U(x,0)=sin(pi x)

A:

Q: Describe the motion of a particle with position (x, y) as t varies in the given interval. x = 3…

A:

Q: t sin(t) + 6 cos(t) t7

A: This question is based on properties of exponents.

Q: Find the area inside of the cardioid r = 3(1+ cos(4)) and outside of the circle r = cos(4). a)13m b)…

A: Given problem is :

Q: (2 cos t, 2 sin t, t), where 0 <t < .

A:

Q: Find the exact length of the helix7(t) = 1t 5 cos 1t 5 sin 12t ) for – 6 <t< 5.

A:

Q: Calculate the length of the side XY given the following data for 29: Sin 29 = 0.485 Cos 29 = 0.875…

A:

Q: dr Find of r = (csc 0 + cot 0)-1? de

A:

Q: pln e" sec? e" dx In 플 Find (a).

A:

Q: The position of a particle moving along a coordinate line is given by: s(t) = 10 cos (t +),t 20 a)…

A: Please refer to the image below.

Q: A particle moves according to the position function s (t) = e2t sin (3t). %3D

A: Definition used -                        v(t)= dsdt                       a(t)=dvdt=d2sdt2…

Q: Given a = 2 cos t + 26 and y = 5 sin? t dz dt dy dt ||

A: Simply take the derivative using basic concept of derivative.

Q: Find Z, , Zy, Zy, Z, for the following equation: ху, Z= a x +cy° + c sin(xy) + d cos(y?), where…

A: We have given Z = a x3 + c y3 + c sin(xy) + d cos(y2)  Where a,b,c,d are constants)

Q: Cos X 2)

A:

Q: Find the area of one leaf of the "four-petaled rose" r = 5 sin 20 shown in the following figure: y…

A:

Q: Show that d?y dY + cot o- +a(@ + 1)Y = 0, 0 < 6 < T, do is transformed into Legendre's equation by…

A: Given:

Q: Convert to rectangular coordinates. x = 1+ sin t, y = 1 + cos t for t in 0, 27

A: The solution are next step..

Q: Find the distance traveled by a particle with position (х, у); Cos t, y = (cos t)², 0 < t < 4TT X =

A: To solve this we have to use two point distance formula

Q: 1. Given y + 0=90°. Find the measurement of angle 0 in the triangle below using cofunction…

A: Given,

Q: Find T, N and k for r(t) = (e' cos t)i + (et sin t)j + (e)k

A:

Q: If the area enclosed by the curve x = 5 cos³ t and y = 5 sin° t (where t E R) is A, then what is A?…

A: