The migratory pattems of the scal can be estimated using the following parametric oquatious: x = 500 sim() and y = -1200cix() fer a: is 2r. The nigratory paltems of the orea (a predalor of seals) cam he estirnated using the follrwing paranmetric equations: x = S00 sim() and y =-1200cim() kr 0sis 2r. Tox these migrationIs, ( -0 represents 1 Jannary in a given year, - 27 Teresents 31 December af the same year and (r.r) represcnts the position of the animal relative to the center of the Pacific Occan measused in miles, ie. (0,0) is the point at the center of the Pacific Ocean. a. If there are any collision points, find the collision points.

Q: Given the the parametric curve Į æ(t) = ecost y(t) = t³ – 243t

A:

Q: Consider the plane curve given by the parametric equations x = t² + 3t - 26 y = t² + 3t - 28 - What…

A:

Q: For the parametric equations: = 26e4 and y = 46et dx () dt %3D dy (ii) dt dy (ii) %3D dx

A:

Q: Find the length of the following parametric curve. x = 6 + 916, y = 5 + 6t°, 0<t < 2.

A: solution is given below

Q: What is the Cartesian form of the parametric equations ¤(t) =t+4 and y(t) =t² +3t +1? Provide your…

A: Given that,           x(t) = t+4    &amp;  y(t) = t2+3t+1  Then               t=x-4 , substituting…

Q: The curve graphed below has the parametrization C = {(v 4 %3|

A: Introduction: A parametric equation is one in which the dependent variables are defined as…

Q: In three dimensions, the cylinder x? + z2 – 10x – 6z – 2 = 0 has radius k i +tj+ and the axis line…

A: Radius =6  r(t)= (5+6cos(thetha))i+tj+(3+6sin(thetha)k

Q: Find the exact length of the parametric curve x =1+3t², y = 4+2r°, 0<t<2.

A:

Q: Find parametric equations for the line segment joining the points (9, 8) and (16, 11). O x=9+7t, y…

A:

Q: What Cartesian equation is equivalent to the given parametric equations? Sx (t) = 2 sint ly (t) = 4…

A: x(t)=2 sin t xt2 = sin t  square both side x24 = sin2 t ...............1   Now, y(t)= 4 cos t yt4 =…

Q: For the parametric equations: = 48e2 and y = 41et da (*) dt (6) dt %D dy (s) da %3D

A:

Q: : Find the length of the following parametric curve. x = 6 + 1", y = 1 + 7t21/2, 0 st s 2.

A:

Q: Determine all points on the parametric curve {x= 2t^3−24t y=t3−6t^2+9t−4 where the tangent slope is…

A:

Q: A curve is defined by the parametric equations x (t) = at² and d² y y (t) = bt where a and b are…

A:

Q: 2. Find the point(s) of intersection of the following two parametric curves, by first eliminating…

A: From x=t+5 we get t=x-5 Then we plug this in the y=t2 So, the equation is: y=(x-5)2   We can plug…

Q: Find the (perpendicular) distance from the line given by the parametric equations æ(t) 3 – 4t %3D…

A:

Q: Consider the parametric curve defned by r=3+5t and y=1+ Over which values of y does t curve has a…

A: Given problem:- Consider the parametric curve defect by   x = 3 + 5t and y = 1 + 3t   Over which…

Q: iminate the parameter in the parametric equations x(f) = 5t – 8 and y(t) = Vt – 5 to find a…

A: Given: The parametric equations are xt=5t-8 and yt=t-5 Given query is to find the Cartesian…

Q: I need a 3d sketch of the equation  Z=x+xsiny+xy

A: z=x+xsiny+xy

Q: Without eliminating the parameter t, find a Cartesian equation for the lin curve C, defined by the…

A:

Q: Find the length of the parametric curve defined over the given interval. A) B) 3 3 2 C) D) 1

A:

Q: ) Find the pdar eawation for the cartesian curve x²-y²= \x?+yz A)rsinz0=2 b)r=ュ )cos 20=1 Dr=cos2@…

A: In polar coordinates, substitute x =r sin(theta) and y= r cos(theta)

Q: Consider the parametric equations: x = 2t2, y =t³. Find at the point t = dx? 8 without eliminating…

A:

Q: Eliminate the parameter in the parametric equations æ(t) = /t – 1 and y(t) = -8t + 6 to find a…

A:

Q: What is the slope at t = −2 ?

A:

Q: consider the following set of parametric equations: x = 6tanhθ ; y = 3sechθ Calculate d^2y/dx^2

A:

Q: [6]. Consider the following set of parametric equations: x = r° - 3t y = 312 – 9 On which intervals…

A:

Q: tind the area of the parametric curve X = t ,4=9t-73

A:

Q: Consider the plane curve given by the parametric equations x = t + 22t – 23 y = t2 + 22t – 5 -- What…

A:

Q: Consider the following parametric curve: x(t) = 3t^2 −6 and y(t) = 3t^4 −3t^2 +12t +10 Find the…

A:

Q: What is the length of the curve defined by the parametric equations æ (t) = t² – 2t and y (t) = t³ –…

A: If x=f(t) and y=g(t)are parametric equations of the curve where t ranges from t1 to t2then…

Q: Consider the following parametric curve. Answer parts a and b.  x=−3+3t​, y=4−9t​;t=2

A:

Q: a) Find the are length of the parametric curve x = B(t. sint), y = B(1+ cost), in the range 0 sts,…

A:

Q: Given two points P(6, 3,1) and Q (5,0, 0), find the parametric equations for a smooth curve, C:x= 5+…

A:

Q: Find the length of the parametric curve x = 2t + 1, y = 3 + 2tž, 0 < t <%.

A: Find the Length of the curve

Q: Eliminate the parameter to find a Cartesian equation of the curve with parametric equations x = e^t…

A: Just put the exponential term value from one equation into the other and easily eliminate the…

Q: Determine the length of the parametric curve given x = 6 sint, y = 6 cost, ㅠ 0 ≤ t ≤=.

A:

Q: consider the following set of parametric equations: x=6tanhθ ; y=3sechθ Calculate dy/dx

A:

Q: Given the parametric curve. x = 5t2 – 6t + 4 y = t² + 6t – 1 Please find 1) The slope of the curve.…

A:

Q: For the parametric curve: x = 4t?, y = 4t, eliminate the parameter and express in .rectangular form…

A: The given parametric curve is                                                       x=4t2, y=4t

Q: Find the length of the parametric curve defined over the given interval. A) B) 64 37 z=t+V = 6. C)…

A:

Q: Consider the parametric equations: x = 2t2, y =43t3. Find d2ydx2at the point t=18 without…

A: Given parametric equations are x=2t2 and y=43t3. To find d2ydx2 at the point t=18 without…

Q: For the parametric equations: a = 16et and y 18e %3D da (i) dt 32*e^(2t) %3D dy (ii) dt 54*e^(3t)…

A:

Q: Find a parametric function for the intersection of r – 3y + 4z = 0 and a? + y² = 9.

A:

Q: Given the parametric curve and value of t x(t) = Vi, y(t) = 6t, t = 9

A:

Q: The parametric equations of a curve are given by = 4t – 7t2 and y = t – 12t a) dy dzr Find in terms…

A:

Q: Consider the parametric curve given by the equations:  x(t) = t2 + 37t - 23 y(t) = t2 + 37t + 48…

A: We need arc length to find the units of distance are covered by the point P(t) = (x(t), y(t))…

Q: Find ,Y, and of the given parametric equations dy d²y dx ' dx² d³y dx3 X = cost, y = 5 sin t in…

A: The given parametric equations,x=cost, y=5 sint

Q: Consider the plane curve given by the parametric equations x = t² + 22t - 23 y = t² + 22t - 5 What…

A:

Q: Find the length of the curve given by the parametric equations z = 2t3/2 0 <t< 4 ' y = 3t + 1

A:

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.