0) have the form: a + bt %3D y c+ dt %3D etric curve starts at (7, –6) when t = 0 and ends at (1,-6) at t = = 1, then find a, b, c, and d.

Q: Identify the length of the arc having parametric equations x = t3 and y = 2t2 from t = -2 to t = 0

A:

Q: The parametric curve x= 414 + 412 + 1, y= 5t 3 – 5t has two tangent lines at the point (9, 0). Find…

A:

Q: Find the equation of the tangent plane to the following surface at the given point. 4y cos (3ar 2)…

A: Given equation of surface and point is

Q: Find the distance between the skew lines with parametric equations x = 1 + t, y = 2 + 6t, z = 2t,…

A: The distance from a point P(x1,y1,z1) to a plane  is

Q: find parametric equations for the given curve. y = x2, translated so that the minimum occurs at…

A:

Q: Starting from the point (3, 1, –1), reparametrize the curve x(t) = (3 + t, 1 – 2t, –1 – 2t) in terms…

A: We need to reparametrize the given curve in terms of arclength. The solution is given below.

Q: set up intergral for the length an of the Curve 3T y%3DZ0* sin cx), 04XE

A:

Q: •x= 5+4 sin 0 and y = -3 + 2 cos 0

A:

Q: 7. Sketch the curve with parametric equations z =e, y =e', teR.

A:

Q: The length of the curve defined parametrically by: x = e*cost, y = e'sint,0 <t <, s equal to: Select…

A: tea

Q: Set up an intergral for the length of the curve, 04X y%3DZE* sin cx), O4 XE

A: Explanation of the answer is as follows

Q: z = In(x²y*) + / x² + y²

A:

Q: Find the distance between the skew lines with parametric equations x = 1 + t, y = 1 + 6t, z = 2t,…

A: Explanation: Given that,  Line 1: x=1+ty=1+6tz=2t Vector 1: 1,6,2 Line 2: x=1+2sy=5+15sz=-2+6s…

Q: The unit circle x² + y=1 can be wrriten in parametric form as x = cos(0) and y : = sino. dy and…

A: Follow the procedure given below

Q: For which values of t is the parametric curve x=8t, y=t+t, -0c0s ts 00 concave up? (Enter your…

A:

Q: Find the tangent line(s) to the parametric curve given by a = t-9t and y =t at (0, 9) %3D %3D

A: We have to find the tangent line

Q: Find the speed of the cycloid c(t) = (4t − 4 sin t, 4 − 4 cost) atpoints where the tangent line is…

A: Given: c(t)=4t-4sin(t), 4-4cos(t)

Q: Calculate a 3 ydz t 13x'y dy, Where Cis the oriented curve given in the figure . 3 Bydr+43xy dy =?…

A:

Q: Find the arc length of the curve on the given interval. Parametric Equations    x = 6t2 , y = 2t3…

A: Given parametric equations are x(t)=6t2, y(t)=2t3

Q: The length of the curve defined parametrically by: x = e'cost, y = eʻsint,0 <t <, is equal to:…

A: given parametric curve x=etcost     y=etsint

Q: Without eliminating the parameter t, find a Cartesian equation for the line tangent to the curve C,…

A: Let's find.

Q: Find the length of the arc of the curve having the parametric equations x = t³ and y = 2t2 from t =…

A:

Q: Obtain the gradient to a curve with the parametric equations given by I = In - and y = sinh 2t whent…

A:

Q: Find the tangent line(s) to the parametric curve given by a = t¹ - 9t² and y=t² at (0, 9).

A:

Q: (iii) dz< 22 + 2 where here y parametrises the straight line segment from 0 to 1- i.

A:

Q: Find parametric equations for the arc of a circle of radius 7 from (0,0) to Q = (14,0). æ(t) y(t)…

A: Given that  Radius of circle is 7  P(0,0)to Q(14,0) To find the parametric equations of the circle

Q: Find the length of the arc of the curve having the parametric equations x = t³3 and y = from t = 0…

A:

Q: Find parametric equations for the semicircle x2 + y2 = a2, y &gt; 0, using as parameter the slope t…

A:

Q: In which direction is the curve x = -2 sin t, y = 2 cos t, for 0 ≤ t &lt; 2π, generated?

A: x = -2 sin t, y = 2 cos t Table for values of x and y: t x y 0 0 2 π 0 -2 π2 2 0 2π 0 2

Q: Find the length of the arc of the curve having the parametric equations x = from t = 0 to t = 1. t…

A:

Q: Find the equation of the tangent line to the curve y = et at the point (0, 1). Give your answer in…

A: Given,            The curve is y=exx2+1 and the point is 0,1.To find : Find the equation of the…

Q: 9) Sketch x = indieate the onientatiba of the 2t°, y = 3t, -4sts4 aud with %3D Curve an arow,

A:

Q: Find symmetric equations for the tangent line to the curve of intersection of the paraboloid zx +y…

A: Given  The equation of Paraboloid Z=x2+y2 The equation of Ellipsoid 2x2+y2+z2=76

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

A: Find the Length of the curve

Q: 6) Find the equation of the osculating plane of the helix x = sin 3t, y = 2t, at the point (-1,л,0).…

A: Given :x=sin3ty=2tz=cos3tpoint -1, π, 0

Q: Starting from the point (2, –1, 2), reparametrize the curve r(t) = (2 – 2t, -1+ 2t, 2 – 3t) in terms…

A:

Q: Consider the curve C parametrized by(x, y) = (5 cos (−12t), 5 sin(−12t)), for −π/2 ≤ t ≤ π/2 What is…

A:

Q: What is the integrating foc tor of the equation %3B

A: Topic:- differential equations

Q: Find the equation of the tangent plane at the point (-2,1 – 3) to the ellipsoid surface + y? + = 3.

A: Find the equations of the tangent plane and normal line at the point (-2, 1, -3) to the ellipsoid…

Q: x = 1+ vt, y = et X =1+1 Y. %3D

A:

Q: Find parametric equations for the semicircle x2 + y2 = a2, y&gt; 0, using as parameter the slope t =…

A:

Q: Starting from the point (-4, 5, 4) reparametrize the curve r (t) = (-4- 3t)i + (5 – 3t)j + (4 + 2t)k…

A:

Q: Find the length of the parametric curve x = sin-1t,y = In V1– t² for 0 <t<-

A:

Q: Consider the given curve: R(f) = (2 cos f, 12f +3,-2 sin f) Reparametrize the curve using arclength…

A:

Q: 2) Find the cartesian eauation for the olar curve r=tan e sece ×ニy )yニxと 2.

A:

Q: TQand TR are secants from Point T to Cirlce A as shown below: s. If mQR = 70° and mSP 34°, what is…

A: Given: To explain the correct of the given statement as follows,