b) The length in first quadrant of the curve x/3 + y2/3 = a²/3 is given by 6ac/2 where parametric equations of curve are x = a cos'0,y = a sin*6. Compute the value of c. Also find the length in first quadrant of the curve (x/a}?/3 + (y/b)³/3 = 1 where parametric equations of curve are x = a cos"0, y = b sin®e.

Q: The equation of the tangent line to the parametric equations, x = sine, y= 20 + cose at 0 = 0 is y =…

A:

Q: 1. Find the second derivative of the parametric equations_x = a cost and y = b sin t

A:

Q: A simplified model of the Earth-Mars system assumes that the orbits of Earth and Mars are circular…

A: (a)To graph:

Q: eliminating the parameter t from the parametric equation x = 3 cost y = 3 sin t, find the…

A: First we square both given equation and then adding both and solve it.

Q: Find the equations of the lines tangent and normal to the curve given by the parametric equations x…

A: Given: x=4 costy=2 sin2tt=π3

Q: The parametric equations for the motion of a charged particle released from rest in electric and…

A: Given x and y values.... Let us find dy/dx to draw the graph....

Q: Consider a projectile launched at a heighth feet above the ground and at an angle with the…

A: The parametric equation of the position of the ball is given by…

Q: #3. Find parametric equations for the tangent line to thể curve with parametric equations x = (sin…

A:

Q: Find parametric equations for the tangent line to the curve with the parametric equations x…

A: Given: The parametric equations, x = t2+3,  y = ln t2+3, z = t and the point 2, ln4, 1. To find: The…

Q: Suppose a curve is traced by the parametric equations x= 6.08 sin(t) and y = 22 -…

A:

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A: Given:

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A:

Q: Find the slope of the tangent line to polar curve r = 6 – 9 sin 0 at the point (6-

A:

Q: 5. Given the parameter 7, constants a and c, show that the parametric equations: X(+) = (cosh () –…

A:

Q: Find parametric equations for the tangent line at the point (cos(−4π/6),sin(−4π/6),−4π/6) on the…

A: Given parametric equation of given curve is x=cos(t), t=sin(t), z=t Differentiate with respect to t.…

Q: 9/Find Parametric equations for the Line that is tangent to the curve r(t) = eti + (Sint)j + In…

A:

Q: curve has the following parametric equations with parameter t. x=2t-1/2t and y=2t+1/2t. Find dy/dx…

A:

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A:

Q: what points does the curve described by the parametric equations x = 2a cos t – a cos 2t d y = 2a…

A:

Q: Eliminate the parameter in the parametric equations x = 7+ sint, y = 2+ sint, for 0sts, and describe…

A:

Q: The equation of the tangent line to the parametric equations, x = sine, y =20+ cose at e = 0 is y =

A:

Q: 1. x (0) = 0 + cos 0 y (0) = 1+ sin 0 given that

A:

Q: 2.) Given the parametric equations x=cos3t and y=sin3t. Find the equation of the normal line at the…

A:

Q: Consider the following parametric equation. #20(cos 0+0 sin 0) y- 20(sin 0-0 cos 0) What is the…

A: Given: x=20cosθ+θsinθy=20sinθ-θcosθ we know length of curveL on interval a,b is given by…

Q: Without using a calculator, sketch the parametric equations by eliminating the parameter. Indicate…

A: The given parametric equation x=4+2cosθ and y=-1+sinθ

Q: 3. A curve has parametric equations r = sin(3t) and y = cos(t) where t takes all real %3D values. dy…

A:

Q: Eliminate the parameter t from the parametric equationsx =3 +sin t and y = cos t - 2.

A: Given: x=3+sint and y=cost-2 We have to eliminate the parameter t from the parametric equations.…

Q: 9. Show that the curve with parametric equations x = sin t and y = sin(t + sin t) for 0st s 2n has…

A: Given that the curve with parametric equations are x=sint,y=sint+sint. First find the slope that is…

Q: 4. Sketch the parametric equations by eliminating the parameter. Be sure to include arrows to…

A: From given equations, we find sin theta and cos theta Then we plug them in the Pythagorean identity…

Q: 10. Find the value of 2 for the parametric curve xx= y = 2t2 -6 at the point (1.-6).

A:

Q: EXAMPLE 5 Sketch the curve with parametric equations x = 2 sin(t), y = 4 sin2(t). SOLUTION Observe…

A:

Q: Find an equation y = f(x) for the parametric curve c(0) = (cos(0), 3 cos(0) + 8 sin²(0)) and compute…

A: The objective is to find y(x) and it's it's derivative .

Q: The parametric equations for the motion of a charged particle released from rest in electric and…

A: Solve by finding slope

Q: Can the parametric curve (t, sin t) be represented as a graph y = f (x)? What about (sin t, t)?

A: Parametric curve is (t, sint) i.e x = t and y = sint

Q: x = 2 cos(3t) – 4 sin( 3t) IT t = 2 y = 3 tan( 6t)

A: given,        x=2cos3t-4sin3t   and y =3tan6t

Q: 4) Find the critical points of the parametric equations x = 5 – In t y = t + Int

A:

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A:

Q: 3. x = 3+ 4 sin t ;y == 3 cos t – 4

A:

Q: Determine the (1) graph, (2) initial and terminal points, (3) orientation, (4) the dy derivative and…

A: x(t)=3+sin(t), y(t)=-2+cos(t)   where π≤t≤2π   Graph

Q: Two parametric equations are given by: x = cos' (t), y sin (t) u = sin(t) v - cos(t) In one figure,…

A: We have to make plots of y versus x and v versus u.

Q: 8/3 Find the slope of the tangent line to polar curve r = 8 sin 0 at the point 3.

A: Explanation of the answer is as follows

Q: {; 4 cos(t) 2 sin(t) at the point 4 Find the slope of the tangent line to the parametric curve

A: We have the parametric equation of curve as x=4cost⇒cost=x4        ⋯⋯1y=2sint⇒sint=y2          ⋯⋯2…

Q: Find the second derivative of y with respect to x from the parametric equations given. x = 3 + 4…

A:

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A: Given  x=e-3tcos8ty=e-3tsin8tz=e-3t

Q: The parametric equations of a curve are given by 2 x = In and y = cosh-(2t). when t = 1. dx Find

A: Given,            The parametric equations of a curve are given by              x=ln2t  and…

Q: The parametric equations: x =ac a cos³ 0,y = a sin 0;0 <0s 2n, define a curve called an asteroid

A: Please refer the attached image for complete solution. THANKYOU.

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A:

Q: Given the parametric equation : X = sin t cos t and y = sin t where 0 < t < 2n a. What is the slope…

A:

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.