Question

1) Find the length of the parametric curve x=2 cos(t) , y=2 sin(t) on the interval [0, pi].

2) A rope lying on the floor is 10 meters long and its mass is 80 kg. How much work is required to raise one end of the rope to a height of 15 meters?

Answer #1

Hope it helps.All the best

1. Graph the curve given in parametric form by x = e t sin(t)
and y = e t cos(t) on the interval 0 ≤ t ≤ π2.
2. Find the length of the curve in the previous problem.
3. In the polar curve defined by r = 1 − sin(θ) find the points
where the tangent line is vertical.

Find the length of the curve
1) x=2sin t+2t, y=2cos t, 0≤t≤pi
2) x=6 cos t, y=6 sin t, 0≤t≤pi
3) x=7sin t- 7t cos t, y=7cos t+ 7 t sin t, 0≤t≤pi/4

With the parametric equation x=cos(t)+tsin(t), y=sin(t)-tcos(t)
, 0 ≤ t ≤ 2π)
Find the length of the given curve. (10 point)
2) In the circle of r = 6, the area
above the r = 3 cos (θ) line
Write the integral or integrals expressing the area of this
region by drawing. (10 point)

7. For the parametric curve x(t) = 2 − 5 cos(t), y(t) = 1 + 3
sin(t), t ∈ [0, 2π) Part a: (2 points) Give an equation relating x
and y that represents the curve. Part b: (4 points) Find the slope
of the tangent line to the curve when t = π 6 . Part c: (4 points)
State the points (x, y) where the tangent line is horizontal

Find the derivative of the parametric curve x=2t-3t2,
y=cos(3t) for 0 ≤ ? ≤ 2?.
Find the values for t where the tangent lines are horizontal on
the parametric curve. For the horizontal tangent lines, you do not
need to find the (x,y) pairs for these values of t.
Find the values for t where the tangent lines are vertical on
the parametric curve. For these values of t find the coordinates of
the points on the parametric curve.

Consider the parametric equations below.
x = t sin(t), y = t
cos(t), 0 ≤ t ≤ π/3
Set up an integral that represents the area of the surface
obtained by rotating the given curve about the x-axis.
Use your calculator to find the surface area correct to four
decimal places

Consider the parametric curve given by the equations:
x = tsin(t) and y = t cos(t) for 0 ≤ t ≤ 1
(a) Find the slope of a tangent line to this curve when t =
1.
(b) Find the arclength of this curve

Show that the curve
x = 7 cos(t), y = 6 sin(t) cos(t)
has two tangents at (0, 0) and find their equations.

The curve given by the parametric equations of x = 1-sint, y = 1-cos t ,
Calculate the volume of the rotational object formed by rotating the x axis use of the parts between t = 0 and t = π / 2.
Please solve this question carefully , clear and step by step.I
will give you a feedback and thumb up if it is correct.

Solve the following differential equations
1. cos(t)y' - sin(t)y = t^2
2. y' - 2ty = t
Solve the ODE
3. ty' - y = t^3 e^(3t), for t > 0
Compare the number of solutions of the following three initial
value problems for the previous ODE
4. (i) y(1) = 1 (ii) y(0) = 1 (iii) y(0) = 0
Solve the IVP, and find the interval of validity of the
solution
5. y' + (cot x)y = 5e^(cos x),...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 1 minute ago

asked 15 minutes ago

asked 17 minutes ago

asked 36 minutes ago

asked 40 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago