Question

An object is moving in the plane according to the parametric equations

* x*(

* y*(

for 0 ≤ * t* ≤ 1

,where time units are seconds and units on the coordinate axes
are feet. The path traveled by the object is a portion of an
ellipse in the first quadrant, as pictured. The location of the
object at time t will be denoted by P(t)=(x(t),y(t)). A laser beam
projects from the object in a direction perpendicular to the
tangent line along what is called a normal line. If
* t*≠ 1/2, the normal line will cross the x-axis at
a point (m(t), 0). .

a) When 0 ≤ t ≤ 1, the equation of the normal line to the path is

b) When t≠ 1/2, the formula for the coordinate m(t)=

c) lim t→1/2 m(t)=

Answer #1

*Please UPVOTE if this answer helps you understand
better.*

*Solution:-*

*Please UPVOTE if this answer helps you understand
better.*

Consider the parametric curve C deﬁned by the parametric
equations x = 3cos(t)sin(t) and y = 3sin(t). Find the expression
which represents the tangent of line C. Write the equation of the
line that is tangent to C at t = π/ 3.

On the parametric curve (x(t), y(t)) = (t − t^2 , t^2 + 3t)
pictured below, determine the (x, y)-coordinates of the marked
point where the tangent line is horizontal.

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

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

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

Determine the tangent line at point t = π/3 of the curve defined
by the parametric equations:
X = 2 sin (t)
Y = 5 cos (t)

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.

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

4)
Consider the polar curve r=e2theta
a) Find the parametric equations x = f(θ), y =
g(θ) for this curve.
b) Find the slope of the line tangent to this curve when
θ=π.
6)
a)Suppose r(t) = < cos(3t), sin(3t),4t
>.
Find the equation of the tangent line to r(t)
at the point (-1, 0, 4pi).
b) Find a vector orthogonal to the plane through the points P
(1, 1, 1), Q(2, 0, 3), and R(1, 1, 2) and the...

Find parametric equations for the rectangular equation y = e^x +
9 using the parameter t = dy/dx . Verify that at t = 1, the point
on the graph has a tangent line with slope 1

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 5 minutes ago

asked 38 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago