Suppose that an imaginary string of unlimited length is attached to a point on a circle and pulled taut so that it is tangent to the circle. Keeping the string pulled tight, wind (or unwind) the string around the circle. The path traced out by the end of the string as it moves is called an involute of the circle (shown in blue). Given a circle of radius r with parametric equations x = r cos θ , y = r sin θ , show that the parametric equations of the involute of the circle are x = r cos θ + θ sin θ and y = r sin θ − θ cos θ .
Suppose that an imaginary string of unlimited length is attached to a point on a circle and pulled taut so that it is tangent to the circle. Keeping the string pulled tight, wind (or unwind) the string around the circle. The path traced out by the end of the string as it moves is called an involute of the circle (shown in blue). Given a circle of radius r with parametric equations x = r cos θ , y = r sin θ , show that the parametric equations of the involute of the circle are x = r cos θ + θ sin θ and y = r sin θ − θ cos θ .
Solution Summary: The author illustrates how an imaginary string of unlimited length is attached to a point on the circle of radius r with parametric equations.
Suppose that an imaginary string of unlimited length is attached to a point on a circle and pulled taut so that it is tangent to the circle. Keeping the string pulled tight, wind (or unwind) the string around the circle. The path traced out by the end of the string as it moves is called an involute of the circle (shown in blue).
Given a circle of radius
r
with parametric equations
x
=
r
cos
θ
,
y
=
r
sin
θ
,
show that the parametric equations of the involute of the circle are
x
=
r
cos
θ
+
θ
sin
θ
and
y
=
r
sin
θ
−
θ
cos
θ
.
For the system consisting of the lines:
and
71 = (-8,5,6) + t(4, −5,3)
72 = (0, −24,9) + u(−1, 6, −3)
a) State whether the two lines are parallel or not and justify your answer.
b) Find the point of intersection, if possible, and classify the system based on the
number of points of intersection and how the lines are related. Show a complete
solution process.
3. [-/2 Points]
DETAILS
MY NOTES
SESSCALCET2 7.4.013.
Find the exact length of the curve.
y = In(sec x), 0 ≤ x ≤ π/4
H.w
WI
M
Wz
A
Sindax
Sind dy max
Утах
at 0.75m from A
w=6KN/M L=2
W2=9 KN/m
P= 10 KN
B
Make the solution handwritten and not
artificial intelligence because I will
give a bad rating if you solve it with
artificial intelligence
Elementary Statistics: Picturing the World (7th Edition)
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Fundamental Theorem of Calculus 1 | Geometric Idea + Chain Rule Example; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=hAfpl8jLFOs;License: Standard YouTube License, CC-BY