Calculus
6th Edition
ISBN: 9781465208880
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 10.3, Problem 19PS
To determine
To find: thevelocity
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5.
The position function of a moving object is given by 7(t) = (, et", cos t). Find its velocity
COS
and acceleration functions.
6. Find the following for the given equation.
r(t) = (e−t, 2t2, 8 tan(t))
(a) r'(t) =
(b) r''(t) =
(c) Find r'(t) · r''(t).
7. The position vector r describes the path of an object moving in space. Find the velocity v(t), speed s(t), and acceleration a(t), of the object.
r(t) = (et cos(t), et sin(t), et )
v(t) =
s(t) =
a(t) =
Consider the following curve.
x = sin(6t), y = -cos(6t), z = 18t
Using the given parametric equations, give the corresponding vector equation r(t).
r(t) = (sin (6t))i (cos (6t))j + (18t)k ✔
Find r'(t) and Ir'(t).
r'(t) = (6 cos (6t))i + (6 sin (6t))j + (18) k
|r'(t) = 6√10
Find the equation of the normal plane of the given curve at the point (0, 1, 3).
Now consider the osculating plane of the given curve at the point (0, 1, 3). Determine each of the following.
T(t) = 1
T'(t) =
|T'(t) =
N(t) =
X
Chapter 10 Solutions
Calculus
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- A gear train consists of three gears meshed together (Figure 9). The middle gear is known as an idler. Show that the angular velocity of the third gear does not depend on the number of teeth of the idler gear (Gear 2).arrow_forwardA two-stage gear train consists of four gears meshed together (Figure 10). The second and third gears are attached, so that they share the same angular velocity (2=4). Find a formula giving the angular velocity of the fourth gear, 2, in terms of 1 and the values of n1,n2,n3andn4.arrow_forwardb. A particle moves in simple harmonic motion according to the equation, S = 09A cos(wt) + 09B cos(wt). Where s is the displacement, w is the angular d2 +ws=0. 'dt2 frequency and A, B are constant. Show that,arrow_forward
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