Please solve problem no 4 Problem 4Problem 5The radius of a circular manhole cover is estimated to The length of a side of a square floor tile is estimated asbe 16 in. with a maximum error in measurement of Lt with a maximum error in measurement of in. Use0.06 in. Use differentials to estimate the maximum error differentials to estimate the maximum error in the caleu-in the calculated area of one side of the cover. What is the lated area, What is the approximate average error and theapproximate average error and the approximate percen-tage error?approximate percentage error?Problem 6Figure 2 (Problem 6)If an object of weight W lb is pulled along a horizontalplane by a force applied to a rope that is attached to theobject, and if the rope makes an angle O with the horizontal,then it can be shown that the magnitude of the force isgiven byµ sin 0 + cos 9where p is a constant called the coefficient of friction.Suppose a man is pulling a 100-pound box along a floor,and that a= 0.2 (see figure). If 0 is changed from 45°to 46°, use differentials to approximate the change in theforce that must be applied.100The Chain RuleProblem 7Figure 3 (Problem 7)CorkOTA cork bobs up and down in a pail of water such that thedistance from the bottom of the pail to the center of thecork at time t 2 0 is given by s(t) = 12 + cos (Ar), wheres(1) is in inches and r is in seconds (see figure).1(t)Problem 8A particle in a vibrating spring is moving verticallysuch that its distance s(t) from a fixed point on the lineof vibration is given by s(t) = 4 + sin (100nt), wheres(t) is in cm and t is in seconds.(a) How long does it take the particle to make onecomplete vibration?(b) Find the velocity of the particle at t = 1, t = 1005,t = 1.01, and t = 1.015.

Answered: Problem 4 Pre The radius of a circular…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Please solve problem no 4

Problem 4
Problem 5
The radius of a circular manhole cover is estimated to The length of a side of a square floor tile is estimated as
be 16 in. with a maximum error in measurement of Lt with a maximum error in measurement of in. Use
0.06 in. Use differentials to estimate the maximum error differentials to estimate the maximum error in the caleu-
in the calculated area of one side of the cover. What is the lated area, What is the approximate average error and the
approximate average error and the approximate percen-
tage error?
approximate percentage error?
Problem 6
Figure 2 (Problem 6)
If an object of weight W lb is pulled along a horizontal
plane by a force applied to a rope that is attached to the
object, and if the rope makes an angle O with the horizontal,
then it can be shown that the magnitude of the force is
given by
µ sin 0 + cos 9
where p is a constant called the coefficient of friction.
Suppose a man is pulling a 100-pound box along a floor,
and that a= 0.2 (see figure). If 0 is changed from 45°
to 46°, use differentials to approximate the change in the
force that must be applied.
100
The Chain Rule
Problem 7
Figure 3 (Problem 7)
Cork
OT
A cork bobs up and down in a pail of water such that the
distance from the bottom of the pail to the center of the
cork at time t 2 0 is given by s(t) = 12 + cos (Ar), where
s(1) is in inches and r is in seconds (see figure).
1(t)
Problem 8
A particle in a vibrating spring is moving vertically
such that its distance s(t) from a fixed point on the line
of vibration is given by s(t) = 4 + sin (100nt), where
s(t) is in cm and t is in seconds.
(a) How long does it take the particle to make one
complete vibration?
(b) Find the velocity of the particle at t = 1, t = 1005,
t = 1.01, and t = 1.015.

Expert Solution

Step 1

Given information:

The radius of a circular manhole cover is estimated to be 16 inches, with a max error in measurement of + or - 0.06 inch.

Concept used:

The area of the circle is $A = {πr}^{2}$ .

Step 2

Calculation:

Differentiate the area of the circle with respect to r.

$\frac{d A}{d r} = π (2 r) dA = 2 πr \cdot dr . . . . . . (1)$

Since, The radius of a circular manhole cover is estimated to be 16 inches, with a max error in measurement of + or - 0.06 inch.

$r = 16, d r = \pm 0.06$

Substitute $r = 16, d r = \pm 0.06$ in equation (1) to find the

$\begin{array}{rcl} dA & = & 2 π (16) \cdot (\pm 0.06) \\ = & \pm 6.032 \end{array}$

Answer: Therefore, the maximum error of the area could be approximately 6.032 sq inch

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