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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 1t with a maximum error in measurement of in. Use 0.06 in. Use differentials to estimate the maximum error in the calculated area of one side of the cover. What is the differentials to estimate the maximum error in the caleu- approximate average error and the approximate percen- tage error? lated area. What is the approximate average error and the approximate percentage error? Problem 6 Figure 2 (Problem 6) If an object of weight W lb is puled along a horizontal plane by a force applied to a rope that is attached to the object, and if the rope makes an angle 0 with the horizontal, then it can be shown that the magnitude of the force is given by u sin 0 + cos 9 where 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 6 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 (t), where s(1) is in inches and tis in seconds (see figure). (r) 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.

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 1t with a maximum error in measurement of in. Use 0.06 in. Use differentials to estimate the maximum error in the calculated area of one side of the cover. What is the differentials to estimate the maximum error in the caleu- approximate average error and the approximate percen- tage error? lated area. What is the approximate average error and the approximate percentage error? Problem 6 Figure 2 (Problem 6) If an object of weight W lb is puled along a horizontal plane by a force applied to a rope that is attached to the object, and if the rope makes an angle 0 with the horizontal, then it can be shown that the magnitude of the force is given by u sin 0 + cos 9 where 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 6 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 (t), where s(1) is in inches and tis in seconds (see figure). (r) 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.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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Please solve problem no 8

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.
Transcribed Image Text: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.
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