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High School Math Calculus PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

Tofind: the tension in each supporting cables when load is 200 pounds.

Tofind: the tension in each supporting cables when load is 200 pounds.

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

8th Edition

ISBN: 9781337904285

Author: Larson

Publisher: CENGAGE L

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Question

Chapter 10, Problem 36CR

To determine

Tofind:the tension in each supporting cables when load is 200 pounds.

Expert Solution & Answer

Answer to Problem 36CR

The tension in each supporting cables when load is 200 pounds is

|u|=105.60|v|=77.05|w|=77.05

Explanation of Solution

Given information:

The figure provided in the question,

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 10, Problem 36CR

Calculation:since the load is 200 pounds,

Thus, the (downward) force of the weight is represented by the vector,

w=〈0,0−200〉

The force vectors corresponding to the ropes are as follows:

u=|u|OA⇀|OA⇀|u=|u|〈0−0,10−0,10−0〉0+100+100 [simplify]u=|u|〈0,12,12〉 [add and simplify]v=|v|OB⇀|OB⇀|v=|v|〈−4−0,−6−0,10−0〉16+36+100 [simplify]v=|v|〈−238,−338,538〉 [add and simplify]z=|z|OC⇀|OC⇀|z=|z|〈4−0,−6−0,10−0〉16+36+100 [simplify]z=|z|〈238,−338,538〉 [add and simplify]

For the system to be in equilibrium, it must be true that,

u+v+z+w=0u+v+z=−w [subtract]

This yields the following system of linear equations,

|v|(−238)+|z|(238)=0|u|12+|v|(−338)+|z|(−338)=0|u|12+|v|(538)+|z|(538)=200

By solving these equations,

|u|=105.60|v|=77.05|w|=77.05

Chapter 10, Problem 35CR

Chapter 10, Problem 37CR

Chapter 10 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

Ch. 10.1 - Prob. 1E Ch. 10.1 - Prob. 2E Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - Prob. 5E Ch. 10.1 - Prob. 6E Ch. 10.1 - Prob. 7E Ch. 10.1 - Prob. 8E Ch. 10.1 - Prob. 9E Ch. 10.1 - Prob. 10E

Ch. 10.1 - Prob. 11E Ch. 10.1 - Prob. 12E Ch. 10.1 - Prob. 13E Ch. 10.1 - Prob. 14E Ch. 10.1 - Prob. 15E Ch. 10.1 - Prob. 16E Ch. 10.1 - Prob. 17E Ch. 10.1 - Prob. 18E Ch. 10.1 - Prob. 19E Ch. 10.1 - Prob. 20E Ch. 10.1 - Prob. 21E Ch. 10.1 - Prob. 22E Ch. 10.1 - Prob. 23E Ch. 10.1 - Prob. 24E Ch. 10.1 - Prob. 25E Ch. 10.1 - Prob. 26E Ch. 10.1 - Prob. 27E Ch. 10.1 - Prob. 28E Ch. 10.1 - Prob. 29E Ch. 10.1 - Prob. 30E Ch. 10.1 - Prob. 31E Ch. 10.1 - Prob. 32E Ch. 10.1 - Prob. 33E Ch. 10.1 - Prob. 34E Ch. 10.1 - Prob. 35E Ch. 10.1 - Prob. 36E Ch. 10.1 - Prob. 37E Ch. 10.1 - Prob. 38E Ch. 10.1 - Prob. 39E Ch. 10.1 - Prob. 40E Ch. 10.1 - Prob. 41E Ch. 10.1 - Prob. 42E Ch. 10.1 - Prob. 43E Ch. 10.1 - Prob. 44E Ch. 10.1 - Prob. 45E Ch. 10.1 - Prob. 46E Ch. 10.1 - Prob. 47E Ch. 10.1 - Prob. 48E Ch. 10.1 - Prob. 49E Ch. 10.1 - Prob. 50E Ch. 10.1 - Prob. 51E Ch. 10.1 - Prob. 52E Ch. 10.1 - Prob. 53E Ch. 10.1 - Prob. 54E Ch. 10.1 - Prob. 55E Ch. 10.1 - Prob. 56E Ch. 10.1 - Prob. 57E Ch. 10.1 - Prob. 58E Ch. 10.1 - 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