course Mth 151 ?6O?????g??{?????assignment #022022. `query 22
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19:46:44 ** There are four criteria for the group: closure, identity, inverse property, and associativity. The lack of any one of these properties means that the set and operation do not form a group. The set is closed on multiplication. The identity is the element that when multiplied by other elements does not change them. The identity for this operation is 1, since 1 * -1 = -1, 1 * 0 = 0 and 1 * 1 = 1. Inverses are pairs of elements that give you 1 when you multiply them. For example -1 * -1 = 1 so -1 is its own inverse. 1 * 1 = 1 so 1 is also its own inverse. However, 0 does not have an inverse because there is nothing you can multiply by 0 to get 1. Since there is an element without an inverse this is not a group. **
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RESPONSE --> NO, INVERSE self critique assessment: 2
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19:47:46 4.5.25 verify (NT)R = N(TR)
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RESPONSE --> (NT) R=VR=M N(TR)=N P=M confidence assessment: 2
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19:48:30 query 4.5.33 inverse of T
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RESPONSE --> T is the Inverse b/c TT gives the identity confidence assessment: 3
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19:49:11 4.5.42. Explain what property is gained when the system of integers is extended to the system of rational numbers.
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RESPONSE --> confidence assessment:
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R?D?{???????§?assignment #023 023. `query 23 College Algebra 12-14-2007
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19:51:21 5.1.18 List all the factors of 172.
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RESPONSE --> 2,86,4,43,1,172 confidence assessment: 3
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20:13:03 5.1.21 divisibility of 25025 by various factors. Explain how each divisibility test works for the number 25025.
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RESPONSE --> 25025 is not divisible by 2 b/c it doesnt end in an even number. 25025 is not divisible by 3 b/c the sum 2+5+0+2+5=14. of these numbers none of them are divible by 3. 25025 is not divisible by 4 b/c its last two numbers dont form a number divisibe by 4. 25025 is divisible by 5 b/c it ends in 5. 25025 is not divisible by 6 b/c its not divisble by 2&3. 25025 is not divisible by 8 b/c it s last 3 digits do not form a # divisble by 8. 25025 is not divisible by 9 b/c the sum 2+5+0+2+5=14 of its digits isnt divisble by 9. 25025 is not divisible 12 b/c its not divislbe by both 3&4. confidence assessment: 3
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20:18:12 5.1.33 What is the prime factorization of 360 and how did you get it?
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RESPONSE --> 360/2=180, 2 is prime 180/2=90, 2 is a prime factor 90/2=45, 2 is a prime factor 45/2= cant be divisble by 2 45/3 = 15, 3 is a prime factor 15/3=5, 3 is a prime factor 5 is a prime 360=2*2*2*3*3*5 confidence assessment: 3
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20:20:59 5.1.60 number of divisors of 2^4*3^4*5^2
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RESPONSE --> powers 4, 4, 2 (4+1)*(4+1)*(2+1)= 5*5*3=75 confidence assessment: 2
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20:23:00 query 5.1.80 is 2*3*...*13+1 prime?
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RESPONSE --> 2* 3* 5 *7 *11* 13+ 1=30031 30031 isnt prime confidence assessment: 2
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