Solve the inequality -9x/11 - 7 < -5. x >22/9 x < -22/9 x <22/9 x > - 22/9
1 answer:
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Answer:
(a) Not a group
(b) Not a group
(c) Abelian group
Step-by-step explanation:
<em>In order for a system <G,*> to be a group, the following must be satisfied </em>
<em> (1) The binary operation is associative, i.e., (a*b)*c = a*(b*c) for all a,b,c in G </em>
<em>(2) There is an identity element, i.e., there is an element e such that a*e = e*a = a for all a in G </em>
<em> (3) For each a in G, there is an inverse, i.e, another element a' in G such that a*a' = a'*a = e (the identity) </em>
<em> </em>
If in addition the operation * is commutative (a*b = b*a for every a,b in G), then the group is said to be Abelian
(a)
The system <G,*> is not a group since there are no identity.
To see this, suppose there is an element e such that
a*e = a
then
a-e = a which implies e=0
It is easy to see that 0 cannot be an identity.
For example
2*0 = 2-0 = 2
Whereas
0*2 = 0-2 = -2
So 2*0 is not equal to 0*2
(b)
The system <G,*> is not a group either.
If A is a matrix 2x2 and the determinant of A det(A)=0, then the inverse of A does not exist.
(c)
The table of the operation G is showed in the attachment.
It is evident that this system is isomorphic under the identity map, to the cyclic group
the system formed by the subset of Z, {0,1,2,3,4} with the operation of addition module 5, which is an Abelian cyclic group
We conclude that the system <G,*> is Abelian.
Attachment: Table for the operation * in (c)
Answer:
One watering system requires 36 minutes to complete the job alone while another watering system requires 12 minutes to complete the job alone.
Step-by-step explanation:
Given:
Both the system can complete the job = 9 minutes
We need find the time required by each system to do the job.
Solution:
Let the time required by another watering system to complete the job be 'x' mins.
Now given:
One watering system needs about three times as long to complete a job as another watering system.
Time required by one watering system =
Rate to complete the job by another watering system =
Rate to complete the job by One watering system =
Rate at which both can complete the job =
So we can say that;
Rate at which both can complete the job is equal to sum of Rate to complete the job by another watering system and Rate to complete the job by One watering system.
framing in equation form we get;
Now taking LCM to make the denominator common we get;
By Cross multiplication we get;
Dividing both side by 3 we get;
Time required by One watering system =
Hence One watering system requires 36 minutes to complete the job alone while another watering system requires 12 minutes to complete the job alone.