Can someone please help me
1 answer:
You might be interested in
Answer:
b = 77
Step-by-step explanation:
a² + b² = c²
36² + b² = 85²
1296 + b² = 7225
b² = 7225 - 1296
b² = 5929
b = 77
Answers:
- a) 2048
- b) 2047
=============================================================
Explanation:
If a set has n elements inside it, then it has 2^n different subsets.
Consider a set like {a,b,c}. It has n = 3 elements.
It has 2^n = 2^3 = 8 subsets
Those 8 subsets are...
- {a,b,c} ..... any set is a subset of itself
- {a,b}
- {a,c}
- {b,c}
- {a}
- {b}
- {c}
- { } .... the empty set
As you can see, each subset consists of items that are selected from the original set {a,b,c}. We can't have any repeat letters.
In that list, items 2 through 4 represent subsets with exactly two things inside it. Items 5 through 7 are known as singletons as they only have one item inside each set. The empty set can be written with the symbol or you could have a pair of braces with nothing inside them. The empty set is a subset of any set.
--------------
Note how I included {a,b,c} as a subset. Any set is a subset of itself.
A proper subset will ignore the original set and only look at smaller subsets. If we say B is a proper subset of A, then set B will have fewer items compared to set A. Without the "proper" in there, it's possible that A = B.
So all we've done really is kick out one set which drops 2^n to (2^n)-1 when counting the number of proper subsets. I'm using parenthesis to indicate the "-1" is not part of the exponent. If you wrote this on your paper, then you would likely write
--------------
For this problem, n = 11
This means there are 2^n = 2^11 = 2048 subsets and (2^n)-1 = 2048-1 = 2047 proper subsets.