Answer:
k=4
Step-by-step explanation:
-The constant of proportionality is defined as the ratio between two directly proportional variables.
-Given that B=4f
#The constant of proportionality is calculated as:
- the equation can be written in the form y=kx,
where y varies directly with x and k is the constant of variation:
Hence, B varies directly with f with a constant of proportionality k=4
Consider the substitution,
so that the integral is equivalent to
Notice that
which means is odd, so
Perhaps more work than necessary, but it does make it easier to see that the original integrand exhibits some symmetry about .
Answers:
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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...
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.
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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
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For this problem, n = 11
This means there are 2^n = 2^11 = 2048 subsets and (2^n)-1 = 2048-1 = 2047 proper subsets.