How to write a fraction as a mixed number?
1 answer:
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A rational function must not have a denominator of 0, since that means the divisor is a 0 and there's no number whatsoever you can multiply it with 0 to get the dividend, the short version of all that is, the fraction is "undefined".
a domain for a rational is any values of "x" that are safe, namely will not make the denominator undefined, there are a few other constraints, but this is the only one in this case.
so, what values "x" cannot take on safely? well, we can find out what makes the denominator to 0, by simply, yeap, you guessed it, zeroing it out, let's do so,
so, if ever "x" becomes -2/5, our handy dandy fraction will go poof.
so the domain is all real numbers for "x", EXCEPT -2/5, or in Set Builder notation, {x | x ∈ ℝ; x ≠ -⅖}
a domain for a rational is any values of "x" that are safe, namely will not make the denominator undefined, there are a few other constraints, but this is the only one in this case.
so, what values "x" cannot take on safely? well, we can find out what makes the denominator to 0, by simply, yeap, you guessed it, zeroing it out, let's do so,
so, if ever "x" becomes -2/5, our handy dandy fraction will go poof.
so the domain is all real numbers for "x", EXCEPT -2/5, or in Set Builder notation, {x | x ∈ ℝ; x ≠ -⅖}
Answer:
attempts are required to find a matching pair if the digital fingerprint is 64 bits long.
attempts are required to find a matching pair if the digital fingerprint is 128 bits long.
Step-by-step explanation:
Each bit has two options. So
How many attempts are required to find a matching pair if the digital fingerprint is 64 bits long?
So for each of the 64 bits, we have the following number of options.
2 - 2 - 2 - 2 -... - 2
So, in all, there are
options.
So, attempts are required to find a matching pair if the digital fingerprint is 64 bits long.
128 bits long?
Using the same logic as the first question.
So, attempts are required to find a matching pair if the digital fingerprint is 128 bits long.