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A very basic example would be as follows: if required.
The best that manufacturers can do is to try to guarantee that the variations will stay within a specified range, often ±1%, ±5%, or ±10%. Use the absolute value function to express the range of possible values of the actual resistance. The absolute value of the difference between the actual and nominal resistance should not exceed the stated variability, so, with the resistance \(R\) in ohms, \[|R−680|\leq34\] Exercise \(\Page Index\) Students who score within 20 points of 80 will pass a test.
Write this as a distance from 80 using absolute value notation.
In this wiki, we intend to discuss this techniques along with strategies on when to use which.
is not a possible solution, but it does not mean it's not a possible solution for Case 1 because we're simply going piece by piece in this piecewise function--in the end we will take the union of all possible solutions.
Recall that in its basic form \(f(x)=|x|\), the absolute value function, is one of our toolkit functions.
How To Solve Problems With Absolute Value
The absolute value function is commonly thought of as providing the distance the number is from zero on a number line.
Until the 1920s, the so-called spiral nebulae were believed to be clouds of dust and gas in our own galaxy, some tens of thousands of light years away.
Then, astronomer Edwin Hubble proved that these objects are galaxies in their own right, at distances of millions of light years.
Algebraically, for whatever the input value is, the output is the value without regard to sign.
Example \(\Page Index\): Determine a Number within a Prescribed Distance Describe all values \(x\) within or including a distance of 4 from the number 5.