Suppose p" must approximate p with relative error at most 10-3 . Find the largest interval in which p* must lie for each value o
1 answer:
Answer:
Step-by-step explanation
The relative error is the absolute error divided by the absolute value of p. for an approximation p*, the relative error is
r = |p*-p|/|p|
we want r to be at most 10⁻³, thus
|p*-p|/|p| ≤ 10⁻³
|p*-p| ≤ |p|* 10⁻³
therefore, p*-p should lie in the interval [ - |p| * 10⁻³ , |p| * 10⁻³ ], and as a consecuence, p* should be in the interval [p - |p| * 10⁻³ , p + |p| * 10⁻³ ]
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To re-phrase this: 50 is a certain percent of 90.
this can be written mathematically as 50=x%*90
let's divide both sides by 10:
5=x%*9
and divide both sides by 9:
which in decimals is approximately 0.56 (but not exactly).
so 0.56=x%
and the x then 56
so 50 is approximately 56% of 90:
exactly 56%of 90 is 50.4
this can be written mathematically as 50=x%*90
let's divide both sides by 10:
5=x%*9
and divide both sides by 9:
which in decimals is approximately 0.56 (but not exactly).
so 0.56=x%
and the x then 56
so 50 is approximately 56% of 90:
exactly 56%of 90 is 50.4