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Y_Kistochka [10]
3 years ago
9

Find all solutions in the integers of the equation ||x−3|−5| = 10, where the bars indicate absolute value.

Mathematics
1 answer:
Helga [31]3 years ago
3 0

Answer:

x = 18 or x = -12.

Step-by-step explanation:

||x-3|-5| = 10 only if |x-3|-5 = 10 or |x-3|-5 = -10, i.e., if |x-3|=15 or |x-3|=-5; but |x-3| cannot be equal to -5, because |x-3| should be a non-negative value. Therefore, the first equation is true only if |x-3|=15. |x-3| = 15 only if x-3 = 15 or x-3 = -15, i.e., x = 18 or x = -12.  We can verify this in the following way: ||18-3|-5|=||15|-5|=|10|=10 and ||-12-3|-5|=||-15|-5|=|15-5|=|10|=10. This verify that our solution is correct.

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3 years ago
A sample of 20 joint specimens of a particular type gave a sample mean proportional limit stress of 8.41 mpa and a sample standa
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For this problem, the confidence interval is the one we are looking for. Since the confidence level is not given, we assume that it is 95%.

 

The formula for the confidence interval is: mean ± t (α/2)(n-1) * s √1 + 1/n


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<span>
</span>

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3 0
3 years ago
HELP ME PLZ ILL GIVE U EXTRA POINTS
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10 32 -9

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hope this helps

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