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xz_007 [3.2K]
2 years ago
13

What types of numbers are undefined when they are under a radical sign? If you were dealing with the number √-1, would it be def

ined if you multiplied it by 2? Would it be defined if you subtracted some real number from it? Would it be defined if you squared it? Would it be defined if you cubed it?
Mathematics
1 answer:
Misha Larkins [42]2 years ago
8 0
The square root of a a negative integer is imaginary.
It would still be a negative under a square root if you multiplied it by 2, therefor it will still be imaginary, or I’m assuming as your book calls it, undefined.
2•(sqrt-1) = 2sqrt-1

If you add a number to -1 itself, specifically 1 or greater it will become a positive number or 0 assuming you just add 1. In that case it would be defined.
-1 + 1 = 0
-1 + 2 = 1

If you add a number to the entire thing “sqrt-1” it will not be defined.
(sqrt-1) + 1 = 1+ (sqrt-1)

If you subtract a number it will still have a negative under a square root, meaning it would be undefined.
(sqrt-1) + 1 = 1 + (sqrt-1)

however if you subtract a negative number from -1 itself, you end up getting a positive number or zero. (Subtracting a negative number is adding because the negative signs cancel out).
-1 - -1 = 0
-1 - -2 = 1

If you squared it you would get -1, which is defined
sqrt-1 • sqrt-1 = -1

and if you cubed it, you would get a negative under a square root again, therefor it would be undefined.
sqrt-1 • sqrt-1 • sqrt-1 = -1 • sqrt-1 = -1(sqrt-1)

Sorry if this answer is confusing, I don’t have a scientific keyboard, I’ll get one soon.
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2(3x + 5) = 9x + 9 - 3x + 1​
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There are 64 people in a movie theater today.1/2 of the people are eating popcorn 3/8 are eating choclate candy, and the rest ar
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3 years ago
A soda bottling plant uses automated filling machines to fill 2-liter bottles with soda. The plant can produce 8000 bottles of s
Kruka [31]

Answer:

0.6892 = 68.92% of bottles are within specification.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

On average, each bottle contains 2.07 liters of soda, with a standard deviation of 0.06 liters.

This means that \mu = 2.07, \sigma = 0.06

The plant’s quality manager wants to determine how well the process is operating.

To do this, we find the proportion of bottles within specification.

The specification limits for a bottle of soda are 2.1 liters and 1.9 liters

This is the pvalue of Z when X = 2.1 subtracted by the pvalue of Z when X = 1.9. So

X = 2.1

Z = \frac{X - \mu}{\sigma}

Z = \frac{2.1 - 2.07}{0.06}

Z = 0.5

Z = 0.5 has a pvalue of 0.6915.

X = 1.9

Z = \frac{X - \mu}{\sigma}

Z = \frac{1.9 - 2.07}{0.06}

Z = -2.83

Z = -2.83 has a pvalue of 0.0023

0.6915 - 0.0023 = 0.6892

0.6892 = 68.92% of bottles are within specification.

7 0
2 years ago
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