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Neko [114]
3 years ago
7

If a^2+1/a^2=79 where (a>0), find the value of a^3 +1/a^3

Mathematics
1 answer:
Nastasia [14]3 years ago
7 0

Note the binomial expansion,

(<em>a</em> + 1/<em>a</em>)³ = <em>a</em> ³ + 3<em>a</em> + 3/<em>a</em> + 1/<em>a</em> ³

so

<em>a</em> ³ + 1/<em>a</em> ³ = (<em>a</em> + 1/<em>a</em>)³ - 3 (<em>a</em> + 1/<em>a</em>)

Similarly,

(<em>a</em> + 1/<em>a</em>)² = <em>a</em> ² + 2 + 1/<em>a</em> ²

We're given <em>a</em> ² + 1/<em>a</em> ² = 79, so

(<em>a</em> + 1/<em>a</em>)² - 2 = 79

(<em>a</em> + 1/<em>a</em>)² = 81

<em>a</em> + 1/<em>a</em> = ±9

but <em>a</em> > 0, so we ignore the negative solution.

Then

<em>a</em> ³ + 1/<em>a</em> ³ = 9³ - 3×9 = 702

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umka21 [38]

Data for the question :

102.05 99.85 112.3 97.15 111.23 105.37 105.64 106.5 102.97 107.82 106.36 111.24 107.28 114.14 106.28 106.96 98.25 111.55 107.75 101.02 101.12 97.7 97.66 100.54 115.77 112.91 111.04 112.15 102.87 101.14 107.13 108.56 109.56 103.57 108.68 104.59 116.74 116.22 100.22 103.97 111.2 109.34 115.78 101.59 107.93 104.23 96.25 103.84 102.47 102.96 99.26 101.42 108.58 107.69 99.88 102.71 111.25 99.4 117.04 106.35 110.44 102.34 107.25 107.63 105.2 109.14 115.54 101.51 108.49 112.32 109.27 97.54 102.46 105.94 109.42 111.05 102.63 106.99 102.03 108.84 118.8 108.64 95.35 105.47 104.45 102.15 111.4 108.27 104.82 108.4 109.05 116.11 103.7 121.2 99.62 102.81 109.56 103.35 113.02 103.79

Answer:

Range = 25.35

Variance = 29.46

Standard deviation = 5.43

The variation in price of Prozac is high

Step-by-step explanation:

The range of the data :

Maximum - Minimum.

121.2 - 95.35 = 25.35

The variance, s :

s² = Σ(X - m²) / n - 1

Mean, m = Σx / n

X = individual data point

m = mean of data

n = sample size

Using a calculator of save time and ensure accuracy :

s² = 29.45522

The standard deviation, s

s = sqrt(variance)

s = sqrt(s²)

s = sqrt(29.45522)

s = 5.42726.

The range, variance and standard deviation, all measure the degree of variation in a dataset. The values of these statistical measure obtain for the price of 1 product across different pharmaceutical stores, suggests thatvthe variation in price is high;

With a range of about 25.35 and standard deviation of 5.43

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Now, we have to caluclate the number of gallons of paint.

1 gallon------------------------400 ft²
x----------------------------------560 ft²

x=(1 gallon * 560 ft²) / 400 ft²=1.4 gallons.

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Answer:

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Oksana_A [137]

Answer:

3 Answers By Expert Tutors

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Step-by-step explanation:

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