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Pepsi [2]
3 years ago
14

If f'(x)=2/x and f(sqrt(e))=5, then f(e)=

Mathematics
1 answer:
docker41 [41]3 years ago
3 0
f'(x)=\dfrac2x
\implies f(x)=\displaystyle\frac2x\,\mathrm dx=2\ln|x|+C

f(\sqrt e)=5\implies 5=2\ln|\sqrt e|+C
\implies 5=\dfrac22\ln e+C
\implies C=4
\implies f(x)=2\ln|x|+4
\implies f(e)=2\ln|e|+4=6
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Vector vector a has a magnitude of 28 units and points in the positive y-direction. When vector vector b is added to vector a ,
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Using the z-distribution, it is found that the 95% confidence interval for the difference is (-1.3, -0.7).

<h3>What are the mean and the standard error for each sample?</h3>

Considering the data given:

\mu_S = 3.8, n = 175, s_S = \frac{1.7}{\sqrt{175}} = 0.1285

\mu_N = 4.8, n = 152, s_N = \frac{1.2}{\sqrt{152}} = 0.0973

<h3>What is the mean and the standard error for the distribution of differences?</h3>

The mean is the subtraction of the means, hence:

\overline{x} = \mu_S - \mu_N = 3.8 - 4.8 = -1

The standard error is the square root of the sum of the variances of each sample, hence:

s = \sqrt{s_S^2 + s_N^2} = \sqrt{0.1285^2 + 0.0973^2} = 0.1612

<h3>What is the confidence interval?</h3>

It is given by:

\overline{x} \pm zs

We have a 95% confidence interval, hence the critical value is of z = 1.96.

Then, the bounds of the interval are given as follows:

  • \overline{x} - zs = -1 - 1.96(0.1612) = -1.3
  • \overline{x} + zs = -1 + 1.96(0.1612) = -0.7

More can be learned about the z-distribution at brainly.com/question/25890103

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A (p + 1) metres long ladder reaches a height
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