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blondinia [14]
3 years ago
15

Find d/dx(e^3ln(x)). a. e^3lnx b.e^3ln(x)/x c.3e^3lnx d.3x^2

Mathematics
1 answer:
kow [346]3 years ago
3 0

Answer:

D. 3x²

General Formulas and Concepts:

<u>Algebra II</u>

  • If you raise e to the natural log, they cancel out and vice versa

<u>Calculus</u>

Basic Power Rule:

  • f(x) = cxⁿ
  • f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

<u>Step 1: Define</u>

<u />f(x)=e^{3lnx}<u />

<u />

<u>Step 2: Rewrite</u>

<u />f(x) = x^3<u />

<u />

<u>Step 3: Take Derivative</u>

  1. Basic Power Rule:                    f'(x) = 3x³⁻¹
  2. Simplify:                                    f'(x) = 3x²
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A simple random sample of 50 items from a population with 7 resulted in a sample mean of 35.
Vilka [71]

The 90% , 99% confidence interval for the population mean is 32.145 < \rm \mu < 35.855 and 31.093 <  \rm \mu < 36.907

<h3>What is Probability ?</h3>

Probability is the study of likeliness of an event to happen.

It is given that

Total Population = 50

Mean = 35

The confidence interval is given by

\rm CI = \mu + z \dfrac{s}{\sqrt n}

\rm \mu is the mean

z is the confidence level value

s is the standard deviation

n is the population width

(a) The 90% confidence interval for the population mean

90% \rm \alpha / 2  = 0.05

Z = 1.64

34 \rm \pm 1.64 * 8 / √50

34 \rm \pm  1.855

32.145 < \rm \mu < 35.855

(b)  The 99% confidence interval for the population mean

99% \rm \alpha / 2  = 0.005

Z=2.57

34  \rm \pm 2.57 * 8 / √50

34 \rm \pm  2.907

31.093 <  \rm \mu < 36.907

Therefore the confidence interval for population mean has been determined.

The complete question is

A simple random sample of 50 items from a population width =7  resulted in a sample mean of 35. If required, round your answers to two decimal places.

a. Provide a 90% confidence interval for the population mean

b. Provide a 99% confidence interval for the population mean

To know more about Probability

brainly.com/question/11234923

#SPJ1

8 0
2 years ago
Write an equation of the translated function of the parent function f(x)=|x| with the following transformations:
MrRa [10]

Answer:

Option b

Step-by-step explanation:

To write the searched equation we must modify the function f (x) = | x | in the following way:

1. Do y = f(x + 4)

This operation horizontally shifts the function f(x) = | x | by a factor of 4 units to the left on the x axis.

y = | x +4 |

2. Do y = f (\frac{1}{4}x)

This operation horizontally expands the function f (x) = | x | in a factor of 4 units. y = |\frac{1}{4}x + 1|

3. Do y = f(x)-4

This operation vertically shifts the function f (x) = | x | by a factor of 4 units down on the y-axis.

y = |\frac{1}{4}x +1| -4

4. After these transformations the function f(x) = | x | it looks like:

f(x) = |\frac{1}{4}x +1| -4

Therefore the correct option is option b. You can verify that your vertex is at point (-4, -4) by making f (-4)

f(-4) = |\frac{1}{4}(-4) +1| -4 = -4

8 0
3 years ago
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Umnica [9.8K]

Step-by-step explanation:

the answer is in the image above

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3 years ago
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Answer:

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Step-by-step explanation:

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Now go back and subsitute,

0.34 * 1/10 = 0.034

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