Long division 6,750÷240=

Find second derivation for function f(x)=x²-(2/x)

Vera_Pavlovna [14]

Hi there!

$\large\boxed{f''(x) = 2 - \frac{4}{x^{3}}}$

$f(x) = x^2 - \frac{2}{x}$

Recall the power rule:

$\frac{dy}{dx} x^n = nx^{n-1}$

Rewrite the function for ease of differentiation:

$f(x) =x^2 - 2x^{-1}$

Use the power rule:

$f'(x) = 2x + 2x^{-2}$

Take the derivative once more:

$f''(x) = 2 - 4x^{-3}$

Rewrite:

$f''(x) = 2 - \frac{4}{x^{3}}$

8 0

3 years ago

A service center receives an average of 0.6 customer complaints per hour. Management's goal is to receive fewer than five compla

Zolol [24]

Answer:

48.68% probability that managment is unhappy with the number of complaints in the next eight hours.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given time interval.

A service center receives an average of 0.6 customer complaints per hour.

This means that $\mu = 0.6n$ , in which n is the number of hours.

Eight hours:

This means that $n = 8, \mu = 0.6*8 = 4.8$

Determine the probability that managment is unhappy with the number of complaints in the next eight hours.

They will be unhappy if they receive five or more complaints.

Either they receive less than five complaints, or they receive at least five. The sum of the probabilities of these events is 1. So

$P(X < 5) + P(X \geq 5) = 1$

We want $P(X \geq 5)$ .

Then

$P(X \geq 1) = 1 - P(X < 5)$

In which

$P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)$

So

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-4.6}*4.6^{0}}{(0)!} = 0.0101$

$P(X = 1) = \frac{e^{-4.6}*4.6^{1}}{(1)!} = 0.0462$

$P(X = 2) = \frac{e^{-4.6}*4.6^{2}}{(2)!} = 0.1063$

$P(X = 3) = \frac{e^{-4.6}*4.6^{3}}{(3)!} = 0.1631$

$P(X = 4) = \frac{e^{-4.6}*4.6^{4}}{(4)!} = 0.1875$

$P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0101 + 0.0462 + 0.1063 + 0.1631 + 0.1875 = 0.5132$

Finally

$P(X \geq 1) = 1 - P(X < 5) = 1 - 0.5132 = 0.4868$

48.68% probability that managment is unhappy with the number of complaints in the next eight hours.

6 0

3 years ago

Find the distance between the points G(−5, 4) and H(2, 6).

Iteru [2.4K]

Answer:

=√18 or 4.24264068712

Step-by-step explanation:

used the distance formula

8 0

3 years ago

Help please look at picture 30 points

Lemur [1.5K]

Answer:

9.434

Step-by-step explanation:

7 0

3 years ago

The polygons below are similar, but not necessarily drawn to scale. Find x. 4 + 36 AM

Mamont248 [21]

Answer:

x = 20

Step-by-step explanation:

In similar polygons, all corresponding sides are proportional. The scale factor between AB and DE is the same as between AC and DF.

$\frac{DE}{AB}=\frac{DF}{AC}\\\\\frac{4+x}{4}=\frac{36}{6}\\\\6(4+x)=4(36)\\24+6x=144\\6x=120\\x=20$

You can confirm that by plugging it back into the original equation:

$\frac{4+x}{4}=\frac{36}{6}\\\\\frac{4+(20)}{4}=\frac{36}{6}\\\\\frac{24}{4}=\frac{36}{6}\\\\6=6$

3 0

2 years ago