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2 years ago

What would be the u to usub and what would be the steps to solving this integral?

Mathematics

1 answer:

shutvik [7]2 years ago

3 0

Presumably, ln⁵(x) is the same as (ln(x))⁵ (as opposed to a quintuply-nested logarithm, log(log(log(log(log(x)))))).

Then substituting u = ln(x) and du = dx/x gives

$\displaystyle\int\frac{\mathrm dx}{x\ln^5(x)} = \int\frac{\mathrm du}{u^5} = -\frac1{4u^4}+C = \boxed{-\frac1{4\ln^4(x)}+C}$

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WRITE AN COMPOUND INEQUALITY FOR THIS SENTENCE

Mila [183]

Hello there!

Write a compound inequality for this sentence: 'w' is less than 4 and greater than or equal to -8
Only use 'w' once.

W is less than four ~ $4 \ \textgreater \ w$

W is greater than or equal to -8 ~ $w \geq -8$

If we were to put this together, it would look like:

$4 \ \textgreater \ w \geq -8$

I hope I helped!

Let me know if you need anything else!

~ Zoe

7 0

3 years ago

The local bike shop sells a bike and accessories package for $266. If the bike is worth 6 times more than the accessories, how m

tatiyna

Do 6x 266 in your calculator that’s ur answer

7 0

3 years ago

Here are the population figures of five different cities. 371,265 635,155 226,710 468,920 724,435 What is the difference between

Aleksandr-060686 [28]

Answer:

497,725

just subtract smallest from largest to get the difference

724,435 - 226,710

4 0

2 years ago

Read 2 more answers

2. The quality assurance department inspects its production line. The product either fails or passes the inspection. Past experi

Oksana_A [137]

Answer:

(a) $E(X) = 950$

(b) $COV = 0.007255$

Step-by-step explanation:

The given problem can be solved using binomial distribution since the product either fails or passes, the probability of failure or success is fixed and there are n repeated trials.

probability of failure = q = 0.05

probability of success = p = 1 - 0.05 = 0.95

number of trials = n = 1000

(a) What is the expected number of non-defective units?

The expected number of non-defective units is given by

$E(X) = n \times p \\\\E(X) = 1000 \times 0.95 \\\\E(X) = 950$

(b) what is the COV of the number of non-defective units?

The coefficient of variance is given by

$COV = \frac{\sigma}{E(X)}$

Where the standard deviation is given by

$\sigma = \sqrt{n \times p\times q} \\\\\sigma = \sqrt{1000 \times 0.95\times 0.05} \\\\\sigma = 6.892$

So the coefficient of variance is

$COV = \frac{6.892}{950}$

$COV = 0.007255$

(c) What is the probability of having more than 980 non-defective units?

We can use the Normal distribution as an approximation to the Binomial distribution since n is quite large and so is p.

$P(X > 980) = 1 - P(X < 980)\\\\P(X > 980) = 1 - P(Z < \frac{x - \mu}{\sigma} )\\\\$

We need to consider the continuity correction factor whenever we use continuous probability distribution (Normal distribution) to approximate discrete probability distribution (Binomial distribution).

$P(X > 980) = 1 - P(Z < \frac{979.5 - 950}{6.892} )\\\\P(X > 980) = 1 - P(Z < \frac{29.5}{6.892} )\\\\P(X > 980) = 1 - P(Z < 4.28)\\\\$

The z-score corresponding to 4.28 is 0.99999

$P(X > 980) = 1 - 0.99999\\\\P(X > 980) = 0.00001\\\\$

So it means that it is very unlikely that there will be more than 980 non-defective units.

8 0

3 years ago

Find 6 3/4 - 4 11/12. Write your answer in simplest form.

Mrrafil [7]

Answer:

1 5/6

Step-by-step explanation:

first convert to /12 and put the wholes in the fraction:

6 3/4 = 81/12

4 11/12 = 59/12

Then perform the subtraction

81/12 - 59/12 = 22/12

... and simplify

22/12 = 11/6

separate the wholes

11/6 = 6/6 + 5/6 = 1 5/6

4 0

2 years ago

Read 2 more answers