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2 years ago

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Show that (cos ax)(cos bx)(cos cz) is an eigenfunction of the Laplacian operator ∇²= ζ²/ζx² + ζ²/ζy²+ ζ²/ζz². An eigenfunction Ψ

a= aΨa, where a is a scalar called the 'eigenvalue'. What is the eigen value for this problem?

1 answer:

Lelechka [254]2 years ago

3 0

Answer:

Please see attachment

Step-by-step explanation:

Please see attachment

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Suppose babies born in a large hospital have a mean weight of 4095 grams, and a standard deviation of 569 grams. If 130 babies a

Butoxors [25]

Answer:

$P =0.3998$

Step-by-step explanation:

Let ${\overline{x}}$ be the average of the sample, and the population mean will be $\mu$

We know that:

$\mu = 4095$ gr

Let $\sigma$ be the standard deviation and n the sample size, then we know that the standard error of the sample is:

$E=\frac{\sigma}{\sqrt{n}}$

Where

$\sigma=569$

$n=130$

In this case we are looking for:

$P(|{\displaystyle{\overline{x}}}- \mu|>42)$

This is:

${\displaystyle{\overline{x}}}- \mu>42$ or ${\displaystyle{\overline{x}}}- \mu$

$P=P({\displaystyle{\overline{x}}}- \mu>42)+ P({\displaystyle{\overline{x}}}- \mu$

Now we get the z score

$Z=\frac{{\displaystyle{\overline{x}}}-\mu}{\frac{\sigma}{\sqrt{n}}}$

$P=P(z>\frac{42}{\frac{569}{\sqrt{130}}}) + P(z$

$P=P(z>0.8416) + P(z$

Looking at the tables for the standard nominal distribution we get

$P =0.1999+0.1999$

$P =0.3998$

6 0

2 years ago

A computer virus is trying to corrupt two files. The first file will be corrupted with probability 0.4. Independently of it, the

Ksivusya [100]

Answer:

$P(X = 0) = 0.42$

$P(X = 1) = 0.46$

$P(X = 2) = 0.12$

Step-by-step explanation:

We have these following probabilities:

40% probability that the first file is corrupted. So 60% probability that the first file is not corrupted.

30% probability that the second file is corrupted. So 70% probability that the second file is not corrupted.

Probability mass function

Probability of each outcome(0, 1 and 2 files corrupted).

No files corrupted:

60% probability that the first file is not corrupted.

70% probability that the second file is not corrupted.

So

$P(X = 0) = 0.6*0.7 = 0.42$

One file corrupted:

First one corrupted, second no.

40% probability that the first file is corrupted.

70% probability that the second file is not corrupted.

First one ok, second one corrupted.

60% probability that the first file is not corrupted.

30% probability that the second file is corrupted.

$P(X = 1) = 0.4*0.7 + 0.6*0.3 = 0.46$

Two files corrupted:

40% probability that the first file is corrupted.

30% probability that the second file is corrupted.

$P(X = 2) = 0.4*0.3 = 0.12$

8 0

2 years ago

Drag the tiles to the boxes to form correct pairs. In the diagram, transversal t cuts across the parallel lines a and b. Match t

yarga [219]

Where are the type of answers for this question

7 0

2 years ago

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Kate and Jean paint a house together in 6 days. If they work alone, Kate takes 5 fewer days than Jean would take to do the same

frutty [35]

Number of jobs=1

Time:
<span>Since ‘x’ is given as a variable in the choices, we should reserve it for Kate and use ‘y’ for Jean as follows: </span>
<span>
Kate: => x </span>
<span>Jean: => y </span>

<span>But y = x - 5 </span>

<span>Combined rate: </span>
<span>1/x+ 1/y </span>
<span>= (x + y)/(xy) </span>

<span>Number of jobs done: </span>
<span>
Number of days X combined rate = number of jobs </span>
<span>6 [(x + y)/(xy)] = 1 </span>
<span>6x + 6y = xy </span>
<span>6x + 6(x - 5) = x(x - 5) </span>
<span>6x + 6x - 30 = x² - 5x </span>
<span>12x - 30 = x² - 5x </span>
<span>x² - 17x + 30 = 0
</span>
Therefore, the answer would be A.

3 0

2 years ago

How much of the 8% solution should we use to make 100g of a 3% solution?

sp2606 [1]

Suppose x grams of 8% solution should be mixed to make 100 g of 3% solution.
here we shall have:
the amount of 3% solution in the 100 g will be:
3/100*100=3 grams
the the equation will be, 8% of what quantity becomes 3g?
(8/100)*x=3
hence solving for x we shall have:
0.08x=3
x=3/0.08
x= 37.8 grams
The implication of this is that, when you have 37.5 grams of 8% solution, that will contain 3 of pure chemical and hence when you add more solvent on top of 37.5 g until you reach 100g, that will be 3% solution.

8 0

2 years ago

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