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3 years ago

Pythagorean theorem Digital Escape Puzzle 4,Need Answer Immediately!!!

Mathematics

1 answer:

Mrrafil [7]3 years ago

5 0

Answer:

AGIB

Step-by-step explanation:

I solved it eh.

Pretty simple honestly.

But school ends!

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The intensity of light with wavelength λ traveling through a diffraction grating with N slits at an angle θ is given by I(θ) = N

Ymorist [56]

Answer:

0.007502795

Step-by-step explanation:

We have

N = 10,000

$\bf d=10^{-4}$

$\bf \lambda = 632.8*10^{-9}$

Replacing these values in the expression for k:

$\bf k=\frac{\pi Ndsin\theta}{\lambda}=\frac{\pi10^4*10^{-4}sin\theta}{632.8*10^{-9}}=\frac{\pi 10^9sin\theta}{632.8}$

So, the intensity is given by the function

$\bf I(\theta)=\frac{N^2sin^2(k)}{k^2}=\frac{10^8sin^2(\frac{\pi 10^9sin\theta}{632.8})}{(\frac{\pi 10^9sin\theta}{632.8})^2}$

The total light intensity is then

$\bf \int_{-10^{-6}}^{10^{-6}} I(\theta)d\theta=\int_{-10^{-6}}^{10{-6}}\frac{10^8sin^2(\frac{\pi 10^9sin\theta}{632.8})}{(\frac{\pi 10^9sin\theta}{632.8})^2}d\theta$

Since $\bf I(\theta)$ is an even function

$\bf \int_{-10^{-6}}^{10^{-6}} I(\theta)d\theta=2\int_{0}^{10^{-6}}I(\theta)d\theta$

and we only have to divide the interval $\bf [0,10^{-6}]$ in five equal sub-intervals $\bf I_1,I_2,I_3,I_4,I_5$ with midpoints $\bf m_1,m_2,m_3,m_4,m_5$

The sub-intervals and their midpoints are

$\bf I_1=[0,\frac{10^{-6}}{5}]\;,m_1=10^{-5}\\I_2=[\frac{10^{-6}}{5},2\frac{10^{-6}}{5}]\;,m_2=3*10^{-5}\\I_3=[2\frac{10^{-6}}{5},3\frac{10^{-6}}{5}]\;,m_3=5*10^{-5}\\I_4=[3\frac{10^{-6}}{5},4\frac{10^{-6}}{5}]\;,m_4=7*10^{-5}\\I_5=[4\frac{10^{-6}}{5},10^{-6}]\;,m_5=9*10^{-5}$

By the midpoint rule

$\bf \int_{0}^{10^{-6}}I(\theta)d\theta\approx\frac{10^{-6}}{5}[I(m_1)+I(m_2)+...+I(m_5)]$

computing the values of I:

$\bf I(m_1)=I(10^{-5})=\frac{10^8sin^2(\frac{\pi 10^9sin(10^{-5})}{632.8})}{(\frac{\pi 10^9sin(10^{-5})}{632.8})^2}=13681.31478$

$\bf I(m_2)=I(3*10^{-5})=\frac{10^8sin^2(\frac{\pi 10^9sin(3*10^{-5})}{632.8})}{(\frac{\pi 10^9sin(3*10^{-5})}{632.8})^2}=4144.509447$

Similarly with the help of a calculator or spreadsheet we find

$\bf I(m_3)=3.09562973\\I(m_4)=716.7480066\\I(m_5)=211.3187228$

and we have

$\bf \int_{0}^{10^{-6}}I(\theta)d\theta\approx\frac{10^{-6}}{5}[I(m_1)+I(m_2)+...+I(m_5)]=\frac{10^{-6}}{5}(18756.98654)=0.003751395$

Finally the the total light intensity

would be 2*0.003751395 = 0.007502795

8 0

3 years ago

What is the x for : -2x^2+24x-72=0

stepan [7]

Answer:

x=6

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

I need help someone help me plz

Tamiku [17]

Answer:

d -w-n²

Step-by-step explanation:

dollars not dollar so n square

3 0

3 years ago

Read 2 more answers

The 99 percent confidence interval for the average weight of a product is from 71.36 lbs. to 78.64 lbs. Can we conclude that μ i

Ilya [14]

Answer:

Step-by-step explanation:

Hello!

To decide over a hypothesis test using a confidence interval the following conditions are to be met:

1. The hypotheses should be two-tailed.

2. The hypotheses and the confidence interval should be made for the same parameter.

3. The confidence level and the significance level should be complementary, so if the CI is 1-α: 0.99 the level of significance should be α: 0.01

If all conditions are met, the decision rule is the following:

If the value stated in the null hypothesis is contained by the CI, the decision is to not reject the null hypothesis.

If the value stated in the null hypothesis is not contained by the CI, the decision is to reject the null hypothesis.

Let's say in this example the hypotheses are:

H₀: μ = 71

H₁: μ ≠ 71

α: 0.01

99% Confidence level is (71.36;78.64).

As you can see, 71 is not contained in the CI so the decision to take is to reject the null hypothesis, in other words, the population mean is not 71.

I hope it helps!

6 0

3 years ago

if all 10 players scored the same number of points, how many would each have to score to get a total of 230

Aliun [14]

Answer:

Each player would have to score 23 points.

Step-by-step explanation:

To answer this question, you must do 230 ÷ 10!

The answer to this is 23.

You can double check your answer by multiplying 23 by 10!

3 0

2 years ago