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4 years ago

10

Linda opened a savings account with $450. She saves $225 per month. Joe opened his savings account the same month with $750. He

saves $125 per month. How much more will Linda have in her savings account after 12 months?

1 answer:

erastova [34]4 years ago

5 0

Linda has $900 more than Joe in her bank account

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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 <em>total light intensity</em> 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 <em>even function</em>

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

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

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

<em>By the midpoint rule</em>

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

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 are the decimals of 176.261 and 91.0213

Alik [6]

If you meant the two numbers then the answer is 267.2823

7 0

4 years ago

100 points for the answer

lora16 [44]

Answer:

83 in.^2

Step-by-step explanation:

The entire polygon consists of a rectangle with length 8 in. and width 5 in., a triangle with base 8 in. and height 7 in., and another triangle with base 5 in. and height 6 in.

The total are is the sum of the area of the rectangle and the two triangles.

area = area of rectangle + area of first triangle + area of second triangle

area = LW + bh/2 (for the first triangle) + bh/2 (for the second triangle)

area = 8 in. * 5 in. + 8 in. * 7 in. / 2 + 5 in. * 6 in. / 2

area = 40 in.^2 + 28 in.^2 + 15 in.^2

area = 83 in.^2

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3 years ago

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A ramp 26 ft long rises to a platform. The bottom of the platform is 17 ft from the foot of the ramp. Find x, the angle of eleva

Likurg_2 [28]

Te respondo en español 26

3 0

3 years ago

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What is the factored form of this expression?

Naddika [18.5K]

Answer:

(x+9)(x-9)

Step-by-step explanation:

3 0

3 years ago