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3 years ago

7

If all the components of a vector are equal to 1, then that vector is a unit vector. if all the components of a vector are equal

to 1, then that vector is a unit vector.
a. True
b. False

1 answer:

RideAnS [48]3 years ago

4 0

The statement to this question is true this is true

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Given the equation y = 2x - 5 and the domain {-1, 4} find the slope

Ksivusya [100]

Answer:

The slope is m=2

Step-by-step explanation:

we have

$y=2x-5$

This is the equation of a line in slope intercept form

$y=mx+b$

where

m is the slope

b is the y-coordinate of the y-intercept

therefore

The slope m is equal to

$m=2$

<em>Alternative Method</em>

we know that

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

$y=2x-5$ and the domain {-1, 4}

For x=-1

$y=2(-1)-5=-7$

point (-1,-7)

For x=4

$y=2(4)-5=3$

point (4,3)

substitute the values in the formula of the slope

$m=\frac{3+7}{4+1}$

$m=\frac{10}{5}$

$m=2$

8 0

3 years ago

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

2 years ago

How much does a $90 investment earn in interest at a yearly rate of 15% over the course of 1 year?

Tomtit [17]

Answer:

$13.50

Step-by-step explanation:

You can use the simple interest formula here: I(interest)=P(principal amount)r(interest rate)t(years). I=Prt. So just plug in the numbers. I=90x.15x1=13.5

8 0

2 years ago

Serena wants to create snack bags for a trip she is going on. She has 6 granola bars and 10 pieces of dried fruit. If the snack

vladimir1956 [14]

I believe its 5 bags, 1 granola bar in each bag and 2 pieces of fruit in each bag.

8 0

3 years ago

Write the first six terms of the sequence, beginning with n=1. a(n)=60n Enter the numbers, separated by commas.

Sever21 [200]

Answer:

60, 120, 180, 240, 300, 360

Step-by-step explanation:

a(n)=60n

At n =1

a(1) = 60(1) = 60

At n = 2

a(2) = 60(2) = 120

At n = 3

a(3) = 60(3) = 180

At n = 4

a(4) = 60(4) = 240

At n = 5

a(5) = 60(5) = 300

At n = 6

a(6) = 60(6) = 360

60, 120, 180, 240, 300, 360

5 0

3 years ago