Answer:
See Below
Step-by-step explanation:
The left side of the equation HAS TO BE GREATER THAN 3
So we take each ordered pair (x,y), plug it into the expression of left side of inequality and see which one is GREATER THAN 3. That's our answer.
A:
0.5x - 2y
0.5(-2) -2(0.5) = -2
NO
B:
0.5x - 2y
0.5(2) -2(1) = -1
NO
C:
0.5x -2y
0.5(2) -2(-1) = 3
NO
D:
0.5x -2y
0.5(-2) -2(-0.5) = 0
NO
None of them are solutions. C would have been a solution if the inequality had an "EQUAL SIGN" -- but it doesn't. Maybe the question is wrong, but if the question is right, then there is no correct answer.
Answer:
a) They have different wavelengths.
b) They have different frequencies.
Step-by-step explanation:
Electromagnetic waves (EM waves) refer to waves carrying electromagnetic radiant energy which are propagated through vacuum or non-vacuum (material medium). They range from radio waves to gamma rays; they travel through space at the speed of light (about 300 million metres per second) and they are measured in photons.
The EM waves have the following characteristics:
1. They have different wavelengths
2. They have different frequencies
3. They travel at the speed of light independent of the medium of propagation (vacuum or material medium)
4. They do not require a media to be propagated
<u>Based on the explanation above, Options </u><u>a</u><u> (They have different wavelengths) and </u><u>b</u><u> (They have different frequencies) are the correct answers</u>
What if you divide it by 100?
![A=\frac{1}{2}\ln17 = 1.417](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%5Cln17%20%3D%201.417)
Step-by-step explanation:
The area <em>A</em> under the curve can be written as
![\displaystyle A = \int_0^2\!\dfrac{4x\:dx}{1+4x^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20A%20%3D%20%5Cint_0%5E2%5C%21%5Cdfrac%7B4x%5C%3Adx%7D%7B1%2B4x%5E2%7D)
To evaluate the integral, let
![u = 1+4x^2 \Rightarrow du = 8xdx\:\text{or}\:\frac{1}{2}du = 4xdx](https://tex.z-dn.net/?f=u%20%3D%201%2B4x%5E2%20%5CRightarrow%20du%20%3D%208xdx%5C%3A%5Ctext%7Bor%7D%5C%3A%5Cfrac%7B1%7D%7B2%7Ddu%20%3D%204xdx)
so the integral becomes
![\displaystyle \int\!\dfrac{4x\:dx}{1+4x^2} = \dfrac{1}{2}\int\!\dfrac{du}{u} = \dfrac{1}{2}\ln |u|](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%5C%21%5Cdfrac%7B4x%5C%3Adx%7D%7B1%2B4x%5E2%7D%20%3D%20%5Cdfrac%7B1%7D%7B2%7D%5Cint%5C%21%5Cdfrac%7Bdu%7D%7Bu%7D%20%3D%20%5Cdfrac%7B1%7D%7B2%7D%5Cln%20%7Cu%7C)
or
![\displaystyle \int\!\dfrac{4x\:dx}{1+4x^2} = \dfrac{1}{2}\ln |1+4x^2|](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%5C%21%5Cdfrac%7B4x%5C%3Adx%7D%7B1%2B4x%5E2%7D%20%3D%20%5Cdfrac%7B1%7D%7B2%7D%5Cln%20%7C1%2B4x%5E2%7C)
Putting in the limits of integration, our area becomes
![\displaystyle A = \int_0^2\!\dfrac{4x\:dx}{1+4x^2} = \dfrac{1}{2}\left.\ln |1+4x^2|\right|_0^2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20A%20%3D%20%5Cint_0%5E2%5C%21%5Cdfrac%7B4x%5C%3Adx%7D%7B1%2B4x%5E2%7D%20%3D%20%5Cdfrac%7B1%7D%7B2%7D%5Cleft.%5Cln%20%7C1%2B4x%5E2%7C%5Cright%7C_0%5E2)
![\;\;\;\;= \frac{1}{2}[\ln (1+16) - \ln (1)]](https://tex.z-dn.net/?f=%5C%3B%5C%3B%5C%3B%5C%3B%3D%20%5Cfrac%7B1%7D%7B2%7D%5B%5Cln%20%281%2B16%29%20-%20%5Cln%20%281%29%5D)
![\;\;\;\;=\frac{1}{2}\ln17](https://tex.z-dn.net/?f=%5C%3B%5C%3B%5C%3B%5C%3B%3D%5Cfrac%7B1%7D%7B2%7D%5Cln17)
Note: ![\ln 1 = 0](https://tex.z-dn.net/?f=%5Cln%201%20%3D%200)