<span>So you have composed two functions,
</span><span>h(x)=sin(x) and g(x)=arctan(x)</span>
<span>→f=h∘g</span><span>
meaning
</span><span>f(x)=h(g(x))</span>
<span>g:R→<span>[<span>−1;1</span>]</span></span>
<span>h:R→[−<span>π2</span>;<span>π2</span>]</span><span>
And since
</span><span>[−1;1]∈R→f is defined ∀x∈R</span><span>
And since arctan(x) is strictly increasing and continuous in [-1;1] ,
</span><span>h(g(]−∞;∞[))=h([−1;1])=[arctan(−1);arctan(1)]</span><span>
Meaning
</span><span>f:R→[arctan(−1);arctan(1)]=[−<span>π4</span>;<span>π4</span>]</span><span>
so there's your domain</span>
The answer is 34.05
The total distance (D) is the sum of three distances (d1, d2, and d3).
The distance formula is
Distance 1: Phoenix (–12, –16) to Blythe (–20, –9)<span>:
</span>
Distance 2: Blythe (–20, –9) to Los Angeles (–33, –4):
Distance 3: Los Angeles (–33, –4) to <span>San Francisco (–36, 5)
</span>
<span>
D = d1 + d2 + d3 = 10.63 + 13.93 + 9.49 = 34.05</span>
If there are 15 boards there are 14 gaps in-between.
But first, 15 boards each 9 and 1/4th inches so you get a total of 138 inches and 3/4th
If you subtract that from 144 you get 5 inches and 1/4th. The remaining amount is the total of all of the distance from the spacing.
Then you divide that by 14 (number of gaps/spacing in-between.)
So you get .375 inches. (3/8)
So width of the spacing between each board is 3/8ths of a inch
(0,a)
it didnt move left or right on the x-axis
it went up a units (since its half of 2a)
Answer:
a) Frequency remains constant
b) Wavelength remains constant
c) speed of the wave remains constant
d) Intensity decreases
e) amplitude of its electric field decreases
Explanation:
a) Frequency can be defined as the number of crests that pass a fixed point in the medium in unit time. It is the source of the wave that will determine the frequency. If the small source is changed to a bigger and faster one then the frequency will change. In our case, there is no change of source of wave, so the frequency remains constant.
b) The speed of of the wave is directly proportional to the wavelength. If we double the speed, the wavelength also doubles. Since the speed has not been doubled in our case, the wavelength will remain constant.
c) As indicated in b) since the wavelength is proportional to speed and it has not changed in our case, then the speed remains constant.
d) The intensity of a wave decreases as it moves further away from the source.
e) The intensity is related to the amplitude. Since the intensity decreases, the amplitude also decreases.
