A common sinusoidal function is:
![y = asin(bx)](https://tex.z-dn.net/?f=y%20%3D%20asin%28bx%29)
so,always amplitude is a, so a=6
and we know period is:
![p = \frac{ |b| }{2\pi}](https://tex.z-dn.net/?f=p%20%3D%20%5Cfrac%7B%20%7Cb%7C%20%7D%7B2%5Cpi%7D%20)
so
![\frac{ |b| }{2\pi} = \frac{2\pi}{3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%7Cb%7C%20%7D%7B2%5Cpi%7D%20%3D%20%5Cfrac%7B2%5Cpi%7D%7B3%7D%20)
![b = + or - \frac{4 {\pi}^{2} }{3}](https://tex.z-dn.net/?f=b%20%3D%20%2B%20or%20-%20%5Cfrac%7B4%20%7B%5Cpi%7D%5E%7B2%7D%20%7D%7B3%7D%20)
and we have 2 equations that while we can consider which is appropriate ,to have its graph!
![6 \sin( \frac{4 {\pi}^{2} }{3}x )](https://tex.z-dn.net/?f=6%20%5Csin%28%20%5Cfrac%7B4%20%7B%5Cpi%7D%5E%7B2%7D%20%7D%7B3%7Dx%20%29%20)
and when you want to shift it 1 unit left we have:
<span>The annual return on $400 in stock is 0.11*400 = $44
</span>
The total return you want is 0.09 * 1600 = $144
Let a be the amount invested at 12% and b be the amount invested at 6%
0.12a + 0.06b = 144 - 44
12a + 6b = 10000
a + b = 1200
Put those 2 equations together and solve for a and b:
12a + 6b = 10000
a + b = 1200
Using elimination, a = $466.67 and b = $733.33
<span>So, out of an additional $1200, invest $466.67 at a rate of 12% and $733.33 at a rate of 6%</span>
Answer: 32 days. This is more than a month.
Step-by-step explanation:
First, convert the 30 pound bag into ounces. To do this you just need to multiply 30 by 16. You will get 480 ounces (so one bag has 480 ounces of food in it. Then, just divide that by the ounces eaten by Socks in a day. 480/15 is 32. So one bag of food lasts 32 days. At the most, one month can have 31 days in it so this bag will last for more than a month. Hope this helps!
<span>(1,625) No
(0,-25) No
(-1,-1) No
Think about what an integer exponent means for an negative base and you'll understand this problem. For instance the powers of -25 would be
-25^1 = -25
-25^2 = (-25) * (-25) = 625
-25^3 = (-25)*(-25)*(-25) = -15625
and so on, giving 390625, -9765625, 244140625, etc.
But that's a different subject. For the ordered pairs given, let's check them out.
(1,625)
-25^1 + 1 = -25 + 1 = -24. And -24 is not equal to 625, so "No".
(0,-25)
-25^0 + 1 = 1 +1 = 2.
Note: Any real number other than 0 raised to the 0th power is 1. And 2 is not equal to -25, so "No".
(-1,-1)
-25^(-1) + 1 = 1/(-25^1) + 1 = 1/-25 + 1 = 24/25.
And 24/25 is not equal to -1, so also "No".</span>