All triangle add up to 180
so 180-(96+48)
which is 36
so 36 is the missing interior angle
now all lines also equal 180
so 180-36=x
x=144
Answer:
(a) The time to complete 1 cycle and return is 16/3
(b) The minimum height is 30 inches and the maximum is 54 inches
Step-by-step explanation:
Given
![f(t) = 12\sin(\frac{3\pi}{8}t) + 42](https://tex.z-dn.net/?f=f%28t%29%20%3D%2012%5Csin%28%5Cfrac%7B3%5Cpi%7D%7B8%7Dt%29%20%2B%2042)
Solving (a): Time to complete 1 cycle and return
This implies that we calculate the period. This is calculated using:
![T = \frac{2\pi}{w}](https://tex.z-dn.net/?f=T%20%3D%20%5Cfrac%7B2%5Cpi%7D%7Bw%7D)
Where:
![w =\frac{3\pi}{8}](https://tex.z-dn.net/?f=w%20%3D%5Cfrac%7B3%5Cpi%7D%7B8%7D)
So, we have:
![T = \frac{2\pi}{\frac{3\pi}{8}}](https://tex.z-dn.net/?f=T%20%3D%20%5Cfrac%7B2%5Cpi%7D%7B%5Cfrac%7B3%5Cpi%7D%7B8%7D%7D)
![T = \frac{2}{\frac{3}{8}}](https://tex.z-dn.net/?f=T%20%3D%20%5Cfrac%7B2%7D%7B%5Cfrac%7B3%7D%7B8%7D%7D)
![T = \frac{2*8}{3}](https://tex.z-dn.net/?f=T%20%3D%20%5Cfrac%7B2%2A8%7D%7B3%7D)
Solving (b): The maximum and the minimum height
To do this, we have:
Which means:
![-1 \le \sin(\frac{3\pi}{8}) \le 1](https://tex.z-dn.net/?f=-1%20%5Cle%20%5Csin%28%5Cfrac%7B3%5Cpi%7D%7B8%7D%29%20%5Cle%201)
So, the minimum is:
![\sin(\frac{3\pi}{8}) =- 1](https://tex.z-dn.net/?f=%5Csin%28%5Cfrac%7B3%5Cpi%7D%7B8%7D%29%20%3D-%201)
And the maximum is:
![\sin(\frac{3\pi}{8}) =1](https://tex.z-dn.net/?f=%5Csin%28%5Cfrac%7B3%5Cpi%7D%7B8%7D%29%20%3D1)
Recall that the height is:
So, the maximum and the minimum of are:
![h_{min} =12 * -1 + 42](https://tex.z-dn.net/?f=h_%7Bmin%7D%20%3D12%20%2A%20-1%20%2B%2042)
![h_{min} =30](https://tex.z-dn.net/?f=h_%7Bmin%7D%20%3D30)
and
Answer:
D) 6.79 x 10^7
Step-by-step explanation:
Company D has the greatest revenue because it is multiplying by 10 to the power of 7 which is the same as multiplying by 10 seven times. The least revenue is company C because it is only multiplying by 10 to the power of 4 which is the same as multiplying by 10 4 times.
6.8 x 10^7 = 68,000,000
9 x 10^4 = 90,000
68,000,000 - 90,000 = 67,910,000.
Convert this back into standard form to get 6.79 x 10^7
36 Cards given away
Roberto has nine so that means everyone else also has nine since they're equal
Therefore
9 cards x 4 other people= 36 cards given