Answer:
165 is the quotient
Step-by-step explanation:
3139 ÷ 19 = 165
(if you want the remainder it would be 4)
Call the point of attachment at the top of the building point T. (Angle T = 25°) The angle N = 180° -32° -25° = 123°. The Law of Sines tells you the relationship ...
... TM/sin(N) = MN/sin(T)
... MN = TM·sin(T)/sin(N) = (200 ft)·sin(25°)/sin(123°)
... MN ≈ 100.8 ft
Answer:
x=2
Step-by-step explanation:
combine like terms to get 15x=30. divide by 15 on both sides to get x=2
Answer:
i dont eather i need to know the ?
Step-by-step explanation:
Answer:
j(x) is shifted right by
units
Step-by-step explanation:
Given
![j(x)= 51 cos(x + \frac{\pi}{2})](https://tex.z-dn.net/?f=j%28x%29%3D%2051%20cos%28x%20%2B%20%5Cfrac%7B%5Cpi%7D%7B2%7D%29)
![k(x)= 51 cos(x - \frac{3\pi}{4})](https://tex.z-dn.net/?f=k%28x%29%3D%2051%20cos%28x%20-%20%5Cfrac%7B3%5Cpi%7D%7B4%7D%29)
Required
Determine the transformation from j(x) to k(x)
The transformation shows a horizontal shift from j(x) to k(x).
First, we need to determine the unit shifter from j(x) to k(x) as follows;
![j(x)= 51 cos(x + \frac{\pi}{2})](https://tex.z-dn.net/?f=j%28x%29%3D%2051%20cos%28x%20%2B%20%5Cfrac%7B%5Cpi%7D%7B2%7D%29)
Express
as ![\frac{5\pi}{4}-\frac{3\pi}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B5%5Cpi%7D%7B4%7D-%5Cfrac%7B3%5Cpi%7D%7B4%7D)
So:
becomes
![j(x) = 51cos(x + \frac{5\pi}{4}-\frac{3\pi}{4})](https://tex.z-dn.net/?f=j%28x%29%20%3D%2051cos%28x%20%2B%20%5Cfrac%7B5%5Cpi%7D%7B4%7D-%5Cfrac%7B3%5Cpi%7D%7B4%7D%29)
Reorder
![j(x) = 51cos(x -\frac{3\pi}{4}+ \frac{5\pi}{4})](https://tex.z-dn.net/?f=j%28x%29%20%3D%2051cos%28x%20-%5Cfrac%7B3%5Cpi%7D%7B4%7D%2B%20%5Cfrac%7B5%5Cpi%7D%7B4%7D%29)
Comparing this to k(x), we have:
![k(x)= 51 cos(x - \frac{3\pi}{4})](https://tex.z-dn.net/?f=k%28x%29%3D%2051%20cos%28x%20-%20%5Cfrac%7B3%5Cpi%7D%7B4%7D%29)
In other words:
![k(x) = j(x - \frac{5\pi}{4})](https://tex.z-dn.net/?f=k%28x%29%20%3D%20j%28x%20-%20%5Cfrac%7B5%5Cpi%7D%7B4%7D%29)
<em>This implies that j(x) is shifted right by </em>
<em> units</em>