Answer:
solutions
Step-by-step explanation:
we know that
The solution for the system of conic sections is the intersection point both graphs
In this problem we have
points of intersection
see the attached figure to better understand the problem
The equation is not well formatted so I assumed it is
![D(t) = 2 \sin(\dfrac{\pi}{3}t + \dfrac{5\pi}{3}) + 5](https://tex.z-dn.net/?f=D%28t%29%20%3D%202%20%5Csin%28%5Cdfrac%7B%5Cpi%7D%7B3%7Dt%20%2B%20%5Cdfrac%7B5%5Cpi%7D%7B3%7D%29%20%2B%205)
Answer:
1.0472 m/s
Step-by-step explanation:
If
, the rate at which the depth is changing is the time-derivative of D(t);
![\dfrac{d}{dt}D(t) = \dfrac{2\pi}{3}\cos(\dfrac{\pi}{3}t + \dfrac{5\pi}{3})](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%7D%7Bdt%7DD%28t%29%20%3D%20%5Cdfrac%7B2%5Cpi%7D%7B3%7D%5Ccos%28%5Cdfrac%7B%5Cpi%7D%7B3%7Dt%20%2B%20%5Cdfrac%7B5%5Cpi%7D%7B3%7D%29)
At 2 am, t = 2 hours after midnight.
Substitute this in the last equation.
To solve we need to isolate
![x](https://tex.z-dn.net/?f=x)
.
Start by adding 1 to both sides:
![4x-1+1=7+1](https://tex.z-dn.net/?f=4x-1%2B1%3D7%2B1)
![4x=8](https://tex.z-dn.net/?f=4x%3D8)
Then divide both sides by 4:
![\frac{4x}{4} = \frac{8}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B4x%7D%7B4%7D%20%3D%20%5Cfrac%7B8%7D%7B4%7D)
Answer:
9 shelters
Step-by-step explanation:
Subtract 64 from the total number of coats to get the total amount of coats donated to shelters:
388 - 64 = 324
Then, divide 324 by 36, since that's the minimum number of coats given to each shelter:
324 ÷ 36 = 9
So at least 9 shelters received coats.
-8y = -4x + 16
Y = 4/8x - 2