ANSWER
The particular solution is:
![y=2-2 \cos(x)](https://tex.z-dn.net/?f=y%3D2-2%20%5Ccos%28x%29)
EXPLANATION
The given Ordinary Differential Equation is
![y'=2 \sin(x)](https://tex.z-dn.net/?f=y%27%3D2%20%5Csin%28x%29)
The general solution to this Differential equation is:
![y=C-2 \cos(x)](https://tex.z-dn.net/?f=y%3DC-2%20%5Ccos%28x%29)
To find the particular solution, we need to apply the initial conditions (ICs)
![y( \frac{\pi}{3} ) = 1](https://tex.z-dn.net/?f=y%28%20%5Cfrac%7B%5Cpi%7D%7B3%7D%20%29%20%3D%201)
This implies that;
![C-2 \cos( \frac{\pi}{3} ) = 1](https://tex.z-dn.net/?f=C-2%20%5Ccos%28%20%5Cfrac%7B%5Cpi%7D%7B3%7D%20%29%20%3D%201)
![C-2( \frac{1}{2} )= 1](https://tex.z-dn.net/?f=C-2%28%20%5Cfrac%7B1%7D%7B2%7D%20%29%3D%201)
![C-1= 1](https://tex.z-dn.net/?f=C-1%3D%201)
![C= 1 + 1 = 2](https://tex.z-dn.net/?f=C%3D%201%20%2B%201%20%3D%202)
Hence the particular solution is
![y=2-2 \cos(x)](https://tex.z-dn.net/?f=y%3D2-2%20%5Ccos%28x%29)
Answer:
Liam pays $24
Step-by-step explanation:
20% off = 20÷100= 1/5
1/5 × $30 = $6
$30 - $6 =$24
Answer:
yes
Step-by-step explanation:
YOU DID IT'S A GOOD DAY
Volume is 4/3(3.14)(r)^2
the radius is 5.2 ft
Using how tall it is over how wide
=>tall/wide
The model 15in/1.5in
The actual x/55ft
Convert everything into the same units so 55ft to inches
There are 12in in 1ft
55ft * 12in/1ft
The ft cross out leaving in
55*12in= 660 in
So
15in/1.5in = x/660in
Now solve for x my multiplying both side by 660in
660in *15in/1.5in=x
x= 6600in tall