1) Since in the USA 8 x 10 ^9 messages are sent every month, that means that approximately 8 billion messages are sent.
2) We can Prime factorize it:
Note that on the right side we've picked only prime numbers. In this case, 2 and 5.
So we can rewrite 8 x 10^9 as prime factors.
3) Hence, the answer is:
Answer:
12 is to the right of -15 on a number line.
Step-by-step explanation:
Hope this helps! - CJ
Yep! Good job, you did it correctly.
Your y-intercept is equal to the constant of the equation (y-int = -2). Your movement/direction (or rise over run) is equal to the variable. Since your variable is x (which can also be written as 1x) means you move up one and over one (rise over run). This is because 1/1 is equal to 1.
Answer:
y = x*sqrt(Cx - 1)
Step-by-step explanation:
Given:
dy / dx = (x^2 + 5y^2) / 2xy
Find:
Solve the given ODE by using appropriate substitution.
Solution:
- Rewrite the given ODE:
dy/dx = 0.5(x/y) + 2.5(y/x)
- use substitution y = x*v(x)
dy/dx = v + x*dv/dx
- Combine the two equations:
v + x*dv/dx = 0.5*(1/v) + 2.5*v
x*dv/dx = 0.5*(1/v) + 1.5*v
x*dv/dx = (v^2 + 1) / 2v
-Separate variables:
(2v.dv / (v^2 + 1) = dx / x
- Integrate both sides:
Ln (v^2 + 1) = Ln(x) + C
v^2 + 1 = Cx
v = sqrt(Cx - 1)
- Back substitution:
(y/x) = sqrt(Cx - 1)
y = x*sqrt(Cx - 1)
