Answer:
The BOD concentration 50 km downstream when the velocity of the river is 15 km/day is 63.5 mg/L
Explanation:
Let the initial concentration of the BOD = C₀
Concentration of BOD at any time or point = C
dC/dt = - KC
∫ dC/C = -k ∫ dt
Integrating the left hand side from C₀ to C and the right hand side from 0 to t
In (C/C₀) = -kt + b (b = constant of integration)
At t = 0, C = C₀
In 1 = 0 + b
b = 0
In (C/C₀) = - kt
(C/C₀) = e⁻ᵏᵗ
C = C₀ e⁻ᵏᵗ
C₀ = 75 mg/L
k = 0.05 /day
C = 75 e⁻⁰•⁰⁵ᵗ
So, we need the BOD concentration 50 km downstream when the velocity of the river is 15 km/day
We calculate how many days it takes the river to reach 50 km downstream
Velocity = (displacement/time)
15 = 50/t
t = 50/15 = 3.3333 days
So, we need the C that corresponds to t = 3.3333 days
C = 75 e⁻⁰•⁰⁵ᵗ
0.05 t = 0.05 × 3.333 = 0.167
C = 75 e⁻⁰•¹⁶⁷
C = 63.5 mg/L
Answer: The correct answer is B. trust me, I just took that test. :)
The asteroid's mass is so small that it has a much smaller acceleration
due to gravity than Earth has. That means that things weigh very very little
on the surface of an asteroid. It also means that the "escape velocity" from
an asteroid is very low, and orbital velocities are very low at any distance off
of its surface.
As an extreme example: You know how when you walk, you naturally rise up
on the toes of one foot while you reach out with the other one to take a step ?
All of those motions are what you learn in Earth's gravity. On an asteroid, that
natural action of rising up on your toes might launch you into a long, high arc,
like a golf ball. Or it might even exceed escape velocity and you'd sail up off
of the asteroid and never come back down to it.