Answer:
Flow-rate = 0.0025 m^3/s
Explanation:
We need to assume that the flow-rate of pure water entering the pond is the same as the flow-rate of brine leaving the pond, in other words, the volume of liquid in the pond stays constant at 20,000 m^3. Using the previous assumption we can calculate the flow rate entering or leaving the tank (they are the same) building a separable differential equation dQ/dt, where Q is the milligrams (mg) of salt in a given time t, to find a solution to our problem we build a differential equation as follow:
dQ/dt = -(Q/20,000)*r where r is the flow rate in m^3/s
what we pose with this equation is that the variable rate at which the salt leaves the pond (salt leaving over time) is equal to the concentration (amount of salt per unit of volume of liquid at a given time) times the constant rate at which the liquid leaves the tank, the minus sign in the equation is because this is the rate at which salt leaves the pond.
Rearranging the equation we get dQ/Q = -(r/20000) dt then integrating in both sides ∫dQ/Q = -∫(r/20000) dt and solving ln(Q) = -(r/20000)*t + C where C is a constant (initial value) result of solving the integrals. Please note that the integral of dQ/Q is ln(Q) and r/20000 is a constant, therefore, the integral of dt is t.
To find the initial value (C) we evaluate the integrated equation for t = 0, therefore, ln(Q) = C, because at time zero we have a concentration of 25000 mg/L = 250000000 mg/m^3 and Q is equal to the concentration of salt (mg/m^3) by the amount of liquid (always 20000 m^3) -> Q = 250000000 mg/m^3 * 20000 m^3 = 5*10^11 mg -> C = ln(5*10^11) = 26.9378. Now the equation is ln(Q) = -(r/20000)*t + 26.9378, the only thing missing is to find the constant flow rate (r) required to reduce the salt concentration in the pond to 500 mg/L = 500000 mg/m^3 within one year (equivalent to 31536000 seconds), to do so we need to find the Q we want in one year, that is Q = 500000 mg/m^3 * 20000 m^3 = 1*10^10 mg, therefore, ln(1*10^10) = -(r/20000)*31536000 + 26.9378 solving for r -> r = 0.002481 m^3/s that is approximately 0.0025 m^3/s.
Note:
- ln() refer to natural logarithm
- The amount of liquid in the tank never changes because the flow-rate-in is the same as the flow-rate-out
- When solving the differential equation we calculated the flow-rate-out and we were asked for the flow-rate-in but because they are the same we could solve the problem
- During the solving process, we always converted units to m^3 and seconds because we were asked to give the answer in m^3/seg
Answer:
housing, savings, and food
housing, food, and transportation
Explanation:
Given: Family Budget comprises of 23% housing, 21% food, 10% savings, 16% transportation, 12% medical, 13% clothing and 5% emergency fund.
To find: categories that make up more than half of the Hernandez family budget
Solution:
clothing + medical + emergency fund = 
clothing + housing + savings = 
housing + savings + food = 
housing + food + transportation = 
food + transportation + emergency fund = 
So, 3 categories that make up more than half of the Hernandez family budget are housing, savings, and food, housing, food, and transportation
Answer:

Explanation:
The question is: <em>Find the magnitude of the centripetal acceleration of the star with mass m₂</em>
The <em>centripetal acceleration</em> is the quotient of the centripetal force and the mass.

Thus, you can write the equations for each star:


As per Newton's third law, the centripetal forces are equal in magnitude. Then:

Now you can clear
:

Answer:
a)
, b) 
Explanation:
a) The uniform dresser is modelled by using the following equations of equilibrium:


After some algebraic manipulation, the following formula is derived:



b) The man is described by the following equations of equilibrium:


After some algebraic manipulation, the following formula for the static coefficient of friction is:



Answer:
leveled cost of electricity LCOE is 0.1159/kwh
Explanation:
given data:
installation cost of system = $1.50/winstalled
capacity factor = 22%
life = 10 year
rate of interest 8%
operation and maintenance cost = $0.04 / kwh generated
capcaitence recovery factor
i= rate of interest
n = annuity period



= 0.1159/kwh + 0.04 /kwh
= 0.1559 /kwh