The bottom of a deposit, of 300l of capacity, is cover by a layer of salt. Assuming that the velocity at which the salt is disolved is proportional to the difference between the concentration at this time and the concentration of the saturated solution ( 1 kg of salt for 3 liters of water), and also take into account that the amount of pure water disolve 1/3 de Kg of salt per minute. Find the ODE giving the amount of salt x(t), as a function of time, integrate it, and determine the amount of salt in the solution after one hour. Find the solutions of the ODE that satisfy the indicated conditions when x → ±[infinity]

Step-by-step explanation:

Assuming x(t) to be the number of salt

The maximum bottom of deposits =300 Litre

Initial Concentration of the saturated salt solution = 1 kg of salt for 3 liters of water

⇒x = 0

The  differential equation is :

Using the first order differential equation of the form :

x' + p(t) x = q(t)

where

  ;  

By integrating the factor:

Thus the differential equation solution  is :

However; we have initial concentration   x(0) = 0

SO;

C = -100

when x → ±[infinity]

Now;  the amount of salt after an hour is as follows:

1 hour = 60  minutes

t = 60 min

= 100 -100 (0.818)

= 100 - 81.8

= 18.2

x(60) = 18.2 kg

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is

111

step-by-step explanation: