A tank contains 10 liters of pure water. A solution of an unknown, but constant concentration of salt is flowing in at 0.5 liters per minute. The water is mixed well and drained at 1 liter per minute. After 20 minutes there are 10 grams of salt in the tank. (i) Give an adequate mathematical model for this scenario. Explain what each of your variables means. (ii) What is the concentration of the incoming salt solution

i) ∴∫  = ∫ ------ ( 1 )

ii) C = 4.303

Explanation:

Given data:

water in tank = 10 liters

concentration of salt flowing in = 0.5 liters/min

10 grams of salt is left in tank after 20 minutes

mixed water is drained at 1 liter per minute

i) Adequate mathematical model for the scenario

lets assume ; A( t ) amount of salt after t minute

A( t ) = 10grams   where t = 20 minutes

differentiate A(t)

dA / dt = ( rate in ) - ( rate out )

           = 0.5 * 0  - A/10

∴∫  = ∫ ------ ( 1 )

ii) hence;  In A =  -----  ( 2 )

at  t = 20 , A = 10grams

find C = In 10 + 2

          = 2.303 + 2 = 4.303

back to ( 2 )

In A =

∴ A = e

when—without warning—something provokes your anger, you may struggle not to succumb to it. since what typically makes you mad is feeling powerless in the face of what seems unfair, your anger is mostly an attempt at a “quick fix” to right the balance. it’s as though you’re raising a fist in protest, proclaiming that you’re not going to capitulate to such injustice.

there are, however, a multitude of problems related to this immediate, push-back reaction of anger. and probably the key one is that almost never does it resolve the issue that gave rise to it. such reactive anger is probably best understood as self-defeating. as david burns, the author of the seminal self- book feeling good, observes: if realistically, acting on your anger is to make any sense, it needs to meet two criteria—which, in almost every case, is frankly impossible. that is, your anger must:

be directed toward a person who has intentionally (and needlessly) behaved in a hurtful way toward you; and

be beneficial or advantageous to you (i.e., assist you in achieving a desired goal).

i think you’ll agree that only rarely can you claim that your anger is both warranted and , whether to yourself or the relationship.

so let me offer you a two-step alternative to abandoning your better judgment and giving in to the temptation of anger—one that should neutralize your anger in seconds. or, when you’re really angry, in minutes.

but keep in mind that you must really want to execute these steps, be sufficiently motivated to perform them. which means overcoming more unconscious resistance than you might ever have imagined. because there are many immediate “advantages” of anger that can interfere with your resolve, i’ll suggest a few of them that might interfere with your employing this powerful method to rid yourself of counter-productive anger.

explanation: