Solve the Problem $\frac { d y } { d t } = 32 - \frac { 5 } { 120 + 3 t } y$

question 24

Multiple Choice

Solve the problem.
-A tank initially contains 120 gal of brine in which 40 lb of salt are dissolved. A brine containing 4 lb/gal of salt runs into the tank at the rate of 8 gal/min. The mixture is kept uniform by stirring and flows out of the tank at The rate of 5 gal/min. Write, in standard form, the differential equation that models the mixing process.

• A) \(\frac { d y } { d t } = 32 - \frac { 5 } { 120 + 3 t } y\)
• B) \(\frac { \mathrm { dy } } { \mathrm { dt } } + \frac { 5 } { 120 - 3 \mathrm { t } } \mathrm { y } = 32\)
• C) \(\frac { d y } { d t } + \frac { 5 } { 120 + 3 t } y = 32\)
• D) \(\frac { \mathrm { dy } } { \mathrm { dt } } + \frac { 8 } { 120 + 3 \mathrm { t } } \mathrm { y } = 20\)

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Definitions:

Oedipal

Relating to the Oedipus complex, a concept in psychoanalytic theory referring to a child's unconscious sexual desire for the opposite-sex parent and jealousy toward the same-sex parent.

Electra Complex

The condition in which, according to Sigmund Freud, girls want to seduce their fathers to gain what they truly desire: a penis. By analogy to a character in several Greek tragedies.

Attachment Theory

A development of the psychoanalytic approach by John Bowlby. According to this view, children form attachments with their parents that become the child’s internalized model for all subsequent relationships. Difficulties in such attachments form the basis for later problems.

Schema

A structured framework or plan outlining the organization of concepts, often used in psychology to describe how information is grouped and interpreted.