Suppose That a Substance a Is Converted to Substance B $y ^ { \prime }$

question 57

Multiple Choice

Suppose that a substance A is converted to substance B at a rate that is proportional to the cube of the amount of B present. The amount of A and B together is always constant, say M. If f( t) = y is the amount of A present at time t, then which of the following differential equation describes the situation?

• A) \(y ^ { \prime }\) = \(k ( M - y ) ^ { 3 }\) ; k < 0
• B) \(y ^ { \prime }\) = \(k ( M - y ) ^ { 3 }\) ; k > 0
• C) \(y ^ { \prime }\) = \(\mathrm { ky } ^ { 3 }\) ; k > 0
• D) \(y ^ { \prime }\) = \(\mathrm { ky } ^ { 3 }\) ; k < 0
• E) none of these

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Definitions:

Lack Of Resistance

A situation in which someone does not oppose or resist something, sometimes indicating consent or acquiescence.

No Means No

A phrase emphasizing that refusal or denial does not require justification and should be respected, often used in the context of sexual consent.

Consent

The agreement between participants to engage in a specific activity, given freely and willingly, and can be withdrawn at any time.

Extrafamilial Child Sexual Abuse

Child sexual abuse by someone unrelated to the child.