Assuming That the Equations Define X and Y Implicitly as Differentiable

question 25

Multiple Choice

Assuming that the equations define x and y implicitly as differentiable functions x = f(t) , y = g(t) , find the slope of the curve x = f(t) , y = g(t) at the given value of t.
- $$2 \mathrm { tx } + 4 \mathrm { t } ^ { 2 } = 4,2 \mathrm { y } - \mathrm { t } ^ { 2 } - \mathrm { t } = 0 , \mathrm { t } = 1$$

• A) \(\frac { 3 } { 2 }\)
• B) \(- \frac { 3 } { 8 }\)
• C) \(- 6\)
• D) \(\frac { 3 } { 8 }\)

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Definitions:

Equity

A condition in which people receive from a relationship in proportion to what they give to it.

Altruism

Selfless concern for the well-being of others, often involving actions done for the benefit of others without expectation of reward.

Social Exchange

A theory in social psychology suggesting that social behavior is the result of an exchange process where individuals aim to maximize benefits and minimize costs.

Passionate Love

An intense emotion that combines physical attraction and emotional attachment to another person, often characterized by ardor and desire.