For the Curve R(t), Find an Equation for the Indicated

question 117

Multiple Choice

For the curve r(t) , find an equation for the indicated plane at the given value of t.
- $\mathbf { r } ( \mathrm { t } ) = ( \mathrm { t } + 6 ) \mathbf { i } + ( \ln ( \cos \mathrm { t } ) - 8 ) \mathbf { j } + 7 \mathbf { k } , - \pi / 2 < \mathrm { t } < \pi \cdot 2 ;$ rectifying plane $\mathrm { at } \mathrm {} \mathrm { t } = \frac { \pi } { 4 }$ .

• A) \(\frac { \sqrt { 2 } } { 2 } \left( x - \left( \frac { \pi } { 4 } + 6 \right) \right) - \frac { \sqrt { 2 } } { 2 } \left( y - \left( \ln \left( \frac { \sqrt { 2 } } { 2 } \right) - 8 \right) \right) = 0\)
• B) \(- \frac { \sqrt { 2 } } { 2 } \left( x - \left( \frac { \pi } { 4 } + 6 \right) \right) + \frac { \sqrt { 2 } } { 2 } \left( y - \left( \ln \left( \frac { \sqrt { 2 } } { 2 } \right) - 8 \right) \right) = 0\)
• C) \(\frac { \sqrt { 2 } } { 2 } ( x - ( 1 + 6 ) ) = 0\)
• D) \(\left. \frac { \sqrt { 2 } } { 2 } \left( x - \left( \frac { \pi } { 4 } + 6 \right) \right) \right) ^ { \prime } + \frac { \sqrt { 2 } } { 2 } \left( y - \left( \ln \left( \frac { \sqrt { 2 } } { 2 } \right) - 8 \right) \right) = 0\)

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Definitions:

Longitudinal Studies

Research designs that involve repeated observations of the same variables (e.g., people) over short or long periods of time.

Age Differences

Variations in behavior, attitudes, and expectations often attributed to individuals being of different chronological ages.

Cohort Differences

Variations in the characteristics or experiences of individuals belonging to different age or generational groups.

Emotional Self-regulation

The ability to monitor and manage one's own emotions, to begin or inhibit behavior in accordance with emotional responses.