Solve the Problem $f ( t ) = 10 \sin \left( \frac { 3 \pi t } { 4 } - \frac { \pi } { 4 } \right)$

question 130

Multiple Choice

Solve the problem.
-A weight suspended from a spring is vibrating vertically with up being the positive direction. The function $f ( t ) = 10 \sin \left( \frac { 3 \pi t } { 4 } - \frac { \pi } { 4 } \right)$ represents the distance in centimeters of the weight from its rest position as a function of time t, where t is measured in seconds. Find the smallest positive value of t for which the displacement of the weight above its rest position is 5 cm.
Round answer to three decimal places, if necessary.

• A) 1.586
• B) 2.293
• C) 0.556
• D) 0.222

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Definitions:

Lewis Base

A substance that can donate a pair of electrons to form a covalent bond, according to Lewis acid-base theory.

Electrophile

A reactive species that seeks out electrons and is attracted to electron-rich sites, often participating in chemical reactions by accepting an electron pair.

Nucleophile

An entity in chemistry that transfers a pair of electrons to an electrophile, enabling the formation of a chemical bond as a part of the reaction process.

Lewis Definition

A theory of acids and bases where acids accept a pair of electrons during a reaction, while bases donate a pair of electrons.