harita must memorize 90 measures of music for her cello solo at a concert. she plans on memorizing 18 new measures for every 3 days of practice. which equation can be used to determine m, the number of measures harita still needs to memorize, as a function of d, the number of days of practice since she began learning the piece?
LectureNotes said Harita must memorize 90 measures of music for her cello solo at a concert. She plans on memorizing 18 new measures for every 3 days of practice. Which equation can be used to determine m, the number of measures Harita still needs to memorize, as a function of d, the number of days of practice since she began learning the piece?
Answer: To determine the number of measures Harita still needs to memorize, we can set up an equation based on the information provided.
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Identify the total number of measures to be memorized: Harita needs to memorize 90 measures in total.
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Determine the rate of memorization: Harita memorizes 18 measures every 3 days. This can be simplified to a rate of 6 measures per day (\frac{18 \text{ measures}}{3 \text{ days}} = 6 \text{ measures per day}).
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Set up the equation:
- Let d be the number of days of practice.
- The number of measures memorized after d days is 6d.
- The number of measures still needed to memorize, m, is the total number of measures minus the number of measures memorized.
Therefore, the equation that represents the number of measures Harita still needs to memorize as a function of d is:
[ m = 90 - 6d ]
Explanation:
- 90 represents the total number of measures to be memorized.
- 6d represents the number of measures memorized after d days of practice.
- Subtracting 6d from 90 gives the number of measures Harita still needs to memorize.
So, the function m(d) = 90 - 6d accurately models the situation described.