Let's solve the problem step-by-step to find the equation that determines the number of measures Harita still needs to memorize as a function of the number of days of practice since she began learning the piece.
1. Initial Information:
- Harita needs to memorize a total of 90 measures of music.
- She plans on memorizing 18 new measures every 3 days.
2. Rate of Memorization:
- To determine the daily rate of memorization, we divide the total measures of music memorized in 3 days by the number of days:
[tex]\[
\text{Measures per day} = \frac{18 \text{ measures}}{3 \text{ days}} = 6 \text{ measures per day}
\][/tex]
3. Derive the Equation:
- Let [tex]\( d \)[/tex] be the number of days of practice.
- The total number of measures Harita memorizes after [tex]\( d \)[/tex] days can be found by multiplying the daily memorization rate by [tex]\( d \)[/tex]:
[tex]\[
\text{Measures memorized after } d \text{ days} = 6d
\][/tex]
- The number of measures she still needs to memorize is the initial total measures minus the measures she has already memorized:
[tex]\[
m = 90 - 6d
\][/tex]
4. Conclusion:
- The equation that represents the number of measures Harita still needs to memorize as a function of the number of days of practice is:
[tex]\[
m = 90 - 6d
\][/tex]
Therefore, the correct equation is:
[tex]\[
m = 90 - 6d
\][/tex]
Among the given options, this corresponds to:
[tex]\[
m = 90 - 6d
\][/tex]
