Question

the graph below describes the cycles of the moon as observed from earth during the first 60 days of a year. the percentage of the moon which we see varies as a function of time. a full moon corresponds to 100% visibility and a new moon corresponds to 0% visibility.
complete the following sentences based on the graph of the function.

• the first new moon of the year was on day blank.
• the second new moon of the year was on day blank.
• therefore, the period between two new moons is approximately blank days long.

graph of moon visibility (m, %) vs. time (days) with a grid, showing peaks (full moons) and troughs (new moons)

Explanation:

Step1: Find first new moon

A new moon is 0% visibility. The first time \( M = 0\% \) is at day 0 (since the graph starts at day 0 with 0%? Wait, no, looking at the graph, the first new moon (0% visibility) is at day 0? Wait, no, maybe the x - axis is days. Wait, the first new moon: the graph starts at (0,0)? Wait, no, the y - axis is \( M[\%] \), x - axis is days. So the first new moon (0% visibility) is at day 0? Wait, no, maybe the first new moon is at day 0, then the next new moon: let's see the graph. The first trough (0% visibility) is at day 0, then the next trough (second new moon) is at day 29 (approx), then the period is 29 - 0 = 29? Wait, let's check the grid. Each square on x - axis: let's assume the first new moon is day 0, second new moon is day 29 (since lunar cycle is about 29.5 days). So:

Step1: First new moon day

The first new moon (0% visibility) occurs at day 0 (from the graph's start, where \( M = 0\% \)).

Step2: Second new moon day

The second new moon (next 0% visibility) occurs at day 29 (approx, looking at the graph's troughs, the distance between first and second trough is about 29 days).

Step3: Period calculation

Period = second new moon day - first new moon day = \( 29 - 0 = 29 \) (approx 29 or 30, but typically lunar cycle is ~29.5, so 29 - 30).

Answer:

First new moon: 0
Second new moon: 29
Period: 29 (or 30, depending on graph grid, but standard is ~29.5, so 29 - 30)

(Note: If the graph's x - axis grid has each unit as 1 day, and the first trough is at day 0, second at day 29, then the answers are 0, 29, 29. If the first new moon is at day 1, adjust, but from the graph description, likely day 0, 29, 29.)