Prompt
You are given a rectangular sheet of cardboard that measures 11 in by 815 in. (see the diagram below). A small square of the
same size is cut from each corner and each side folded up along the cuts to from a box with no lid.
1. Anya thinks the cut should be 1.5 inches to create the greatest volume, while Terrence thinks it should be 3 inches.
• Explain how both students can determine the formula for the volume of the box.
• Determine which student's suggestion would create the larger volume.
• Explain how there can be two different volumes when each student starts with the same size cardboard.
2. Why is the value of x limited to 0 in. <
< 425 in.?

In new york city at the spring equinox there are 12 hours 8 minutes of daylight. the longest and shortest days of the year very by two hours and 53 minutes from the equinox in this year the equinox falls on march 21 in this task you use trigonometric function to model the hours of daylight hours on certain days of the year in new york city a.what is the independent and dependent variables? b.find the amplitude and the period of the function. c.create a trigonometric function that describes the hours of sunlight for each day of the year. d. graph the function you build in part c. e. use the function you build in part c to find out how many fewer daylight hours february 10 will have than march 21. you may look at the calendar.