The length of an australian flag is twice its width and the diagonal length is 45cm.
a. if x cm is the width of the flag, find the length in terms of x.
b. draw a diagram of the flag marking in the diagonal. mark the length and the width in terms of x.
c. use pythagoras’ theorem to write an equation relating the lengths of the sides to the length of the diagonal.
d. solve the equation to find the dimensions of the australian flag. around your answer to the nearest cm.

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.