Aplumber has a very long piece of pipe that is used to run the city water parallel to a major roadway. the pipe is cut into two sections. one section of the pipe is 12ft shorter than the other. if 3/4 of the length of the shorter pipe is 120ft how long is the longer piece. write an algebraic equation to solve your answer

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.

Determine the domain and range of the given function. the domain is all real numbers all real numbers greater than or equal to –2{x: x = –2, –1, 0, 1, 2}{y: y = –2, –1, 0, 1, 2}. the range is all real numbers all real numbers greater than or equal to –2{x: x = –2, –1, 0, 1, 2}{y: y = –2, –1, 0, 1, 2}.

The biologist has a second culture to examine. she knows that the population of the culture doubles every 15 minutes. after 1 hour and 15 minutes, her assistant found that 80,000 bacteria were present. a) what was the size of the initial population? b) predict the size of the culture at t=3 hours. what was the size of the population at 40 minutes? explain and justify your answers. c) create a graph of the population as a function of time. find an equation that can be used to predict the size of the population at any time t. d) examine the rate at which the bacteria culture is growing. how fast is the culture growing after 1 hour? after 1.5 hours? after 2 hours? use a time interval of h = 0.01 hours to estimate these rates. interpret these rates in terms of the context of the problem situation. how do these three rates compare?