In an experiment, it is discovered that the temperature difference( in °c) between a glass of hot water and the room decreases by 4 % every minute. suppose that the original temperature of the glass of hot water is 100°c and the room temperature is 20 °c. let d °c be the temperature difference between the glass of hot water and the room after t minutes. (a) express d in terms of t. (b) find the temperature of the glass of hot water after 15 minutes, correct to the nearest °c. (c) (i) make t the subject of the equation in (a). (ii)find the time required for the temperature of the hot water to decrease to 30°c, correct to the nearest minute.

The tuition costs, c, for a local community college are modeled by c(h) = 250 + 200h, where h represents the number of credit hours taken. the local state university has tuition costs, s, modeled by the function s(h) = 300 + 180h. how many credit hours will a student have to take for the two tuition costs to be equal? round the answer to the nearest tenth of an hour.

After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. you notice the rainbow is the shape of a parabola. the equation for this parabola is y = -x2 + 36. graph of a parabola opening down at the vertex 0 comma 36 crossing the x–axis at negative 6 comma 0 and 6 comma 0. in the distance, an airplane is taking off. as it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points. create a table of at least four values for the function that includes two points of intersection between the airplane and the rainbow. analyze the two functions. answer the following reflection questions in complete sentences. what is the domain and range of the rainbow? explain what the domain and range represent. do all of the values make sense in this situation? why or why not? what are the x- and y-intercepts of the rainbow? explain what each intercept represents. is the linear function you created with your table positive or negative? explain. what are the solutions or solution to the system of equations created? explain what it or they represent. create your own piecewise function with at least two functions. explain, using complete sentences, the steps for graphing the function. graph the function by hand or using a graphing software of your choice (remember to submit the graph).

If 5x - 2 = -12, then x = a) -50 b) -4.4 c) -2.8 d) -2