An engineering student is studying the effects of cryogenic treatments on a particular material. the treatment involves cooling the material with specific applications of liquid nitrogen. the temperature of the material in degrees celsius, y, can be modeled by the following graph, where x represents the time, in hours, since the treatment began. here are the answer choices: a.) the material's initial temperature is -30 degrees celsius. b,) the material's temperature reaches a maximum at 25 hours. c.) the material returned to its initial temperature after 40 hours. d.) the material's temperature reaches a minimum at 15 hours.

an advantage of the standard deviation is that it increases as the dispersion of the data increases. e. the interquartile range is preferred when the data are not skewed or no have outliers. an advantage of the standard deviation is that it uses all the observations in its computation.

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.