Use the Newton forward difference formula to construct interpolating polynomials of degree three for the following data. Approximate f(–0.3) f(-0.75) = -0.0718, f(-0.5) = -0.0247, f(-0.25) = 0.3349, f(0) = 1.1010

The rate of change of an autocatalytic chemical reaction is kQxkx2 where Q is the amount of the original substance, x is the amount of substance formed, and k is a constant of proportionality. Factor the expression.

On a certain winter day, the temperature of a northern city from 6 a.m. to 6 p.m. can be modeled by the function T(x) = -0.3x² - 8.6x - 2.3 where T(x) is the temperature (in degrees Celsius) and x is the number of hours after 6 a.m. Which of the following expressions would give the average temperature of the city between 8 a.m. (x = 2) and 3 p.m. (x = 9)? 9 (-0.12³ (-0.1x³-4.3x² - 2.3x) dx 9 © ¦ / (-0.12³ 4.3x² - 2.3x) dx 9 (-0.3x² -8.6x - 2.3) dr (-0.3x² -8.6x - 2.3) de

The function​ A(s) given by ​A(s)=0.245s+51 can be used to estimate the average age of employees of a company in the years 1981 to 2009. Let​ A(s) be the average age of an​ employee, and s be the number of years since​ 1981; that​ is, s=0 for 1981 and s=9 for 1990. What was the average age of the employees in 2003 and in​ 2009?

Which is larger, f(0) or g(0)?

Plot the functions x, x2, exp(-x), exp(-x2) on a single graph for x between 0 and 5. Repeat the previous question where you plot the function on four different graphs (two rows and two columns).