Suppose a spring with spring constant 5 n/m is horizontal and has one end attached to a wall and the other end attached to a 4 kg mass. suppose that the friction of the mass with the floor (i. e., the damping constant) is 1 n⋅s/m. set up a differential equation that describes this system. let x to denote the displacement, in meters, of the mass from its equilibrium position, and give your answer in terms of x, x′,x′′. assume that positive displacement means the mass is farther from the wall than when the system is at equilibrium. (equations) find the general solution to your differential equation from the previous part. use c1 and c2 to denote arbitrary constants. use t for independent variable to represent the time elapsed in seconds. enter c1 as c1 and c2 as c2. your answer should be an equation of the form x=…. (equations) is this system under damped, over damped, or critically damped? enter a value for the damping constant that would make the system critically damped. n⋅s/m (numbers)

The table shows population statistics for the ages of best actor and best supporting actor winners at an awards ceremony. the distributions of the ages are approximately bell-shaped. compare the z-scores for the actors in the following situation. best actor best supporting actor muequals42.0 muequals49.0 sigmaequals7.3 sigmaequals15 in a particular year, the best actor was 59 years old and the best supporting actor was 45 years old. determine the z-scores for each. best actor: z equals best supporting actor: z equals (round to two decimal places as needed.) interpret the z-scores. the best actor was (more than 2 standard deviations above more than 1 standard deviation above less than 1 standard deviation above less than 2 standard deviations below) the mean, which (is not, is) unusual. the best supporting actor was (less than 1 standard deviation below more than 1 standard deviation above more than 2 standard deviations below more than 1 standard deviation below) the mean, which (is is not) unusual.

Divide. write in simplest form 41/6 divided by 10

Daniel expanded the expression as shown below -2(-8x-4y+3/4)=-10x-8y-11/4 what errors did he make? check all that apply