Amass that weighs 8 lb stretches a spring 24 in. the system is acted on by an external force of 4sin(4t). if the mass is pulled down 6 in and then released, determine the position of the mass at any time t. assume that the u-axis is directed downwards and g = 32 ft/s^2. express your answer in as a linear combination of sin at and cos at. u(t) = where u is in feet and t is in seconds. determine the first four times at which the velocity of the mass is zero. exclude t = 0 as trivial. first zero: t =

On new year's day, the average temperature of a city is 5.7 degrees celsius. but for new year's day 2012, the temperature was 9.8 degrees below the average. i) if a represents the average temperature on new year's day and 7 represents the temperature on new year's day 2012, what formula accurately relates the two values together? ii) what was the temperature on new year's day 2012? dt a 0.8 ii) - 4 1 degrees celsius da-t-98 ii) 59 degrees celsius 1) 7 = -9,8 11) 59 degrees celsius ii) l degrees celsius

Astore has clearance items that have been marked down by 60%. they are having a sale, advertising an additional 55% off clearance items. what percent of the original price do you end up paying?

Factor the polynomial 4x4 – 20x2 – 3x2 + 15 by grouping. what is the resulting expression? (4x2 + 3)(x2 – 5) (4x2 – 3)(x2 – 5) (4x2 – 5)(x2 + 3) (4x2 + 5)(x2 – 3)