Suppose your professor handed you a test tube with 3 ml of an e. coli culture in it and told you to make a 10-3 dilution of the entire culture volume with water. what would your final volume (v2) of the dilution need to be in order to get this dilution? hints: use v1d1 =v2d2 and remember to use the d1 of a stock (undiluted sample)

Industrial processes often require the damping of vibrations. consider a workbench that uses four large ideal springs in place of traditional legs, with each spring supporting one corner of the workbench and exhibiting a force constant of 47500 n/m. this workbench is used when creating products that involve highly unstable chemicals. according to specifications, the acceleration of the manufacturing equipment must be held to less than 22.3 m/s2 for the manufacturing process to proceed safely. the amplitude of vibrations are expected to remain under 0.622 mm throughout. given that the workbench and maufacturing equipment combine to 6.05 kg, find the maximum acceleration expected of the equipment and workbench. (ignore the mass of the springs.)