An unknown metal has been found and the following experimental results have been tabulated in the table below. The table contains the grams of the unknown metal and the volume in milliliters of water displacement. Find a linear model that express volume as a function of the mass. Round your answers to 3 decimal places Volume in ml grams 19 171.6 20.5 186.9 22 194.7 23.5 214.3 25 223.5 26.5 236.9 28 247.8

It takes a force of 21,882 lb to compress a coil spring assembly from its free height of 6 inches to its fully compressed height of 3 inches. a. What is the assembly's force constant? b. How much work does it take to compress the assembly the first half inch? the second half inch? Answer to the nearest in-lb. a. k= lb/in

An object is dropped straight down from a helicopter. The object falls faster and faster but its acceleration (rate of change of its velocity) decreases over time because of air resistance. The acceleration is measured in ft/sec² and recorded every second after the drop for 5 sec, as shown. Find the following estimates. to 1 2 3 4 5 a 32.00 19.41 11.77 7.14 4.33 2.63 a. Find an upper estimate for the speed when t = 5. ft/sec b. Find a lower estimate for the speed when t = 5. ft/sec c. Find an upper estimate for the distance fallen when t = 3. ft

Water is flowing into a tub for washing clothes. The table shows the rate at which the water flows, in gallons per minute. The tub initially had five gallons of water in it before the faucet was turned on. t, in minutes 0 0.5 1 1.5 2 2.5 3 3.5 Flow rate, in 0.5 1 1.2 1.4 1.7 2 gal/min 2.1 3 Use the information in this problem to determine the amount of water in the tub after the first 3 minutes have passed. a) Calculate the amount of water in the tub using left approximating rectangles. b) Calculate the amount of water in the tub using right approximating rectangles. c) Use the two answers above to determine the most accurate answer you can.