The birth rate of a population is b(t) = 2500e0.024t people per year and the death rate is d(t)= 1460e0.017 people per year, find the area between these curves for 0 S t s 10. (Round your answer to the nearest integer.) 11930 X people What does this area represent? This area represents the number of births over a 10-year period. This area represent the number of children through high school over a 10-year period. This area represents the increase in population over a 10-year period. This area represents the number of deaths over a 10-year period. This area represents the decrease in population over a 10-year period. Need Help? Read It 4. [3/4 Points] DETAILS PREVIOUS ANSWERS SESSCALC2 7.6.011. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A cable that weighs 6 Ib/ft is used to lift 750 lb of coal up a mine shaft 700 ft deep. Find the work done. Show how to approximate the required work by a Riemann sum. (Let x be the distance in feet below the top of the shaft. Enter xi* as xi.) lim 750 + 6(xi) Ax 7-90 =1 X Express the work as an integral and evaluate. 700 750 + 6x dx = 1995000 ft - lb Need Help? Read It 6. [0/2 Points] DETAILS PREVIOUS ANSWERS SESSCALC2 7.6.018. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the following figure. (a) The tank shown is full of water. Given that the water has a density of 1000 kg/ms, find the work required to pump the water out of the spout. (Assume r = 6 m and h = 2 m. Use 9.8 m/s2 for g.) 35900000 X (b) What if the tank is half full of oil that has a density of 900 kg/m3? Need Help? Read It Submit Answer 7. [0/1 Points] DETAILS PREVIOUS ANSWERS SESSCALC2 7.6.020.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER When gas expands in a cylinder with radius r, the pressure P at any given time is a function of the volume V: P = P(V). The force exerted by the gas on the piston (see the figure) is the product of the pressure and the area: F = mr2P. The work done by the gas when the volume expands from volume V1 to volume V2 is W = P av . In a steam engine the pressure and volume of steam satisfy the equation PV1.4 = k, where k is a constant. (This is true for adiabatic expansion, that is, expansion in which there is no heat transfer between the cylinder and its surroundings.) Calculate the work done by the engine during a cycle when the steam starts at a pressure of 140 lb/in and a volume of 100 in and expands to a volume of 600 in. (Round your answer to two decimal places.) W = 1333.52 x ft-lb