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- A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the time read exactly 3:40 p.m. At this time, he started pumping gas into the tank. At exactly 3:44, the tank was full and he noticed that he had pumped 10.7 gallons. What is the average rate of flow of the gasoline into the gas tank?Van der Waals Equation In Exercise 18 at the end of Section 2.3, we discussed the ideal gas law, which shows the relationship among volume V, pressure p, and temperature T for a fixed amount 1 mole of a gas. But chemists believe that in many situations, the van der Waals equation gives more accurate results. If we measure temperature T in kelvins, volume V in liters, and pressure p in atmosphere 1 atm is the pressure exerted by the atmosphere at sea level, then the relationship for carbon dioxide is given by p=0.082TV0.0433.592V2atm What volume does this equation predict for 1 mole of carbon dioxide at 500 kelvins and 100 atm?Suggestion: Consider volumes ranging from 0.1 to 1 liter.A 400-gal capacity tank contains 200 gallons of water. Brine solution containing 4 pounds per gallon is fed to the tank at a rate of 4 gallons per minute. The well-mixed solution leaves the tank at 2 gallons per minute. Calculate the amount and concentration of salt in the tank after 75 minutes, the time for the tank to overflow, the amount and concentration of salt in the tank after 120 minutes.
- Water flows from a storage tank at a rate of 900 − 7t liters per minute. Find the amount of water that flows out of the tank during the first 17 minutes. ____ LThe average cost per unit, y, of producing x units of a product is modeled by y= 750,000 + 0.55x /x. Describe the company's production level so that the average cost of producing each unit does not exceed $ 8.05Solve using differential equation A certain chemical dissolves in water at a rate proportional to the product of the amount undissoved and the difference between the concentration in a saturated solution and the concentration in the actual solution. In 100 grams of a saturated solution, it is known that 50 g of the substance are dissolved. If when 30 g of the chemical are agitated with 100 g of water, 10 g are dissolved in 2 hrs, how much will be dissolved in 5 hrs?
- BASIC INTEGRATION ∫(-8/∜x + 15/(∛x - 1/x^3 )dxUsing differentials, solve for the approximate change in the hypotenuse of a right triangle if the lengths of its legs change from 8 meters and 15 meters to 8.1 meters and 14.75 meters, respectively. Express your answers in four (4) decimal places.INTEGRATION TECHNIQUES: solve
- Draining a tank Water is drained from a 3000-gal tank at a rate that starts at 100 gal/hr and decreases continuously by 5%/hr. If the drain is left open indefinitely, how much water drains from the tank? Can a full tank be emptied at this rate?Using differentials, solve for the approximate change in the hypotenuse of a right triangle if the lengths of its legs change from 8 meters and 15 meters to 8.1 meters and 14.75 meters, respectively. Express your answer in 4 decimal places. Hint: Set up the equation of the hypotenuse in terms of its legs.Solve with Differential Equation A tank contains 400 liters of brine. Brine containing 0.1 kg/liter of salt flows in at 8 liters/minute, and the mixture kept uniform by stirring, flows out at the rate of 12 liters/minute. If the concentration of the salt is 0.096 kg/liter at the end of 60 – minutes, how much was the initial concentration of the brine in the tank?