Mixture In Exercises 35-38, consider a tank that at time
Let Q be the amount of concentrate (in pounds) in the solution at any time t. Show that
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Calculus: Early Transcendental Functions (MindTap Course List)
- Projectile Motion In Exercises 75 and 76, consider the path of an object projected horizontally with a velocity of v feet per second at a height of s feet, where the model for the path is x2=v216ys. In this model (in which air resistance is disregarded), y is the height (in feet) of the projectile and x is the horizontal distance (in feet) the projectile travels. A ball is thrown from the top of a 100-foot tower with a velocity of 28 feet per second. (a) Write an equation for the parabolic path. (b) How far does the ball travel horizontally before it strikes the ground?arrow_forwardTemperature In Exercises 29 and 30, the figure shows the boundary temperatures in degree Celsius of an insulted thin metal plate. The steady-state temperature at an interior junction is approximately equal to the mean of the temperatures at the four surrounding junctions. Use a system of linear equations to approximate the interior temperatures T1,T2,T3, and T4.arrow_forwardGrazing Rabbits and Sheep This is a continuation of Exercise 21. In addition to the kangaroos, the major grazing mammals of Australia include merino sheep and rabbits. For sheep, the functional response is S=2.82.8e0.01V, and for rabbits, it is H=0.20.2e0.008V, Here S and H are the daily intake measured in pounds, and v is the vegetation biomass measured in pounds per acre. a. Find the satiation level for sheep and that for rabbits. b. One concern in the management of rangelands is whether the various species of grazing animals are forced to complete for food. It is thought that competition will not be a problem if the vegetation biomass level provides at least 90 of the satiation level for each species. What biomass level guarantees that competition between sheep and rabbits will not be problem?arrow_forward
- A typical glass of wine contains about 21 grams of alcohol. Consider a 96-pound woman with approximately 6 liters (6,000 mL) of blood drinks two glasses of wine. A. If all alcohol were IMMEDIATELY absorbed into her bloodstream. What would her blood alcohol content be? B. Again assume all alcohol is absorbed IMMEDIATELY, but now assume her body eliminates the alcohol (though metabolism) at a rate of 12 grams per hour. What is her blood alcohol content three hours after drinking the wine?arrow_forwardA tank contains 50 gallons of a solution composed of 90% water and 10% alcohol. A second solution containing 50% water and 50% alcohol is added to the tank at a rate of 4 gallons per minute. As the second solution is being added, the tank is being drained at a rate of 5 gallons per minute. The solution in the tank is stirred constantly. How much alcohol is in the tank after 10 minutes?arrow_forwardA large tank initially contains 500 litres of brine in which 5 kilograms of salt is dissolved. Starting at t=0, brine containing 0.06 kilograms of salt per litre flows into the tank at the rate of 2.5 litres per minute. The mixture is kept uniform by stirring and the well-stirred mixture leaves the tank at the rate of 2 litres per minute. • (a) Find the amount of salt c(t) in the tank after t minutes. • (b) How much salt is in the tank when the tank contains 1000 litres of brine?arrow_forward
- 6. A 50 gallons tank initially contains 10 gal of fresh water. At t = 0, a brine solution containing 1 lb of salt per gallon is poured into the tank at the rate of 4 gal/min, while the well-stirred mixture leaves the tank at the rate of 2 gal/min. Find a. the amount of time required for overflow to occur b. the amount of salt in the tank at the moment of overflowarrow_forwardSailing A sailboat is running along a straight course with thewind providing a constant forward force of 50 lb. The only otherforce acting on the boat is resistance as the boat moves throughthe water. The resisting force is numerically equal to five timesthe boat’s speed, and the initial velocity is 1 ft/sec. What is themaximum velocity in feet per second of the boat under this wind?arrow_forwardA tank has pure water flowing into It at 10 L/ min. The contents of the tank are kept thoroughly mixed, and the contents flow out at 10 L/ min. Initlally the tank contains 10 kg of salt in 100 L of water. How much salt will be there after 30 mins?arrow_forward
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