At time t = 0, a tank contains 100 liters of water. The piecewise - linear graph below shows the rate R(t), in liters per minute, at which water is being pumped into the tank during a 55 minute period. R() (20, 30) (35, 30) 30- 20- 10 (0, 10) (55, 0) 0+ 10 20 30 40 50 Time (minutes) a). How many liters of water have been pumped into the tank from time t =0 to time t = 55 minutes? Show the work that leads to your answer. (sin t) b). At time t = 10 minutes, water begins draining from the tank at a rate modeled by the function D, where D (t) = 10e 10 liters per minute. Water continues to drain at this rate until time t = 55 minutes. How many liters of water have drained from the tank from time t =0 to time t = 55 minutes? Set up a definite integral to represent this situation, and use a graphing calculator/desmos to evaluate the definite integral. Round or truncate answer to 3 decimal places. c). How many liters of water in the tank at time t = 55 minutes? Show the work that leads to your answer. Round or truncate answer to 3 decimal places. d). Using the functions R and D, determine whether the amount of water in the tank is increasing or decreasing at time t = 45 minutes. Justify your answer. Rate (liters per minute)

Q: For males born in a certain country in the year 1991, their life expectancy was 66.4 years. For…

A: We have to solve the given problem by given data.

Q: The life expectancy E of a main-sequence star depends on its mass M. The relation is given by the…

A: Given formula for the life expectancy E in terms of mass M is  E = M^(-2.5) Here, the value E = 1…

Q: The predator satiation model for population growth specifies that the reproductive rate of an…

A:

Q: In 1994, the moose population in a park was measured to be 3500. By 1999, the population was…

A:

Q: Life expectancy is the key metric for assessing population health. The following graph shows the…

A: Given, U(t) represents the life expectancy in the united states and A(t) represents the life…

Q: The life expectancy E of a main-sequence star depends on its mass M. The relation is given by the…

A: Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: A population of fish is modeled by the equation dP/dt = .00016P(1300-P)+20 with an initial…

A: Roots of quadratic equation Plotting of graph of Quadratic equation with the help of roots. Basic…

Q: he projected world population (in billions of people) t years after 2000 is modeled by the function…

A: To find: The value of r if the expected population for the year 2012 is 7 billion. Given: The…

Q: To create a saline solution, salt water with a concentration of 40 g/L is added at a rate of 500…

A:

Q: The crime rate of a certain city is increasing according to the function A = 350e02t, where t is the…

A: We have to find the number of crimes in year 2001 and 2033.

Q: A runner's speed is given by the function s(h)=2h and the associated time is given by the function…

A: Given:- Runner' speed sh=2h Time th=34h Let dh represents distance of runner travel

Q: t .. Find the speed at time to = 3. t+ 2 An object moves along a coordinate line, its position at…

A:

Q: The marriage rate in a certain country in 1990 was 0.95%, and there were about 351,000 marriages…

A: 1990 corresponds to t=0 So, M0= 351000 And r= 0.95% = 0.0095 So the model is:

Q: Let f(x) be the height of a maple tree in inches and x the number of years since 2000. A linear…

A: Given that Equation is f(x) =9.44x + 84.182

Q: Ohm’s law says that the current, I, (in amps) obeys the formula I =V/R where V represents the…

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.