A tank that contains 20 gal of water in which 3 kg of salt has been dissolved completely is to be filled by a hose with water carrying 0.25 kg/gal of salt at a rate of 4gal/min. The mixture is then stirred and the solution is being pumped out at the same rate. Find the function ofsalt in the tank at any given time.

Q: Assume that it costs that same company approximately C(x)=71,230++6,670x+0.03x^2 dollars to…

A: Given data-  C(x)=71,230+6,670x+0.03x^2. We have to find the average cost function= C¯(x).

Q: 2. A container that has 5 L of water with 1 kg salt dissolved is to be filled by pure water at a…

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A: Introduction: It is given that there are 12 bears per square mile of the park. Further, the number…

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A:

Q: If f and g are functions of time, and at time t = 3, f equals 8 and is rising at a rate of 3 units…

A: From the question we have  f(3)=8   and  dfdtt=3=3 i.e f'(3)=3 Similarly, g(3)=6   and  dfdtt=3=8…

Q: Let ff be the function given by f(x)=2x3−5x2+8x+1f(x)=2x3−5x2+8x+1 on the closed interval…

A: According to question, Given function, fx = 2 x3 -5x2 + 8 x + 1

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Q: The number N of cars produced at a certain factory in 1 day after t hours of operation is given by…

A: Given problem:- The number N of cars produced at a certain factory in 1 day after t hours of…

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A:

Q: If f and g are functions of time, and at time t = 2, f equals 3 and is rising at a rate of 5 units…

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Q: It is estimated that between the hours of noon and 7:00pm, the speed of highway traffic past a…

A: Check S(t) for all values of t

Q: in an intramural basketball league for men, the gas 12-rizal has won 12 out of 25 games. express a…

A: they want to win 3 game in a row to meet 60% detailed solution with explanation is given below

Q: Let L(x) be the linearization of the cube root function at x=8. When using L(x) to approximate the…

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Q: If f and g are functions of time, and at time t = 2, f equals 2 and is rising at a rate of 3 units…

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Q: A stock analyst plots the price per share of a certain common stock as a function of time and finds…

A: Given, Stock price as a function of time S(t) = 40+9e-0.03t We have to find the average price of…

Q: As machines get older, the cost of maintaining them tends to increase. Suppose for a particular…

A: Answer to the subparts are given ,

Q: The Cobb-Douglas production function for an automobile manufacturer is f(x, y) = 100x0.6,0.4, where…

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Q: Calculate the average rate of change of the given function over the interval [2, 6] f (x) = x² - 9 O…

A: Given function

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A: The general solution of a differential equation always contains a constant of integration. The…

Q: A major car company analyzes its revenue, Ríz), and costs Cx), in millions of dollars over a…

A: The revenue function and the cost function is given as:…

Q: Find the function whose tangent line has the slope 3x² + 1 for each value of x and whose graph…

A: We have to find the function whose tangent line has the slope 3x2+1 for each value of x and whose…

Q: Suppose that a liquid carries a drug with concentration 0.1 g/cc into a 400-cc organ at a rate of 5…

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Q: 11. Show that if positive functions f(x) and g(x) grow at the same rate as x→∞, then f = 0(g) and g…

A:

Q: An articlet in The New York Times states, "The number of gas stations [in a city] grows only in…

A: We will use the given relation between population and gas station.

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Q: A certain radioactive substance has a half-life of 22 days. As a sample of the radioactive substance…

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Q: Given the function h(x)=−x2−9x+26h(x)=−x2−9x+26, determine the average rate of change of the…

A: Given: The function is  h(x)=-x2-9x+26,     -6≤x≤-1   To determine: The average rate of change of…

Q: If x is large, which function grows faster, f(x) = 2x or g(x) = x2 ?

A: Given,            fx=2x or gx=x2To find : if x is large, then which function grows faster.

Q: If f and g are functions of time, and at time t = 2, f equals 2 and is rising at a rate of 3 units…

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Q: As machines get older, the cost of maintaining them tends to increase. Suppose for a particular…

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Q: If an object moves along a line so that it is at y=f(x)=3x2−2x at time x​ (in seconds), find the…

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Q: The total number of units produced by a worker in t hours of a 10 hour shift can be modeled by the…

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Q: f and g are functions of time, and at time t = 3, f equals 9 and is rising at a rate of 2 units per…

A: It is application of derivative.

Q: As machines get older, the cost of maintaining them tends to increase. Suppose for a particular…

A: We get the answer using integrating.

Q: A mouse wheel is 16 cm im diameter and the base of the wheel is 2 cm off i ground. If the hamster…

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Q: There is a bacteria cell in a Petri dish that is reproducing at a rate of              r(t) = 2t^2+1…

A: Solution:

Q: A manufacture has been selling 1850 television sets a week at $390 each. A market survey indicates…

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Q: In a certain state, the sales tax T on the amount of taxable goods is 5% of the value of the goods…

A: here T is taxable  value on purchase  x is purchase value and T = 5% given  further calculation…

Q: The average number of email messages sent and received per corporate user per day in a year day in…

A: (a) The function giving the projected average number of legitimate (non spam) emails sent and…

Q: Let L(x) be the linearization of the cube root function at x=64. When using L(x) to approximate the…

A: The linearization L(x) for tge function f(x) at x =a is given as L(x) = f'(a) (x-a) + f(a)

Q: The size P of a small herbivore population at time t​ (in years) obeys the function P(t)=700e0.24t…

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Q: The size P of a small herbivore population at time t​ (in years) obeys the function P(t)=1000e0.2t…

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Q: The demand for nurses in the US between 2000 and 2015 is estimated to be: D(t) = 0.7t2 + 0.265t +…

A: Derivative indicates the rate of change. Positive derivative meaning positive slope, which indicate…

Q: If f and g are functions of time, and at time t = 3, f equals 9 and is rising at a rate of 4 units…

A: Given,            If f and g are functions of time. At t = 3 , f equals to 9 and is rising at rate…

Q: Express the area A of a right triangle as a function of the height h if the base of the triangle is…

A:

Q: From a 12-cm by 12-cm piece of cardboard, square comers are cut out so that the sides can be folded…

A: Given:  From a 12‐cm by 12‐cm piece of cardboard, square corners are cut out so that the sides can…