Water flows into a tank at a rate of r (t) = 140 – 7t liters per minute for 0

Q: Water is drained from a swimming pool at a rate given by |(-0.2)t R(t) = 100e' gallons per hour. If…

A: Solution : We have given the rate of water drain form a swimming pool is R(t) = 100e(-0.2)t…

Q: When a vertical beam of light passes through a transparent medium, the reason that its intensity I…

A: We have to find What is the beam intensity at 15 feet below the surface.

Q: We found that salt is added to the tank at a constant rate and it is removed from the tank at a rate…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: In a simple electric circuit, Ohm's law states that V IR, where V is the voltage in volts, I is the…

A: From the given problem: dVdt=-0.01 volts per second ; dRdt=0.03 ohms per secondR=300 ohms ; I=0.04…

Q: A particle moves along the curve y = x^(3/2) in the first quadrant in such a way that its distance…

A: Let (x,y) is a point on y = x^(3/2)Distance of (x,y) from (0,0) is given by:

Q: The temperature of a sample of a fluid that is being heated in a laboratory is given by h(t) = 30t −…

A: The rate of increase in temperature of a sample of a fluid is given by ht=30t-t2 degree Celsius,…

Q: When polluted water begins to flow into an unpolluted pond, the concentration of pollutant, c, in…

A:

Q: Find the average rate of change of f(x) = cos x from 0 to π /2 .

A: Given: fx=cosx  0,π2

Q: Estimate the instantaneous rate of change at the point indicated. f (x) = ex ; x = e

A: To find the instantaneous rate of change at indicated point:f(x)=ex;x=e. Solution: we know, the…

Q: (b) Find the instantaneous rate of change of g with respect to x at x = 3, or state that it does not…

A: 3. given graph of function is                                                       Also,…

Q: Ecologists estimate that, when the population of a certain city is x thousand persons, the average…

A: Solve for the value

Q: Determine the average rate of change of the function y = sinx from X = 0 to x = 2 O1 2

A: The average rate of change of the function f(x) can be calculated using the formula Average rate of…

Q: Alice measures a radioactive sample at 1400 counts/minute on a Geiger counter. If the radioactive…

A: Given: Initial value, R0=1400 counts/min Ending value, R = 1000 counts/min Time that has passed, t =…

Q: A culture initially has P number of bacteria. At t = 3hour the number of bacteria is measured to be…

A:

Q: Find the rate of change of the distance between the origin and a moving point on the graph of the…

A:

Q: A particle is traveling upward and to the right along the curve y = ln x. Its x-coordinate is…

A: Given a particle is travelling upward and to the right long the curve y=lnx. It is given that dxdt=x…

Q: The population of a town grows at a rate proportional to the population present at time t. The…

A: Y(t)=Population in year tY(0)=700Y(15)=700+20%700=700+140=840

Q: Given the function f(x) √x f(x) = COS 2 1 + √r dr Determine the instantaneous rate of change at x =…

A: Using Leibniz rule of derivative

Q: 3. Water is being poured into a 10 liter leaky container so that the volume of the water, V,…

A: A differential equation is an equation that contains functions and their derivatives.  A…

Q: Find the instantaneous rate of change of 7. y = (x + 1)*(x – 3) at a = 1.

A:

Q: a) The marginal profit for a product is modeled by dP -0.0002x + 14. 2 dx Apply the integration to…

A:

Q: A tank contains 10m^3 of free water, brine having a concentration of 15kgsalt/m^3 is sent into the…

A:

Q: 5. A termite population begins with 150 termites and increases at a rate of m'(t) termites per week.…

A: Termite population starts with 150 termites and increases with the rate of m'(t) termites per week

Q: A certain radioactive substance has a half-life of 38 hours. The rate of change in the decay is…

A: In this we are going to use decay formula so I'm providing hand written solution for this

Q: An evolved kind of green fungi is shrinking at an initial rate following f(t) = vVE + 5, where t is…

A:

Q: | Suppose that electricity is draining from a capacitor at a rate proportional to the voltage V…

A: The given differential equation is dVdt=-140V, where V is the voltage and t is the time in seconds.…

Q: Given the function f(x) = e-3x cos 3x, x = [0, 2π]. When is the rate of change of f(x) a maximum?

A: Here, the given function is: f(x)=e-3xcos(3x) Now, the rate of change is given by: f'(x)=e-3xddx(cos…

Q: 2. Find the instantaneous rate of change for y= arctan- at x = 3. 2 12 A. 85 2 В. 13 3n D. 4 С. О

A:

Q: The average rate of change of the function y = x² in the interval 2 sx< 5 is %3D

A:

Q: A honeybee population starts with 100 bees and increases at a rate of n' (t) bees per week. What…

A: Integral formula is ∫abf(x)dx=F(b)-F(a) ∫04n'(t)dt=n(4)-n(0) From the given integral…

Q: 4. A culture initially has No number of bacteria. After one hour the number of bacteria is measured…

A: We have to determine the time necessary for the number of bacteria to triple.

Q: What is the average rate of change of y = cos(2x) on the interval 0,? a. = b. -1 с. О d. 4 e.

A:

Q: Suppose that a company can produce 12,000 units when the number of hours of skilled labor y and…

A: The number of hours of skilled labor is y and unskilled labor is x.

Q: Under certain conditions, cane sugar in water is converted into dextrose at a rate proportional to…

A:

Q: Determine the instantaneous rate of change of the function y = 5x + 2x² 1 with respect to x at x-4.…

A: Find instantaneous rate of change

Q: Because of heavy rainfall, the water level in a reservoir is rising at a rate of g(t) feet per hour,…

A: Given problem :- Because of heavy rainfall, the water level in a reservoir is rising at a rate of…

Q: The population of a town grows at a rate proportional to the population present at time t. The…

A:

Q: g) For how long do we have to invest $1000 at a rate of 2.5% compounded continuously to obtain a…

A:

Q: The rate of increase in the number N of bacteria in a certain culture is given by dN = 0.15N where t…

A:

Q: A culture initially has P0 number of bacteria. At t=3 hour the number of bacteria is measured to be…

A:

Q: The half-life of a radioactive material whose rate of disintegration is proportional to the amount…

A: Given that, The half-life of a radioactive material whose rate of disintegration is proportional to…

Q: Suppose that a factory worker starts to make face masks at t = 0 and his rate of change of…

A:

Q: A new fast-food firm predicts that the number of franchises for its products will grow at the rate…

A: Given

Q: Let H(t) be the amount of raw honey at time t. During processing, the amount of raw honey present…

A: We have to use exponential decay function to solve the problem

Q: Show that an investment that pays out R dollars per year continuously for T years has a PV of R(1…

A:

Q: What is the rate of change of y = In x at x = 1 O?

A: Given: y=lnx at x=1

Q: Because of job outsourcing, a town predicts that its public school population will decrease at the…

A: .