| Suppose that electricity is draining from a capacitor at a rate proportional to the voltage V across its terminals and that, if t is measured in seconds, dV - -ly 40 dt How long will it take the voltage to drop to 20% of its original value?

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

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Q: Let B = 5 T as in Example 3. Estimate the instantaneous rate of change of B with respect to T when…

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Q: Suppose that a company can produce 12000 units when the number of hours of skilled labor y and…

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Q: The population ( in hundreds ) of fish in a pond is given by P(t) = 2t + sin(2t –10) t months from…

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Q: What is the closest value to the instantaneous rate of change of the following function at x = T?…

A: Ans:  Given  fx=2 cosx-π2  at  x=π          ⇒fx=2cosx coπ2+ sinπ2         ⇒fx=2cosx 0+sinx1…

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

A:

Q: if two resistors with resistances R1 and R2 are connected parallel, then the total Resistance R…

A: Given,

Q: The projected rate of increase in enrollment in a new college is estimated by dE/dt= ( at+1)^-1(…

A: Given the projected rate of increase in enrollment in a new college is dE/dt= ( at+1)^-1( a+1). We…

Q: dN The rate of the growth of species of bacteria is estimated by = 800 + et dt Where Nis the number…

A: Given function is form of differential equation. we will integrate this function to get the N(t).

Q: b. A thermistor is being used to measure temperature. For a given resistance Rthe temperature is…

A: The temperature, T for a resistance R is given by, T=1T0+1βlnRR0−1

Q: A particle that moves along a straight line has velocity v(t) = t'e-2t meters per second after t…

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Q: 3. If f (t) = -t + 5t + 3, describes the distance that a ball has traveled in meters, what is the…

A: We are allow to solve only one question at a time  Thank you for your question

Q: Find the rate of change of total profit, in dollars, with respect to time where R(x) = 4x and dx…

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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: Two students are calculating the instantaneous rate of change of y= sin(x) at x = Student A claims…

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Q: Consider and solve the initial value problem of a new form of life discovered on a distant planet.…

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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: The impedance Z (ohms) in aseries circuit is related to the resistance R (ohms) and reactanceX…

A: Given that The impedance Z (ohms) in a series circuit is related to the resistance R (ohms) and…

Q: If a baseball is thrown upward with a velocity of 45 m/s, its height in meters t seconds later is…

A: We know that, Average velocity          = change in position/time elapsed.

Q: Suppose x and y are functions of third variable t. In the equation *+y=45, what are the values of…

A: Given,   x2+y2=45To find dydt, when dxdt=-2 and x=3

Q: OP ) at t = 0?t = 2? t = 20? (Be dt 4. How fast is the amount of antibiotic changing (this means…

A: The given antibiotic function is Q=Ae-kt. Differentiate Q with respect to t. dQdt=ddtAe-kt=-Ake-kt…

Q: A forester finds that a certain type of forest tree grows in such a way that its height h(t) after t…

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Q: A population of E. coli bacteria will grow at a rate given byw′(t) = (3t + 2)1/3,where w is the…

A: Given: w't=3t+21/3

Q: Suppose a quantity described by the function y(t) = y0ekt, where t is measured in years, has a…

A: yt=y0ekt The quantity has a doubling time of 20 years. That is, yt=2y0 when t=20.

Q: (a) If A is the area of a circle with radius r and the circle expands as time passes, find in terms…

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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

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Q: A particle moves in a straight line and any time t seconds, its velocity v m/s is given dx by e-".…

A: Note that velocity is rate of change of displacement. Hence displacement will be integration of…

Q: Consider and solve the initial value problem of a new form of life discovered on a distant planet.…

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Q: A particle moves along a straight line and its position from a reference fixed point O is given by…

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

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

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

A: The number of franchises for its products will grow at the rate  dndt=4t+1 where t is the number of…

Q: 7. Find dy and hence determine the rate of change of y with respect to x for the following…

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Q: A NASA spacecraft measures the rate R of at which atmospheric pressure on Mars decreases with…

A: Unit Conversion Formula:

Q: If V(t) is the volume of water in a reservoir at time t (seconds), v(t) is the rate of change,  then…

A: Rate Change: Rate change is defined as the change in one quantity with respect to any other quantity…

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: What does r'(t)dt represent if r'(t) is the rate of growth of a dog in pounds for the t year?

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Q: (b) If n'(t) is the growth rate of a bee population in bees per week, what does n'(t)dt represent?

A: Given,n'(t)=growth rate of bee populationt=time in weeks

Q: The population ( in hundreds ) of fish in a pond is given by P(t) = 2t + sin(2t – 10) t months from…

A:

Q: Suppose h(t) = t² + 11t + 7. Find the instantaneous rate of change of h(t) with respect to t at t =…

A:

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Q: .................... ..................... A new fast-food firm predicts that the number of…

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Q: Estimate the instantaneous rate of change ot P(t) = 3t?+4 at the point t= -2,

A: NOTE: Refresh your page if you can't see any equations. . to find the instantaneous rate of change,…

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

A: Given

Q: Suppose x and y are functions of third variable t. In the equation x2+y2=45, what are the values of…

A:

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

A: Given: y=lnx at x=1

Q: Find a function f satis fying the equation | VF()dt = ælnæ.

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Q: Given the function f(x) = x which of the following is a valid formula for the instantaneous rate of…

A: The given function fx=x23 The instantaneous rate of change is given by limh→0fa+h-fah

Q: 1 - Find a formula for the rate of change dv/dt of the volume of a balloon being inflated such that…

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…