Find the rate of change of total profit, in dollars, with respect to time where R(x) = 90x – 0.5æ2 and - dæ = 50x + 6, when x = 17 and dt C(x) = 20.

Q: 7x ar Find the rate of change of total profit, in dollars, with respect to time where R(x) dx C(x) =…

A: Given that: R(x)=7xC(x)=0.06x2+0.6x+80

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

A: Given,

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Q: Find the supply function x = f(p) that satisfies the initial conditions. dx 10 x = 160 when p = $1…

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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: Cane sugar, when placed in water, converts to dextrose at a rate proportional to the amount of…

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Q: Let the rate of growth dN/dt of a colony of bacteria be proportional to the square root of the…

A: Let N(t) denotes the number bacteria present at time t. Use the proportionality constant k, to get…

Q: |The projected rate of increase in enrollment at Newhampton College is estimated |by dE 5000(t +…

A: Isolate the variables E and t in the given differential equation. dEdt=5000t+1-32dE=5000t+1-32dt

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: Given that x and y are functions of time, find the indicated rate of change dx/dt, when x = 2, y =…

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Q: . The derivative of y = xe + e" is D. ex А. хе В. хе + е^ С. exе-1 + е‑

A: Given: y=xe+eπ

Q: Find dy/dt when x=4 and dx/dt=-3, given that x^3+y^3=72

A: First obtain the derivative of the given equation as follows.

Q: Consider the function f(x, y) = y³ – 2y – x². Find the direc- tion of greatest increase at the point…

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Q: In some chemical reactions, the rate at which the amount of a substance changes with time is…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: A company estimates that its revenue grows continuously at a rate given by R'(t)= 2e^2t, where t is…

A: By Using simple integration

Q: dx 2. the rate at which the total average number of COVID cases is increasing at x = 10 tents and =…

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

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Q: Find the present value P of a continuous income flow of c(t) dollars per year using c(t)e-rt dt, J-…

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Q: Given that x and y are functions of time, find the indicated rate of change. dx when x 6, y = 3, and…

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Q: Given that x and y are functions of time, find the indicated rate of change. dy when x 2 and dt dx…

A: Compute the value of y as follows.Substitute x = 2 in x3 + y3 = 16.

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

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Q: Find the equation of the line tangent to xe^1−x at x = 1 and x/e * ln x at x=e.

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Q: A moving object has a constant acceleration of -9.8 meters per square second. If its initial…

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Q: When a company produces and sells x thousand units per week, its total weekly profit is P thousand…

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Q: d) Prove that the rate of growth, dt is given by NP (500 N) %3D dt 4000

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Q: You are a process control engineer in a water purification plant. In a certain subprocess, water…

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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: |The projected rate of increase in enrollment at Newhampton College is estimated by dE 5000(t +…

A: Given, The projected rate of increase the enrollment student at Newhampton college is estimated by…

Q: The combined electrical resistance R of two resistors R1 and R2, connected in parallel, is given by…

A: Consider the following equation: 1R=1R1+1R21R=R1+R2R1·R2R=R1·R2R1+R2 Differentiate the above…

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: Find the rate of change of total revenue, cost, and profit with respect to time. Assume that R(x)…

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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: 1 What is the instantaneous rate of change of Y at x = 2? O -1 none of these -1 1 3 4

A: Given : y = 1/x

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: 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: An oil storage tank ruptures at time t =0 and oil leaksfrom the tank at a rate of r(t)  = 100e-0.01t…

A: Given: Oil leaks from the tank at the rate r(t)= 100e-0.01t liters per minute. we have to find how…

Q: 18. Estimate the instantancous rate of change of the function f(x) = x' +4x - 11x-30 at x = 1. Round…

A: Given,  f(x)=x3+4x2-11x-30, x=1

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

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Q: A 200-gal tank is half full of distilled water.At time t = 0, a solution containing 0.5 lb / gal of…

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

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

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Q: Given that x and y are functions of time, find the indicated rate of change. iON dx dy = 2, given…

A: Consider the given equation

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

A: Given that, dndt=6t+1 where t is the number of years, 0≤t≤15

Q: If oil leaks from a tank at a rate of  r(t) gallons per minute attime t , what does ∫0120 r(t) dt…

A: Oil leaks from a tank at a rate of  r(t) gallons per minute at time t.

Q: Suppose both x and y are functions of time (t). Find the rate of change of y with respect to t, that…

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Q: Find the rate of change of total revenue, cost, and profit with respect to time. Assume that R(x)…

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Q: If f(x) = 5x -3 , compute the instontoneus rate of change of Sx) at x-2. OA -3/49 O8.7/41 oc-7/41…

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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…