Suppose that a steel company views the production of its continuous caster as a continuous income stream with a monthly rate of flow at time t given by f(t) = 36,000e°. 0.06t (dollars per month). ind the function that gives the total income T from 0 to t months. (t) = ind the total income from this caster in the first year. (Round your answer to the nearest dollar.)

Q: If the position function of a moving object is S(t) =t - 3t + 2 meters from zero in t seconds, then…

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Q: The size P of a small herbivore population at time t (in years) obeys the function  P(t)e^0.28t if…

A: The size P of a small herbivore population at time t (in years) obeys the function When P(t)=4000…

Q: Suppose that f(t) = 3t + 2 – 12t. а. What is the average rate of change of f (t) over the interval 2…

A: We are given the function f(t) = 3t+2-12t => f(t) = 2-9t. For (a), The average rate of change of…

Q: Suppose a stone is dropped from a height of 100 ft. Its position at time t is s(t) =-6r +100. Find…

A: To find the time t when instantaneous velocity equal to its average velocity.

Q: Suppose that a steel company views the production of its continuous caster as a continuous income…

A: Given the income function as, ft=24,000e0.05t.

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A: Given, P'(t) = 1 + 5t+1 when t = 120 hours  then P(t) = 250  Thenm  when t = 0 hours then P(t) = ?

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: A rocket will carry a communications satellite into low Earth orbit. Suppose that the thrust during…

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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-…

A:

Q: Suppose that a steel company views the production of its continuous caster as a continuous income…

A: Given that a steel company views the production of its continuous caster as a continuous income…

Q: Given the following function, determine the maximum rate of change of it at the point P(0,0, 1/2).…

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Q: Find the amount of medicine to which the body is most sensitive by finding the value of M that…

A: Given

Q: A. If r = r(t) represents the position function at time t of a certain particle, then what do you…

A: first derivative of position gives- velocity

Q: If a ball is thrown in the air with a velocity 48 ft/s, its height in feet t seconds later is given…

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Q: The value of the instantaneous velocity at t = 1 is

A: Consider the position function To calculate the instantaneous velocity

Q: Suppose the function p(t)=(t^2 - 2)e^2t represents the position of a particle at time t. Determine…

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Q: A mining expert estimates that the production growth rate of copper overtime, or "/dt, is given by…

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Q: Q3 Given the following function, determine the maximum rate of change of it at the point P(0,0,…

A: For a three-dimensional function f(x,y,z), the maximum rate of change of the function at the point,…

Q: The pressure in P = 10T/V     of a gas in a cylinder is given by   with T in kelvins (K) and V…

A: Given as : P=10TV By differentiating it with respect to t: dPdt=10VdTdt-TdVdtV2 ......1 1). If T is…

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

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Q: Let r(t) be the rate at which the world’s oil is consumed,where is measured in years starting at t…

A: Given: Let r(t) be the rate at which the world’s oil is consumed,where is measured in years starting…

Q: The price of a particular crop per bushel at time t (in months) is approximated by f(t) = 3 +…

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Q: Find the present value P of a continuous income flow of c(t) dollars per year using where t1 is the…

A: Given, c(t)=100,000+4000, r=5%, t1=10 p=∫0t1c(t)e-rtdt Now plug the values of t1  and r…

Q: The rate of flow of a continuous income stream (in thousands of dollars per day) is given by f(t) =…

A: the total income produced during the first thirty days of operation -  The rate of flow of a…

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…

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Q: Let F(s) = 5s² + 2s + 4. Find a value of d greater than 0 such that the average rate of change of…

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Q: A small brewery considers the output of its bottling machine as a continuous income stream with an…

A: According to the total income of Continuous Income Stream: If the rate of receipt of revenue is ft…

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Q: A particle moves along a straight line and has acceleration given by s"(t) = 5t +3- Its initial…

A: Given,  s''(t)=5t+3, s'(0)=-4, s(0)=7

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: Which of the following is true about the net distance traveled by an object from time t = a to time…

A: Given,           The net distance traveled by an object from time t=a to time t=b where…

Q: A company that services a number of vending machines considers its income as a continuous stream…

A: Given,

Q: What limit must be calculated to find the rate of change of a function g(t) at t = t0?

A: The rate of change of a function g(t) at t = t0 is given by g'(t0).

Q: Suppose a stone is dropped from a height of 200 ft. Its position at time t is s(t) =-12r +200. Find…

A: To find the time t when instantaneous velocity equal to average velocity.

Q: A radioactive material went through a decaying process as given in the following function f(t): f(t)…

A: If the input variable t of a function changes, its output also changes. In this problem, the…

Q: Suppose that the rate at which the concentration of a drug in the blood changes with respect to time…

A: Given:The rate of change of concentration of a drug in blood with respect to time t is

Q: Suppose the position of an object moving in a straight line is given by the specified function. Find…

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Q: Find the maximum rate of change of f(s,t)=te^(st) at the point (0,−5).

A: We have to solve

Q: The rate of flow of a continuous income stream (in thousands of dollars per day) is given by f(t) =…

A:

Q: The pressure in P = 10T/V     of a gas in a cylinder is given by   with T in kelvins (K) and V…

A:

Q: Given the following function, determine the maximum rate of change of it at the point P(0,0, 1/2).…

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Q: If s(t) is the position on the x-axis of a particle at time t, then the quantitys(t + h)−s(t) / h…

A: If s(t) is the position on the x-axis of a particle at time t,

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

A: Given that the flow is maintained such that qi-q0>0 and their difference is the product of the…

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: The population of a city (in millions) at time t (in years) is P(t)=2.8e0.008t, where t=0 is the…

A: Given data:   The expression for the given population at any time t is: P(t)=2.8e0.008t.     The…

Q: A radioactive material went through a decaying process as given in the followin function f(t): f(t)…

A: Given  f(t)=5e^-at We need to sketch the decaying process and find Fourier transform

Q: - If a particle's position at a time t is given by f (t) = t³ + 1, i. Find its average velocity over…

A: f(t) = t3 + 1 i. Average velocity over the interval [-1,1] is given as

Q: If a ball is thrown into the air with a velocity of 44 ft/s, its height in feet t seconds later is…

A: Given data is: The ball is thrown in the air with a velocity of 44 ft/sec The height after t second…

Q: A particle moves along the x-axis so that at time t 0 its position is given by a(t) = -t + 4ť² – 4t.…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.