for S(x)=200((2x+1)/(3x+4))^0.5 Find the rate at which the S changes with respect to x

Q: A 13ft ladder rests against a vertical wall. If the bottom of the ladder is sliding away from the…

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Q: 2. Find the average rate of change of g (x) =x*-3x¯+2x from x=1 to x=3.

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Q: A breeder reactor converts relatively stable uranium 238 into the isotope plu- tonium 239. After 15…

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Q: second. At what rate x changing when x = . O-16 O 16 8 O-8 in such way that the y-value increases at…

A: The given equation is;  y=x3-2x2+x-1.

Q: A tank initially contains 200 L of fresh water. Brine containing 2.5 N/L of dissolved salt runs into…

A: Let "s" represents the quantity of salt in the tank. dSdt=(8×2.5)-8S200dSdt+0.04S=20   and S(0)=0…

Q: What is the average rate of change of this function between x=2 to x=10 based of the graph of a…

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Q: A potter forms a piece of clay into a cylinder. As he rolls it, the length, L, of the cylinder…

A: Differentiate volume wrt t

Q: A woman 1.5 m tall walks directly away from a street light which is 6 m above the ground at a rate…

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Q: Find the average rate of change for each function over the given interval: y = ln x between x = 2…

A: Given: The function is y=lnx. Formula used: The average rate of change can be calculated as,…

Q: A bacteria culture starts with 4 bacteria and grows at a rate proportional to its size. After 2…

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Q: A rectangle is growing in such a way that when its length is 5 ft and its width is 2 ft, the length…

A: When length is:= 5 ft; When width is:= 2 ft; Rate of increasing length= 3 ft/s; Rate of increasing…

Q: What is the rate of change of y = In x at x = 10?

A: Explanation: Given that,  y=lnx   Concept Used: To find the rate of change we will find the…

Q: In monitoring the blood alcohol content of a person, the bloodstream, which is composed of 5L of…

A: We will formed a differential equation and then solve it to get amount of blood

Q: Find the antiderivative of antiderivative of x2(ln(10x))2

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Q: s projected that x years from now the population of a certain city will be changing at the rate of…

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Q: If the total revenue function for a blender is R(x) = 41x – 0.01x² where x is the number of units…

A: Given that, the revenue R (in dollars) for a blender is given by  R(x) = 41x - 0.01x2 where x is the…

Q: Suppose that $15,000 is invested and at the end of 3 yr, the value of the account is $19,356.92. Use…

A: Given :            $15,000 is invested and at the end of 3 yr, the value of the account is…

Q: A certain radioactive material is known to decay at a rate proportional to the present amount. If…

A:

Q: What are three methods that can be used to estimate the instantaneous rate of change in g(x) at x =…

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

A: Given that,  At time, t=0, the amount of cane sugar in water =75kg At time, t=30minutes, the amount…

Q: nown to grow at a rate proportional

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Q: A storage battery discharge at a rate which is proportional to the charge. If the charger is reduced…

A: Solve by making equation

Q: A square with side x, is changing with time where x(t) =3t + 1. What is the formula for the rate of…

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Q: 7. The top of a ladder slides down a vertical wall at a rate of 0.15 m/s. At the moment when the…

A: Given data A ladder slides a vertical wall at rate of 0.15 m/s  find the length of ladder = ?

Q: The population of bacteria in a culture grows at a rate proportional to the number of bacteria…

A:

Q: A perfectly spherical balloon is losing volume at a rate of 3 in3 per sec. How fast is the balloon’s…

A:

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

A: Given: when the initial time t=0 amount of the cane sugar is 75 kg, and the time t=30 minutes amount…

Q: The area of a rectangle remains 30 cm2. One side of the rectangle is expanding at a rate of 1 cm/s.…

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Q: A certain population of microorganisms grows at a rate proportional to the amount present under a…

A: Given that, A certain population of microorganisms grows at a rate proportional to the amount…

Q: Find the average rate of change for the function over the given interval.  y= square root of 2x…

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Q: The radius of the base of a cylinder is increasing at a rate of 1 m/h and the height of the cylinder…

A: Given,         The radius of the base of a cylinder is increasing at a rate of 1 m/h and the height…

Q: A mold grows at a rate proportional to its present size. If the original amount doubles in one day,…

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Q: Find the rate of change of x with respect to p. 500 – X 0 < x < 500 8x

A:

Q: 1. For a certain radioactive element decays at a rate of 37.7% per day (tis measured in days). How…

A: We need to find time.

Q: A tank initially contains 100 L of a well-mixed water-and-salt solution, with salt concentration of…

A: As the solution well mixed water and solution solution and flowing out with the constant rate of 2 L…

Q: A certain radioactive material is known to decay at a rate proportional to the amount present.…

A: Given a certain radioactive material is known to decay at a rate proportional to the amount present.…

Q: A colony of bacteria with originally 100 cells has now grown to 900 in 2 hours. Assuming the rate of…

A:

Q: The length of a rectangle is decreasing at the rate of 5 cm/s and its width is increasing at the…

A: Area of a rectangle = length× width Rate of change with respect to time is D/Dt

Q: estimate the instantaneous rate of change at the point indicated.f (x) = ln x; x = 3

A: To find the instantaneous rate of change at x=3 we need f'(3) We find f'(x)

Q: There's a tank containing 50 L of a solution into which 10 g of salt is dissolved in. A solution…

A: image is attached

Q: Find the instantaneous rate of change of g(x)=(x^3-sqrt(x))e^x+(x^5-2x+3)ln(x) when x=3. Round to…

A: The instantaneous rate of change of g(x) is:…

Q: The length of a rectangle is increasing at a rate of 2 ft/s, and its width is increasing at a rate…

A: Here we have, The length of a rectangle is increasing at a rate of 2 ft/s, and its width is…

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

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Q: An apple pie with an initial temperature of 170 -C is removed from the oven and left to cool in a…

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Q: If f(x) = 12x2 − x3, what is the rate of change of f '(x) at  (−1, 13)?

A:

Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A: In mathematics, two varying quantities are said to be in a relation of proportionality,…

Q: A tank contains 200 liters of fresh water. Brine containing 2.5 N/L of dissolved salt runs into the…

A:

Q: If the rate of change of y with respect to x is equals to 2-y and y=8 and x=0. Find y when x=ln(2).

A: Given: The rate of change of y with respect to x  is equal to 2-y. That is, dydx=2-y

Q: A rectangle is growing in such a way that when its length is 5 ft and its width is 2 ft, the length…

A:

Q: Consider that sugar dissolves in water at a rate proportional to the amount still un-dissolved.…

A: 50kgs of sugar is present and at 5-hour mark there's only 20kg of sugar is left.

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.