PlZ solve and give correct ans 12:40י ןוה.ו1!•..Attachm.312398-1Problem 2drin terms ofdt(a) If A is the area of a circle with radius r and the circle expands as time passes, finddAdt(b) Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at aconstant rate of 2 m/s, exactly how fast (in m2/s) is the area of the spill increasing when the radius is 39 m?

Given that, Suppose oilspills from a ruptured tanker and spreads in a circularpattern. If the radius…

Answered: Problem 2 dA (a) If A is the area of a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A population of E. coli bacteria will grow at a rate given by w'(t)=(3t+2)^1/3 where w is the weight in mg after t hours If the region is enclosed by y=x^2 and y=2x, estimate the area by the right endpoints with 4 subintervals
Two large tanks, each holding 24 liters of a brine solution, are interconnected by pipesas shown in the figure. Fresh water follows into tank T1 at a rate of 6L/min and fluid is drainedout of tank T2 at the same rate; also 8L/min of fluid are pumped from tank T1 to tank T2 and2L/min from tank T2 to tank T1. The liquids inside each tank are kept well stirred. If, initially, thebrine solution in tank T1 contains 1 kg of salt and that in tank T2 contains 6 kg of salt, determinethe mass of salt in each tank at time t > 0
An industrial food-manufacturing operation wishes to expand, and it requires an improved water supply. They propose to construct a fully penetrating well in an infinite, horizontal, confined, homogeneous, isotropic aquifer, and they plan to pump at a constant rate of 20 L/s. If T = 1.3 x 10-2 m2/s, and S is 2.0 x 10-4, make the following calculations. a. Calculate the drawdown that would occur in an observation well 60 m from a pumping well at times of 1, 5, 10, 50 and 210 min after the start of pumping. The environmental regulator has imposed a limitation on the drawdown from the well in order to prevent impacts to surrounding groundwater users. If the drawdown limit is set to a maximum of 1.5 m at a distance of 250 m, after ten days of pumping, is this well likely to be in compliance with the regulation?
A cylinder of radius r and height h has volume V = nr 2h.(a) Use the Linear Approximation to show that (b) Estimate the percentage increase in V if r and h are each increasedby 2%.
Suppose that we are interested in the amount of salt (in kg) at a certain moment in time, denoted by A(t), in a well-mixed, infinitely large tank with 400-L of water initially. Further, suppose we have set-up the experiment such that a salt solution containing 16 kg/L flows into the tank at a rate of 9 L/sec. If we allow the solution to flow out at 6 L/sec, then what is the volume of water in the tank at time t? V(t) = _____? ( (DO NOT use commas in your answer) Construct a model for the change of salt in the tank at time t. [To ensure you are marked correct, please use A to represent the amount of salt in the tank at time t not A(t)]. dA/dot=_________?
Suppose a spherical balloon grows in such a way that after t seconds, its volume V is given by V = 4 t1/2 cm3. After 100 seconds the radius of the balloon is r = 2.121568836 units? sec cm cm^2 cm^3 cm/sec cm^2/sec cm^3/sec . How fast is the radius changing after 100 seconds? dr dt = units? sec cm cm^2 cm^3 cm/sec cm^2/sec cm^3/sec

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