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A: NOTE: Refresh your page if you can't see any equations. . the water leaving the tank at a rate of…
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A: for function f(x,y) to have maximum value at (a,b) is rt-s2>0,r<0
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A: The answer of the above question is given below.
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A: Explanation of the answer is as follows
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A: In this question we have to compute kf(1).
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A: To find the linear approximation of given function.
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Q: 2. Consider the three functions below: S(z) = 2z S(z) =r S(x) = 2"
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- Show mathematically that MRS is increasing for U=1-ex +e2y and is diminishing for U=lnX +LnYJesaki Inc will sell N units of product after spending $x thousand in advertising, as given by N= 66 x−x2. Use differential approximations to estimate the increase in sales that will result by increasing the advertising budget from $10,000 to $10,589. Round to the nearest integer. $Find the general solution using reduction of order. 1. y''=ln(x)
- In an effort to make the distribution of income more nearly equal, the government of a country passes a tax law that changes the Lorenz curve from y = 0.98x2.1for one year to y = 0.32x2 + 0.68x for the next year. Find the Gini coefficient of income for both years. (Round your answers to three decimal places.) after beforeA cylindrical tank holds 22 liters of water. At time t = 0, two taps are opened simultaneously, the upper tap that feeds the water tank with a constant speed of v1 liters per minute and the lower tap that expels the water from the tank with a constant speed of v2 liters per minute . Suppose that v1 = 11 liters / minute and v2 = 3 liters / minute. If the tank has a capacity of 75 liters, when will the tank be filled?Solve the initial value problems for x as a functionof t. (3t4 + 4t2 + 1) dx/dt = 2√3, x(1) = -π√3/4
- Suppose a tank contains 60 gallons of pure water. A mixture consisting of 1 pound of salt per gallon is flowing into the tank at a rate of 2 gallons per minute, and the mixture is continuously stirred. Meanwhile, the brine in the tank is allowed to empty out the tank at the same time at a rate of 3 gallons per minute. If the tank is completely empty after 1 hour, Önd the amount of salt in the tank at any time t.Suppose that I years from now, one investment plan will be generating profit at the rate of P1'(t)= 90e0.1t thousand dollars per year, while a second investment will be generating profit at the rate of P2'(t)= 140e0.07t thousand dollars per year. (a) For how many years does the rate of profitability of the second investment exceed that of the first? (b) Compute the net excess profit assuming that you invest in the second plan for the time period determined in part (a). (c) Sketch the rate of profitability curves y = P1'(t) and y = P2'(t) and shade the region whose area represents the net excess profit computed in part (b).The population, P, of the city of Hazelton has grown according to the mathematical model P = 65,000(1.075)*, where t is the number of years since 2005. a) At what percentage is the population growing? b) If this trend continues, during which year will the population reach approx. 100,000?
- A tank initially contains s0 lb of salt dissolved in 100 gal of water, where s0 is some positive number. Starting at t = 0, water containing 0.5 lb of salt per gallon enters the tank at a rate of 2 gal/min, and the well-stirred solution leaves the tank at the same rate. Letting c(t) be the concentration of salt at time t, show that the limiting concentration–i.e., limt→∞ c(t)–is 0.5 lb/gal. (1) Set up an initial value problem using the situation described above. It may help to draw a diagram. (2) Solve the differential equation, and use the initial value to solve the initial value problem, and use this function to write an explicit formula for c(t). (3) Show that limt→∞ c(t) = 0.5. (4) Discuss what this limit implies about the importance of the unknown quantity s0.A 200-gal tank is half full of distilled water.At time t = 0, a solution containing 0.5 lb / gal of concentrate entersthe tank at the rate of 5 gal/ min, and the well-stirred mixtureis withdrawn at the rate of 3 gal / min. At what time will the tank be full?Determine the AV at time 9 of $100 invested at time 4 given the accumulation function a(t)=0.05t2+1.