Find the solution of the given initial value problems 1) y' +(3/t)y = (cost) /t³, y(t)=0, t>0. 2) ty' + (t+1)y=t, y(ln 2) = 1, t>0.
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- Find the consumers' surplus if the demand function for a particular beverage is given by D(q)=6000/(6q+1)^2 and if the supply and demand are in equilibrium at q=5.Solve for the implicit solution y' = 4 + 1² cost y + xFind the consumers' surplus if the demand function for a particular beverage is given by D(q)=3000/(3q+7)^2 and if the supply and demand are in equilibrium at q=6. The consumers' surplus is?
- Find the solution of y'' (x) = y(x) that fits in origo and goes through the point (ln2,(3/2) )Solve IVP Y'=AY, A= [-1 3² ], Y(0) = (-3 √3 2find the consumers surplus if the demand function for a particular beverage is given by D(q)=(3000)/((3q+2)^(2)) and if the supply and demand are in equilibrium at q=5
- A construction company has an expenditure rate of E (x)-eox dollars per day on a particular paving job and an income rate of l'(x) = 122.8 - e10 dollars per day on the same job, where x is the number of days from the start of the job. The company's profit on that job will equal total income less total expenditures. Profit will be maximized if the job ends at the optimum time, which is the point where the two curves meet. anol, (a) Find the optimum number of days for the job to last. (b) Find the total income for the optimum number of days. (c) Find the total expenditures for the optimum number of days. (d) Find the maximum profit for the job. Pn for (a) days (Round to the nearest integer as needed) (b) The total income for the optimum number of days will be S (Round to the nearest.cent as needed.) (c) The total expenditures for the optimum number of days will be 5 (Round to the nearest cent as needed.) (d) The maximum profit for the job will be S (Round to the nearest cent as needed.)Please assist with the step in solving the problem below. A company manufactures travel clocks. The daily marginal cost function associated with producing these clocks is C'(x)=0.000006x^2-0.001x+3 where C'(x) is measured in dollars/units and x denotes the number of units produced. Management has determined that the daily fixed cost incurred in producing these clocks is $130. Find the total cost incurred by the company in producing the first 600 travel clocks/day.Find y' if y= y'=0 - 14 3√x