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Let A(x,y) be the area of a rectangle not degenerated of dimensions x and y, in a way that the rectangle is inside a circle of a radius of 10.
A mass of clay of volume 432 in^3 is formed into two cubes. What is the minimum possible total surface area of the two cubes? What is the maximum?
Let g(v) be the distance the same car goes on one liter of gas at velocity v. what is the relationship between f(v) and g(v) ? find g(80) and g1(80).
Find the relative maxima, relative minima, and saddle points of the function (x^2)*y - 6*(y^2) - 3*(x^2).
A company paid off a $10,000 long-term note by issuing common stock to the creditor. This transaction would be reflected on the company's statement of cash flow
What value of t will maximize the government's tax revenue? What is the government's maximum tax revenue?
Find the differential equation that governs the position of the body over time relative to the equilibrium position of the spring.
Substitution Methods and Exact Equations. Verify that the given differential equation is exact; then solve it.
Show that the substitution v = lny transforms the differential equation dy/dx + P(x)y = Q(x)(ylny) into the linear equation dv/dx + P(x) = Q(x)v(x)
Show that the one parameter family of straight lines described by y(x) = Cx + g(C) is a general solution of y = xy' + g(y').
Determine the radius of the convergence of each series, and identify the general solution in terms of familiar elementary functions.
Write a linear cost function for each situation. Identify all variable used. A parking garage charges 50 cents plus 35 cent per half-hour.
Assuming that all sets will be sold, how many of each type should produced in order to maximize profit? What is the maximum profit?
Acme estimates marginal revenue on a product to be 200q-1/3 dollars per unit when the level of production is q units.
Acme estimates marginal revenue on a product to be 200q^-1/3 dollars per unit when the level of production is q units.
Is Homer traveling backwards at any time during the first 7 seconds of his escape attempt? If so, during what time interval(s) is the gear shift in reverse?
A solution containing 1 pound of the chemical runs into the tank at a rate of 4 gallons per minute.
Consider the system y···+ 6y·· +11y· + 6y = 6u . Determine the transfer function of the system in terms of Laplace transform.
Eliminate the parameter. Find a retangular equation for the plane curve defined by the parametric equations. X=3t, y=t+7
Suppose Anytown, USA has a fixed population of 200,000. On March 1, 3000 people have the flu. On June 1, 6000 people have it.
Find the volume of the solid generated by revolving R around the y-axis by the method of cylindrical shells.
R is the region that lies between the curve and the x-axis from x = -3 to x = -1. Find: The volume of the solid generated by revolving R around the x-axis.
Find the general solution of the second-order equation that models the motion of the oscillator.
Explain (politely) why the behavior pictured in the figure is impossible with standard suspension systems that are accurately modeled.
Parameters z1 and z2 can represent an external introduction of species at a constant rate (positive values) or an external harvesting of the species.