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Suppose that in Example 1 of Section 8.1 a pair of rabbits leaves the island after reproducing twice. Find a recurrence relation for the number of rabbits on the island in the middle of the nth month.
The dimensions of a closed rectangular box are measured as 86 cm, 61 cm, and 19 cm, respectively, with a possible error of 0.2 cm in each dimension. Use differentials to estimate the maximum error in calculating the surface area of the box.
Find the consumers' surplus if the demand function for a particular beverage is given by D(q) = 4000/(2q+5)3 and if the supply and demand are in equilibrium at q=3
The city of Madison regularly checks the water quality at swimming beaches located on area lakes. The concentration of fecal coliforms, in number of colony forming units (CFU) per 100 ml of water, was measured on fifteen days during the summer at ..
Find the general solution to the differential equation: t2dy/dt+t(t+2)y=et t>0
Pollution control rules were introduced in 1902 and were properly followed in city Y, butnot in city X. If all other factors remain constant, then what could be the approximate expected distribution of light and dark coloured moths in 1950?
Show that the following quadrature formula has degree of precision equal to 3, -1∫1 f(x) dx = f(-√3 / 3) + f( -√3 / 3).
Find the standard equation of a parabola with vertex at (5,1) passing through the point (10,-4). Remember to write your answers as exact numbers (fractions), rather than a decimal approximation.
What activities have flexibility in completion that would not impact the overall project timeline?
Please response to the following: Reason each step and explain the mathematical mistake if there is one.
What is the marginal cost of oil production. What is the marginal revenue for oil production. Find the production level that maximizes profit.
An open rectangular box is to be constructed from material that costs $12/ft2 for the bottom and $10/ft2 for its sides. Find the dimensions of the box of greatest volume that can be constructed for $81.
A rectangular package can have a maximum combined length and girth (perimeter of a cross section) of 108 inches. Find the dimensions of the package of maximum volume. Assume cross section is square.
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