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Find b(t) in terms of b(0) using the value of k found in (a). Simplify your answer by using the power properties of the exponential function.
Use Liebniz rule to differentiate the expression u(x) = ?10 y(x-1)ƒ(y)dy+?1x x(y-1)(y)dy twice with resect to x.
Find an equation of the line, say y=mx+b, which passes through the point (-3,8) and is perpendicular to the line 3x+3y=33. y=?
In an experiment, a student is randomly selecting a letter from one of 4 boxes after selecting the first box at random.
Isaac earns a base salary of $1250 per month and a graduated commission of 0.4% on the first $100,000 of sales, and 0.5% on sales over $100,000.
Taxes in Oz are calculated according to the formula T=.01I^2 where T=thousand of dollars of tax liability and I=income measured in thousands of dollars.
A calculus instructor has determined that the arc of an individual diving into a swimming pool is defined by the function, f(x) = sin (.4x).
The Millers are planning to buy a home in the near future and estimate that they will need a 30 yr fixed-rate mortgage for $120,000.
Find the tangents and the normals at any point of the following curves: 1) y=1/x^2+2 (1,1/2)
Scripps Hospital surveyed 10 patients on each floor every day in February. Did this study use a sample or the population?
When should Bob release the slingshot so that he can knock Evil Bart the Blackbird out of the sky? Explain how you know.
Prove that isomorphic graphs have the same number oƒ vertices.
Suppose that f has a critical point at x = 1. Find all possible value(s) of k. If there is more than one answer, enter them separated by commas.
The speed of sound at sea level using the standard atmosphere is about 340.29 meters per second. There are 3.280840 feet in one meter.
The predator prey system below has a term for the carrying capacity of the prey species. Initially the prey population N(0) = 330 and the predator population.
Please also explain when we should use ordinary derivatives and when we should use partial derivatives.
Suppose you have a cookie stand, and when you charge $3 per cookie box you sell 200 boxes. But when you raise your price to $4 you only sell 120 boxes.
Find the point of intersection of the line containing the points (3; 2; 1) and (4; 3; 3), and the plane containing the points (5; 4; 2), (3; 1; 6) and (6; 5; 3)
Use dynamic programming to maximize the probability that the computer will work properly, given that $600 is available for spare units.
Find a self complementary graph with five vertices.Prove that if a self-complementary graph has n vertices,then n = 0 (mod 4) or n = 1(mod 4).
When solving an ODE, the simplest approach is to group together the x terms and the y terms so that we might integrate .
List some possible retirement balances if my friend is currently 50 yrs old. (hint: some folks retire at 60 and some at 62).
Find (or estimate) the number of births (instantaneous rate of change) in 2009 and use this value to estimate the population in 2010.
Construct the profit function and list the key points or roots of the function. What happens to profit as Mick increases his price?
Graph the balance on account against time and discuss or identify the effective yield of her security.