Find the number of possible outcomes
How can you find the number of possible outcomes of a playoff between two teams where the first team to win four games wins the playoff?
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Find a linear differential operator that annihilates the given function. (Use D for the differential operator.)
Suggest: f : R----> R is continuous, a, b are functions from R to R and are differentiable on R. g(x) = integral of f(t)dt with upper limit = b(x) and lower limit = a(x) the problem is to determine a general formula for the derivative of g at x
Prove the validity of the limit lim x->x_0 (ax+b)=ax_0+b by converting to a statement about sequences.
Use the method of variation of parameters to determine a general solution to differential equation: ty''+(1-2t)y'+(t-1)y=te^t given that y1=e^t and y2=e^t (ln t) are two linearly independent solutions to the corresponding homogenous equation.
Determine the general solution of given differential equation. Provide largest interval over which the general solution is defined. Find out transient term.
Use reduction of order or formula to find a second solution
The radioactive isotope of lead, Pb-209, decays at the rate proportional to the amount present at time t and has a half-life of 3.3 hours. If 1 gram of this isotope is present initially, how long will it take for 95% of the lead to decay?
Corporations which invest surplus funds in floating-rate preferred stock benefit from getting the relatively stable price, which is desirable for liquidity portfolios, and they also benefit from 70% tax exemption on the preferred dividends receive
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