Hello John, This cannot be solved for analytically in terms of elementary functions. I did solve it numerically to obtain a very good approximation. x=-40.7459009034... The attached graph shows

I think the trace of X should be zero. Here's my derivation: Traces have some simple and useful properties, such as (for a matrices A and B) 1. Tr(A +B) = Tr(A) + Tr(B) 2. Tr(A) = Tr(A^t) 3

Hello Giulia, As far as I know, this has no general solution in terms of elementary functions. A computer algebra system (Maple) gives the following result: y(x) = KummerM((1/2)*e/b, 1/2, b*(d-x)^2/a^2)*_C2+KummerU((1/2)*e/b

Hello Kenneth I misunderstood your question. It is the number of gallons that is the dependent variable which is directly proportional to the number of miles and to the number of trips. g = kmt, so

Hello Julian, Without additional info there are literally infinitely many possibilities! The relationship could be (1) linear, (2) quadratic, (3) cubic, (4) exponential, (5) logarithmic, (6) power

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