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Answers by Hassan H.

Vaibhav,   Sorry, I forgot about this question over the weekend, as I got pretty busy. Perhaps you already have decoded the solution, but based on what you wrote, I will give you my interpretation of what is going on.     From the solution you present, it seems that...

Mackenzie,   I can only guess at the exact wording your teacher is looking for, but here a some acceptable answers:   1) A solution is defined as a uniform mixture in a single phase.  ('Single' could probably also be 'steady' or 'constant'.)   2)...

Sammy,   The matrix of L w.r.t. the standard basis is gotten by simply taking the coefficients of x as one column, and the coefficients of y as the next column.   M = (3  -1; 1  1; -1  0)   To get the matrix w.r.t. the new bases of R2 and...

Complex Analysis (answer)

Hi Lucy,   This is a residue calculus question, so you will want to find a complex-valued extension of the integrand or else a complex-valued integrand whose real part coincides with the integrand, and then integrate it over an appropriately chosen contour and do some estimates on the...

Complex Analysis (answer)

Lucy,   Some things to think about...   a)  What is the residue of f(z) = 1/z4 at z=0?   b)  I can't make out what limit you are trying to represent.   c)  If you choose w=0 for the pole for simplicity, and you represent f and g...

To Someone in San Antonio, You haven't stated what it is you want to integrate, only the vector field and the surface. I'll have to assume you mean to integrate curl F ⋅ dS over the surface S stated, so that Stokes' Theorem can be invoked.   In that case, the...

Justin,   I would suggest computing the probability that the player loses.   So, compute   P(losing) = P(No H in 12 turns)⋅P(losing | No H) + P(1 H)⋅P(losing | 1 H) + ⋅⋅⋅ + P(12 H)⋅P(losing | 12 H)   and then take the complementary...

Hi Sarah,   Since f is a one-to-one function, (x,y) is on the graph of f if and only if (y,x) is on the graph of f-¹.  See if you can take it from there.   Regards, Hassan

Hello Kyle,   Just to make sure I understand the problem, by N5 do you mean the null graph on five vertices?     If so, the set V would contain all the possible pairs of vertices from a set of five vertices.  The standard description of a graph has the vertex...