# Tutor profile: Meredith W.

## Questions

### Subject: Applied Mathematics

A loan offers a 6.15% interest rate compounded daily over a year. What is the effective annual rate?

$$i_e = (1+\frac{r}{m})^m -1$$ $$i_e = (1+\frac{0.0615}{365})^{365} - 1 = 0.0634$$ 6.34% APR

### Subject: Calculus

If $$f(x) = \frac{x^2 − 4}{x − 2}$$ and $$g(x) = x + 2$$, can we say that the two functions are equal/the same?

No, even though both functions simplify to the same thing, f(x) is not defined at 2, thus are defined on different domains.

### Subject: Civil Engineering

A 12 ft. long cantilever beam is fixed at end A and has a 3 kip/ft uniform distributed load. Calculate the moment at 4 feet from side A.

Maximum reaction force, located on the fixed end. $$R = V $$ $$R= w*L = 3 kip/ft * 12 ft = 36 kip$$ The moment at any location along a cantilever beam can be expressed by the function: $$M(x) = \frac{w}{6}{(L^2 - 3x^2)}$$ Plug in values for x, w, and L. $$M(4 ft) = 60 kip*ft$$

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