Find the domain of h(x)=x-3/x^3-36x

There is some ambiguity here which could be removed by using parentheses.  I'm going to assume that you actually meant:

               x-3

h(x) =

          (x^3-36x)

To determine the domain of this function, factor the denominator:

x^3 - 36x = x(x^2 - 36) = x(x-6)(x+6)

The given function h(x) is undefined when the denominator = 0, which happens at {-6, 0, 6}.

Thus, the domain is "the set of all real numbers not equal to -6, 0 or 6."

Symbolically, the domain is   (-infinity, -6) ∪ (-6, 0) ∪ (0, 6) ∪ (6, +infinity).

she will sew have sewn five dresses   and be 1/3 done with the sixth one in an hour.

step-by-step explanation:

3/4 of an hour=45 mins

lucy makes 1 dress per 11.25 minutes

45 mins+11.25 mins=56.25 mins

60 mins- 56.25 mins=3.75 mins

3.75 mins is 1/3 of of 11.25 mins

therefore she the other 1/3 would be part of the hour and she will have sewn 5 dresses and begun the sixth.

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