Let (x,)
be a topological space. a nonempty collection sof open subsets of x
is called a subbasis for
if the collection of all finiteintersections of members of s forms
a basis for
.
let x be a nonempty set and s the collection of all subsets x \
{x}for

prove s is a subbasis for the finite- closed topology on x.

Suppose that the price p (in dollars) and the weekly sales x (in thousands of units) of a certain commodity satisfy the demand equation 4p cubedplusx squaredequals38 comma 400. determine the rate at which sales are changing at a time when xequals80, pequals20, and the price is falling at the rate of $.20 per week.

1. which of the following algebraic equations is equivalent to ? x^n = a a^n = x a^x = n x^a = n 2. 16^1/4= 1/2 2 4 3. (-36)^1/2= -6 1/6 no real number 4. 8^2/3= 4 8 16√2 )^5/2= 7,776 1/7,776 no real number 6. m ^ the square root of a^2m simplified is: 7. the square root of 3^3 times the square root of 2 simplified and in radical form is:

Louis wants to carpet the rectangular floor of his basement.the basement has an area of 864 square feet.the width of the basement is 2/3 it's length. what is the length of louis's basement