Let P2 denote the vector space of all polynomials with degree less than or equal to 2. (a) Show that B = {1 + x + x 2 , 1 + 2x − x 2 , 1 − 2x − x 2} is a basis for P2. (b) Find the coordinate vector of p(x) = 1 + 2x + 3x 2 relative to the basis B.

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Determine if the function below is continuous. a. continuous b. not continuous, 1 hole c. not continuous, > 2 holes d. not continuous, 2 holes

At the beginning of year 1, carlos invests $600 at an annual compound interest rate of 4%. he makes no deposits to or withdrawals from the account. which explicit formula can be used to find the account's balance at the beginning of year 5? what is, the balance?