Consider an elastic string of length L whose ends are held fixed. The string is set in motion with no initial velocity from an initial position u(x, 0) = f(x). Let L = 10 and a = 1 in parts (b) and (c). (A computer algebra system is recommended.) f(x) = 2x L , 0 ≤ x ≤ L 2 , 2(L − x) L , L 2 < x ≤ L (a) Find the displacement u(x, t) for the given initial position f(x). (Use a to represent an arbitrary constant.)

Use addition and subtraction to simplify the following polynomials. a. add polynomials: (3 – 4x + 8x^2) + (–6 + 2x – 5x^2) step 1: rewrite the polynomials without the parentheses. step 2: write the polynomial in descending order and use parentheses around like terms. step 3: add the like terms identified in step 2 to simplify the polynomial. b. subtract polynomials: (3x – 5 – 7x^2) – (–2 + 6x^2 – 5x) step 1: rewrite the polynomials without the parentheses. remember to multiply each term in the second parentheses by –1. show your work. step 2: write the polynomial in descending order and use parentheses around like terms. step 3: add the like terms identified in step 2 to simplify the polynomial.

The position of a moving particle is given by the position function: f(t)=-9t-t^2-0.2t^3+0.1t^4 a. at what time does the particle reverse direction? b. when is the displacement positive? (round one decimal place and answer in interval notation) c. when is the displacement negative? (round one decimal place and answer in interval notation) d. when is the particle’s acceleration positive? (round one decimal place and answer in interval notation) e. when is the particle’s acceleration negative? (round one decimal place and answer in interval notation)

Why is studying fractions important