b . Reasoning Without doing the calculation , what is the greatest number of restrictions the quotient (x ^ 2 + 8x + 7)/(x ^ 2 - x - 12) + (x ^ 2 + 2x - 8)/(x ^ 2 + 13x + 24) could have? Explain.

Use the graph to determine the range. which notations accurately represent the range? check all that apply. (–∞, 2) u (2, ∞) (–∞, –2) u (–2, ∞) {y|y ∈ r, y ≠ –2} {y|y ∈ r, y ≠ 2} y < 2 or y > 2 y < –2 or y > –2

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)

The function v(r)=4/3pir^3 can be used to find the volume of air inside a basketball given its radius. what does v(r) represent