answer:As the MPC increases, the spending multiplier also increases. This is because a higher MPC means that consumers will spend a larger proportion of any additional income, leading to a greater increase in aggregate demand and a larger multiplier effect.

answer:The factored form of the given quadratic is -2 left(x - frac{46}{3}right) (x - 5).

answer:To find the intervals where g(x) is decreasing, follow these steps: 1. Calculate the derivative g'(x). 2. Determine the intervals where g'(x) is negative. Quickest Method: Sketch the function y = sin x and apply the following transformations: 1. Horizontal compression by a factor of 2 (to obtain y = sin 2x). 2. Vertical stretch by a factor of 5 (to obtain g(x) = 5sin 2x). Then, identify the intervals where the transformed graph is decreasing. Applying these transformations, we find that g(x) is decreasing for xin [frac{pi}{2},pi]cup[frac{3pi}{2},2pi].

answer:The mass of the third piece can be calculated as: ``` m3 = m - m1 - m2 = 2.30 x 10^6 kg - 5.00 x 10^5 kg - 8.40 x 10^5 kg = 9.60 x 10^5 kg ``` To determine the direction of motion of the third piece, we can use the conservation of momentum: ``` mv = m1v1 + m2v2 + m3v3 ``` Since the first piece moves backward (negative velocity) and the second piece moves forward (positive velocity), the third piece must move backward to conserve momentum. Therefore, the direction of motion of the third piece is backward.