Consider an economy with three sectors, Chemicals & Metals, Fuels & Power, and Machinery. Chemicals sells 30% of its output to Fuels and 60% to Machinery and retains the rest. Fuels sells 70% of its output to Chemicals and 20% to Machinery and retains the rest. Machinery sells 40% of its output to Chemicals and 30% to Fuels and retains the rest. Complete parts (a) through (c) below a. Construct the exchange table for this economy. Distribution of Output from: Chemicals Fuels Machinery (Type integers or decimals.) Purchased by: Chemicals Fuels Machinery

3) Find the general solution to the following differential equation. d²x = +4x sin² (2t) dt²

2) Find the general solution to the following differential equation. d²x dt² - dx 6 +25x = 64e¯* dt

1) Solve the following initial value problem. y' + xy = x y(0) = −1

Calculate gross pay for each employee. All are paid overtime wage rates that are 1.5 times their respective regular wage rates. should be rounded to two decimal places at each calculation.

Calculate gross pay for each employee. All are paid overtime wage rates that are 1.5 times their respective regular wage rates. should be rounded to two decimal places at each calculation.

No chatgpt pls will upvote

1. 2. Show that the following are not logically equivalent by finding a counterexample: (p^q) →r and (db) V (d←d) Show that the following is not a contradiction by finding a counterexample: (pV-q) AqA (pv¬q Vr) 3. Here is a purported proof that (pq) ^ (q → p) = F: (db) v (bd) = (db) v (bd) =(qVp) A (g→p) = (¬¬q V ¬p) ^ (q→ p) (db) V (db) = =¬(a→p)^(a→p) = (gp) ^¬(a → p) =F (a) Show that (pq) ^ (q→p) and F are not logically equivalent by finding a counterex- ample. (b) Identify the error(s) in this proof and justify why they are errors. Justify the other steps with their corresponding laws of propositional logic.

5 Show by multiplying matrices that the following equation represents an ellipse: 5 - -7 I (x)(3)()=30. y) 7 7)