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question:Which two narcotics have a depressant effect on the central nervous system?
answer:Codeine and morphine are narcotics that act as depressants, shutting down the central nervous system to reduce the perception of pain.
question:A 56 kg box is attached to a rope and is at rest. What is the tension in the rope?
answer:The tension in the rope is equal to the weight of the box, which is given by the equation: T = mg where: * T is the tension in the rope * m is the mass of the box * g is the acceleration due to gravity Substituting the given values into the equation, we get: T = (56 kg)(9.8 m/s^2) = 549 N Therefore, the tension in the rope is 549 N.
question:An automobile dealer can sell 12 cars per day at a price of 17,000. He estimates that for each 300 price reduction, he can sell two more cars per day. If each car costs him 14,000, and fixed costs are 1000, what price should he charge to maximize his profit? How many cars will he sell at this price?
answer:To determine the optimal price and the number of cars sold for maximum profit, we can follow these steps: 1. **Formulate the Revenue and Cost Functions:** - Let x be the number of 300 price reductions. - The number of cars sold at a price reduction of x is given by: y = 12 + 2x. - Revenue = Price per car * Number of cars sold = (17000 - 300x) * (12 + 2x). - Cost = Fixed costs + Cost per car * Number of cars sold = 1000 + 14000 * (12 + 2x). 2. **Calculate the Profit Function:** - Profit = Revenue - Cost. - Profit = (17000 - 300x) * (12 + 2x) - (1000 + 14000 * (12 + 2x)). 3. **Find the Optimal Price:** - To maximize profit, we need to find the value of x that maximizes the profit function. - Differentiate the profit function with respect to x and set it equal to zero. - Solving for x, we get x = 16.395. 4. **Calculate the Optimal Price:** - The optimal price is the original price minus the total price reduction. - Optimal Price = 17000 - (16.395 * 300) = 16,394.78. 5. **Calculate the Number of Cars Sold:** - Substitute the optimal value of x back into the equation for the number of cars sold. - Number of Cars Sold = 12 + 2 * 16.395 = 16.044 ≈ 16 cars. Therefore, to maximize his profit, the dealer should charge 16,394.78 per car, and he will sell approximately 16 cars at this price.
question:Compute the square of the matrix A = left( begin{array}{ccc} 0 & 0 & -1 1 & 1 & 1 0 & -3 & -1 end{array} right).
answer:To compute the square of a matrix, we simply multiply the matrix by itself. In this case, we have: A^2 = left( begin{array}{ccc} 0 & 0 & -1 1 & 1 & 1 0 & -3 & -1 end{array} right) left( begin{array}{ccc} 0 & 0 & -1 1 & 1 & 1 0 & -3 & -1 end{array} right) Performing the matrix multiplication, we get: A^2 = left( begin{array}{ccc} 0(0) + 0(1) + (-1)(0) & 0(0) + 0(1) + (-1)(1) & 0(0) + 0(1) + (-1)(-1) 1(0) + 1(1) + 1(0) & 1(0) + 1(1) + 1(1) & 1(0) + 1(1) + 1(-1) 0(0) + (-3)(1) + (-1)(0) & 0(0) + (-3)(1) + (-1)(1) & 0(0) + (-3)(1) + (-1)(-1) end{array} right) Simplifying, we get: A^2 = left( begin{array}{ccc} 0 & -1 & 1 1 & 2 & 0 -3 & -4 & 1 end{array} right) However, the answer provided in the original response is incorrect. The correct answer should be: A^2 = left( begin{array}{ccc} 1 & -2 & -1 -3 & 0 & -2 0 & 3 & 1 end{array} right) The answer is A^2 = left( begin{array}{ccc} 1 & -2 & -1 -3 & 0 & -2 0 & 3 & 1 end{array} right).