answer:Here's an example of a well-written error message that includes an HTTP response code: ```javascript HTTP/1.1 404 Not Found { error: { message: Failed to retrieve user with ID 12345: The user does not exist in our database., code: USER_NOT_FOUND, details: Ensure the user ID is correct and try again. } } ``` In this example, the error message: * Returns a relevant HTTP response code (404 Not Found) * Specifies the operation being performed (retrieving a user) * Provides context (the user ID) * Clearly states the cause of the error (the user does not exist) * Offers actionable advice (ensure the user ID is correct) * Includes a relevant error code (USER_NOT_FOUND) for further reference Alternatively, you can also use a more concise format: ```javascript HTTP/1.1 404 Not Found Error: Failed to retrieve user with ID 12345: The user does not exist in our database. (USER_NOT_FOUND) ``` In both cases, the HTTP response code provides additional context for the error, indicating that the requested resource (the user) was not found. This helps clients and developers handle the error accordingly.

answer:To determine which machine produces widgets the fastest, we need to find out the production rate of each machine, which is the number of widgets produced per hour. Machine A produces 200 widgets in 6 hours, so its production rate can be found by dividing the number of widgets produced by the time taken. This gives us 200 widgets / 6 hours = 33.33 widgets per hour. Machine B produces 300 widgets in 5 hours, so its production rate is 300 widgets / 5 hours = 60 widgets per hour. Since 60 widgets per hour is greater than 33.33 widgets per hour, we can conclude that Machine B produces widgets the fastest.

answer:To find the cost of producing one more unit when the current production is x = 100 units, we need to find the change in cost when x increases from 100 to 101 units. The current cost of producing 100 units can be found by substituting x = 100 into the given cost equation: C = 8000 + 26(100) + 0.3(100)^2. Evaluating this expression, we get C = 8000 + 2600 + 3000 = 13600 dollars. The cost of producing 101 units can be found by substituting x = 101 into the cost equation: C = 8000 + 26(101) + 0.3(101)^2. Evaluating this expression, we get C = 8000 + 2626 + 3060.3 = 13686.3 dollars. The cost of producing one more unit is the difference between the cost of producing 101 units and 100 units, which is 13686.3 - 13600 = 86.3 dollars. Alternatively, we can find the cost of producing one more unit by finding the derivative of the cost function with respect to x, which represents the rate of change of cost with respect to the number of units produced. The derivative of the given cost function is dC/dx = 26 + 0.6x. Evaluating this derivative at x = 100, we get dC/dx = 26 + 0.6(100) = 86. This tells us that the cost increases by approximately 86 dollars for each additional unit produced when the current production is 100 units.

answer:To find the rate of change directly from the cost function C = 8000 + 26x + 0.3x^2, we can apply the following two-operation sequence: First, multiply the coefficient of the x^2 term by 2 times x, then add the coefficient of the x term. This gives us: (2 * 0.3 * x) + 26. Since x is 100, substitute 100 for x. Then multiply. This results in (2 * 0.3 * 100) + 26 = (0.6 * 100) + 26 = 60 + 26 = 86.