The actual torque being applied to the spark plug by the mechanic using a wrench at a 40-degree angle is approximately 10.79 N·m, which does not match any of the provided options.
The mechanic is trying to apply torque to a spark plug using a 25 cm long wrench. When calculating the effective torque being applied, one must consider not only the force and the length of the wrench but also the angle at which the force is applied. The torque (τ) can be calculated using the formula τ = r * F * sin(θ), where r is the wrench length, F is the force applied, and θ is the angle of force application. In this case, τ = 0.25 m * 67 N * sin(40°).
To find the sine of 40°, we can use a calculator or trigonometric tables, which gives us approximately 0.6428. Now, we calculate the effective torque: τ = 0.25 m * 67 N * 0.6428 ≈ 10.79 N·m. This is the actual torque being applied to the spark plug. However, as there are no options that match this value, it is possible that there is a typo in the question, or the actual question is asking for the additional torque needed to reach a certain value. Please review the question for any discrepancies.