Reem is a test driver for an automobile company. The following formula gives the total distance, d, in feet that Reem drove a luxury car in the first t seconds after idling at a speed of 0 miles per hour, up to the time when she passed a particular safety cone.d=15.69t2Compared to the time it took Reem to pass the safety cone, how long did it take to pass a sensor that was 94 of the distance from the start?Choose 1 answer:A) 8116 of the time it required to pass the cone(B) 94 of the time it required to pass the cone(C) 32 of the time it required to pass the cone(D) 49 of the time it required to pass the cone
Q. Reem is a test driver for an automobile company. The following formula gives the total distance, d, in feet that Reem drove a luxury car in the first t seconds after idling at a speed of 0 miles per hour, up to the time when she passed a particular safety cone.d=15.69t2Compared to the time it took Reem to pass the safety cone, how long did it take to pass a sensor that was 94 of the distance from the start?Choose 1 answer:A) 8116 of the time it required to pass the cone(B) 94 of the time it required to pass the cone(C) 32 of the time it required to pass the cone(D) 49 of the time it required to pass the cone
Understand relationship: Understand the relationship between distance and time in the given formula.The formula provided is d=15.69t2, which indicates that the distance d is proportional to the square of the time t. This means that if the distance changes by a factor, the time will change by the square root of that factor.
Calculate time to pass sensor: Calculate the time it takes to pass a sensor that is (4/9) of the distance from the start.Let's denote the time it took to pass the safety cone as T. The distance to the safety cone is d=15.69T2. If the sensor is at (4/9) of the distance to the cone, the distance to the sensor is (4/9)d. We need to find the time it takes to reach this distance, which we'll call tsensor.
Set up equation: Set up the equation for the distance to the sensor.Using the formula d=15.69t2, we can write the equation for the distance to the sensor as (94)d=15.69tsensor2.
Substitute distance: Substitute the distance to the cone into the equation for the sensor.Since d=15.69T2, we can substitute this into our equation for the sensor to get (94)(15.69T2)=15.69tsensor2.
Simplify equation: Simplify the equation to solve for tsensor. Divide both sides of the equation by 15.69 to get (94)T2=tsensor2.
Take square root: Take the square root of both sides to solve for tsensor.tsensor=(94)T2=(94)∗T=(32)∗T.
Determine correct answer: Determine the correct answer from the given options.The time it took to pass the sensor is (32) of the time it took to pass the cone, which corresponds to answer choice (C).