Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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=15.69t^(2)
Compared to the time it took Reem to pass the safety cone, how long did it take to pass a sensor that was 
(4)/(9) of the distance from the start?
Choose 1 answer:
A) 
(16)/(81) of the time it required to pass the cone
(B) 
(4)/(9) of the time it required to pass the cone
(C) 
(2)/(3) of the time it required to pass the cone
(D) 
(9)/(4) of the time it required to pass the cone

Reem is a test driver for an automobile company. The following formula gives the total distance, d d , in feet that Reem drove a luxury car in the first t t seconds after idling at a speed of 00 miles per hour, up to the time when she passed a particular safety cone.\newlined=15.69t2 d=15.69 t^{2} \newlineCompared to the time it took Reem to pass the safety cone, how long did it take to pass a sensor that was 49 \frac{4}{9} of the distance from the start?\newlineChoose 11 answer:\newlineA) 1681 \frac{16}{81} of the time it required to pass the cone\newline(B) 49 \frac{4}{9} of the time it required to pass the cone\newline(C) 23 \frac{2}{3} of the time it required to pass the cone\newline(D) 94 \frac{9}{4} of the time it required to pass the cone

Full solution

Q. Reem is a test driver for an automobile company. The following formula gives the total distance, d d , in feet that Reem drove a luxury car in the first t t seconds after idling at a speed of 00 miles per hour, up to the time when she passed a particular safety cone.\newlined=15.69t2 d=15.69 t^{2} \newlineCompared to the time it took Reem to pass the safety cone, how long did it take to pass a sensor that was 49 \frac{4}{9} of the distance from the start?\newlineChoose 11 answer:\newlineA) 1681 \frac{16}{81} of the time it required to pass the cone\newline(B) 49 \frac{4}{9} of the time it required to pass the cone\newline(C) 23 \frac{2}{3} of the time it required to pass the cone\newline(D) 94 \frac{9}{4} of the time it required to pass the cone
  1. Understand relationship: Understand the relationship between distance and time in the given formula.\newlineThe formula provided is d=15.69t2d = 15.69t^2, which indicates that the distance dd is proportional to the square of the time tt. This means that if the distance changes by a factor, the time will change by the square root of that factor.
  2. Calculate time to pass sensor: Calculate the time it takes to pass a sensor that is (4/9)(4/9) of the distance from the start.\newlineLet's denote the time it took to pass the safety cone as TT. The distance to the safety cone is d=15.69T2d = 15.69T^2. If the sensor is at (4/9)(4/9) of the distance to the cone, the distance to the sensor is (4/9)d(4/9)d. We need to find the time it takes to reach this distance, which we'll call tsensort_{\text{sensor}}.
  3. Set up equation: Set up the equation for the distance to the sensor.\newlineUsing the formula d=15.69t2d = 15.69t^2, we can write the equation for the distance to the sensor as (49)d=15.69tsensor2(\frac{4}{9})d = 15.69t_{\text{sensor}}^2.
  4. Substitute distance: Substitute the distance to the cone into the equation for the sensor.\newlineSince d=15.69T2d = 15.69T^2, we can substitute this into our equation for the sensor to get (49)(15.69T2)=15.69tsensor2(\frac{4}{9})(15.69T^2) = 15.69t_{\text{sensor}}^2.
  5. Simplify equation: Simplify the equation to solve for tsensort_{\text{sensor}}. Divide both sides of the equation by 15.6915.69 to get (49)T2=tsensor2\left(\frac{4}{9}\right)T^2 = t_{\text{sensor}}^2.
  6. Take square root: Take the square root of both sides to solve for tsensort_{\text{sensor}}.tsensor=(49)T2=(49)T=(23)Tt_{\text{sensor}} = \sqrt{\left(\frac{4}{9}\right)T^2} = \left(\sqrt{\frac{4}{9}}\right) * T = \left(\frac{2}{3}\right) * T.
  7. Determine correct answer: Determine the correct answer from the given options.\newlineThe time it took to pass the sensor is (23)(\frac{2}{3}) of the time it took to pass the cone, which corresponds to answer choice (C).

More problems from