First one to answer gets the distance d in meters traveled by a skateboard on a ramp is related to the time t in seconds. this os modeled by the function: d(t) = 4.9t ^2 - 2.3t + 5. what is the maximum distance the skaeboard can travel, and at what time would it achieve this distance? round your answer to the nearest hundredth.

The maximum distance traveled is 4.73 meters in 0.23 seconds.

Step-by-step explanation:

We have that the distance traveled with respect to time is given by the function,

.

Now, differentiating this function with respect to time 't', we get,

d'(t)=9.8t-2.3

Equating d'(t) by 0 gives,

9.8t - 2.3 = 0

i.e. 9.8t = 2.3

i.e. t = 0.23 seconds

Substitute this value in d'(t) gives,

d'(t) = 9.8 × 0.23 - 2.3

d'(t) = 2.254 - 2.3

d'(t) = -0.046.

As, d'(t) < 0, we get that the function has the maximum value at t = 0.23 seconds.

Thus, the maximum distance the skateboard can travel is given by,

.

i.e. .

i.e. .

i.e. .

i.e. d(t) = 4.73021

Hence, the maximum distance traveled is 4.73 meters in 0.23 seconds.