Create a piecewise function of the following scenario where Upper D left-parenthesis t right-parenthesis is the total distance walked (in miles) as a function of time t (in minutes): “You begin a walk from your home at a fast pace of 3 miles per hour for 25 minutes. You rest for 15 minutes, and then you continue walking at a leisurely pace of 1 mile per hour for 30 minutes."

Question

Create a piecewise function of the following scenario where Upper D left-parenthesis t right-parenthesis is the total distance walked (in miles) as a function of time t (in minutes): “You begin a walk from your home at a fast pace of 3 miles per hour for 25 minutes. You rest for 15 minutes, and then you continue walking at a leisurely pace of 1 mile per hour for 30 minutes."

For the first two piecewise functions I got: D(t)= 0.05t 0≤x≤25 & D(t)= 1.25 25<x≤40. I believed the answer for the third piecewise function to be D(t)=0.01666667t+1.25, but the answer will not be accepted by WileyPLUS.

Answer 1

your functions are correct. You need to find out what syntax the software expects.

Maybe you could try using fractions:

D(t) =
t/20 0<=t<=25
5/4 25<t<=40
5/4 + t/60 40<t<=70

or maybe the x's confused it.

Answer 2

In order to create the correct piecewise function for this scenario, let's break it down step by step.

First, you begin a walk at a fast pace of 3 miles per hour for 25 minutes. Since you're walking at a constant speed, the distance covered during this time can be calculated using the formula: distance = speed × time.

So the distance covered during the first 25 minutes can be expressed as: D1(t) = 3t/60, where t is the time in minutes.

Next, you rest for 15 minutes. During this time, you're not covering any distance, so the function for this period can be written as a constant value: D2(t) = 0.

Finally, you continue walking at a leisurely pace of 1 mile per hour for 30 minutes. Similar to the first part, the distance covered during this time can be calculated using: D3(t) = 1t/60.

Now, let's combine these pieces together to form the complete piecewise function:

D(t) = D1(t) for 0 ≤ t ≤ 25
D(t) = D2(t) for 25 < t ≤ 40
D(t) = D3(t) for t > 40

Based on this information, the correct piecewise function for the scenario would be:

D(t) = 3t/60 for 0 ≤ t ≤ 25
D(t) = 0 for 25 < t ≤ 40
D(t) = t/60 for t > 40

Note that the "1.25" in your third piecewise function seems incorrect because it is not clear how you arrived at that value. Double-check the problem statement to ensure you are using the correct information.