On a trip, the total distance (in miles) you travel in x hours is represented by

Chesley

Chesley

Answered question

2021-09-10

On a trip, the total distance (in miles) you travel in x hours is represented by the piccewise function.
d(x)={55x,if 0x265x20,if 2<x5
How far do you travel in 4 hours?

Answer & Explanation

Cristiano Sears

Cristiano Sears

Skilled2021-09-11Added 96 answers

Calculation: The given function: d(x)={55x,if 0x265x20,if 2<x5
Use the second equation because 2<4<5.
d(x)=65x20
d(4)=65(4)20
d(4)=26020
d(4)=240
Therefore the distance travel in 4 hours is 240 miles.

RizerMix

RizerMix

Expert2023-06-10Added 656 answers

Result:
The total distance traveled in 4 hours is 240 miles.
Solution:
For 0x20, the function is given by d(x)=55x. We can substitute x=4 into this equation:
d(4)=55·4
Simplifying the expression:
d(4)=220
So, if 0x20, the distance traveled in 4 hours is 220 miles.
Now, let's check the second condition: 2<x5. For this range, the function is given by d(x)=65x20. Again, we substitute x=4 into this equation:
d(4)=65·420
Simplifying further:
d(4)=26020
d(4)=240
Therefore, if 2<x5, the distance traveled in 4 hours is 240 miles.
Since the value of x=4 satisfies the condition 2<x5, we use the second equation d(x)=65x20 and find that the distance traveled in 4 hours is 240 miles.
Vasquez

Vasquez

Expert2023-06-10Added 669 answers

For the first interval, where 0 ≤ x ≤ 20, the equation is:
d(x)=55x
Substituting x = 4:
d(4)=55(4)
Simplifying:
d(4)=220
Therefore, the distance traveled in 4 hours is 220 miles.
Don Sumner

Don Sumner

Skilled2023-06-10Added 184 answers

To solve the problem, we need to find the distance traveled in 4 hours using the given piecewise function:
d(x)={55x,if 0x2065x20,if 2<x5
We are interested in the second case, where 2<x5. In this case, the formula for distance is 65x20. Therefore, we can substitute x=4 into this formula to find the distance traveled in 4 hours.
d(4)=65(4)20
Simplifying the expression, we have:
d(4)=26020
d(4)=240
Therefore, you would travel 240 miles in 4 hours.
Let's summarize the solution:
d(4)=65(4)20=240
The distance traveled in 4 hours is 240 miles.

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