Question

In a certain state the maximum speed permitted on freeways is 75 mi/h and the minimum speed is 50 mi/h. The fine for violating these limits is $25 for every mile per hour above the maximum speed or below the minimum speed. Express the amount of the fine F as a function of the driving speed x.

Answer 1

Answer: The amount of fine F as a function of the driving speed x would be

$25(50-x)\ ;\ 0\leq x<50\\\\0\ ;\ 50\leq x\leq 75\\\\25(x-75)\ ;\ x> 75$

Step-by-step explanation:

Since we have given that

Maximum speed = 75 mi/hr

Minimum speed = 50 mi/hr

Fine for every mile per hour above the maximum speed or below the minimum speed = $25

So, Amount of fine for below the minimum speed would be

$25(50-x)\ ;\ 0\leq x<50$

Amount of fine for above the maximum speed would be

$25(x-75)\ ;\ x> 75$

There will be no fine in between the following range:

$0\ ;\ 50\leq x\leq 75$

Hence, the amount of fine F as a function of the driving speed x would be

$25(50-x)\ ;\ 0\leq x<50\\\\0\ ;\ 50\leq x\leq 75\\\\25(x-75)\ ;\ x> 75$

Answer 2

The function that represents the given situation is required.

The required function is

$f(x)=\begin{cases}25(50-x) & \text{ if } 0\leq x<50 \\0 & \text{ if }  50\leq x\leq75\\25(x-75) & \text{ if } x>75 \end{cases}$

Let $x$ be the speed of the car

Maximum speed limit is 75 mi/h

Minimum speed limit is 50 mi/h

Any speed above the maximum speed and any speed below the minimum speed the fine is $25 dollar per mile per hour.

$f(x)=25(50-x),\ 0\leq x<50$

$f(x)=25(x-75),\ x>75$

There is no fine if the speed is between the given limits.

$f(x)=0,\ 50\leq x\leq75$

Learn more:

https://brainly.com/question/2805538?referrer=searchResults