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vovikov84 [41]
3 years ago
10

A bicyclist travels at a constant speed of 12 miles per hour for a total of 45 minutes. (Use set notation for the domain and ran

ge of the function that models this situation.)
Mathematics
2 answers:
Tems11 [23]3 years ago
8 0

Answer:

Domain: \{t|0\leq t\leq 0.75\},

Range: \{d|0\leq d\leq 9\}

Step-by-step explanation:

We have been given that a bicyclist travels at a constant speed of 12 miles per hour for a total of 45 minutes. We are asked to write the domain and range of the function in set notation.

\text{Distance}=\text{Speed}\times \text{Time}

Since the bicycle travels at constant rate, so the distance traveled by bicycle at any time t (in minutes) would be d(t)=12t.

We know that domain of a function is set of all values of independent variable. We can see that independent variable is time (t).

45\text{ minutes}=\frac{45}{60}\text{ hours}=0.75\text{ hours}

Since the bicycle travels for a total of 45 minutes that is 0.75 hours , so domain of our function is restricted to interval 0\leq t\leq 0.75 that is \{t|0\leq t\leq 0.75\} in set notation.

To find the upper limit of range of our given function, we will substitute t=0.75 in our function as:

d(t)=12t

d(0.75)=12(0.75)

d(0.75)=9

Therefore, the range of our given function would be 0\leq d\leq 9 that is \{d|0\leq d\leq 9\} in set notation.

Mamont248 [21]3 years ago
5 0

A bicyclist travels at a constant speed of 12 miles per hour for a total of 45 minutes.

We know the formula , Distance = speed * time

Speed is constant and it is 12. So it  is linear

The function becomes d = 12t, x is the t is the time and d is the distance

At the starting point, t=0  and distance d=0

End point , t=45 min = 0.75 hours and distance = 12 * 0.75 = 9

So domain (t) is {x|0}

Range (d) is {y|0}

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