John is participating in a marathon that is 26.2 miles and he finishes in 4.5 hours. his distance, d, depends on his time, t. which is an appropriate domain for this situation?

the complete question is

John is participating in a marathon that is 26.2 miles and he finishes in 4.5 hours. his distance, d, depends on his time, t. which is an appropriate domain for this situation?

A.)0<t<26.2

B.)0<t<4.5

C.)0<d<4.5

D.)0<d<26.2

we know that

in this problem

t is the independent variable

and

d the dependent variable

so

the domain refers to the possible values of time t

therefore

we know that

John finishes in 4.5 hours

so

t<4.5 hours

and time t must be positive> t>0

the answer is the option

B.)0<t<4.5

The appropriate domain for the given situation is 0 < t < 4.5.

Step-by-step explanation:

According to the given information John is participating in a marathon that is 26.2 miles and he finishes in 4.5 hours.

Domain is the set of input values or the values of dependent variable.

Range is the set of output values or the values of independent variable.

It is given that the distance, d, depends on his time, t. It means the d is dependent variable and t is independent variable.

He participating in a marathon so the time must be greater positive, i.e., t>0.

He finishes in 4.5 hours. So, t < 4.5.

Therefore the appropriate domain for the given situation is 0 < t < 4.5.

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50

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