ok, so I need to come up with an answer for this question-
A car traveling 65mph on the hwy gets 25 miles per gallon.
Write the function that represents the distance d(t) in miles that the car travels in t hours.
*Then,
Write a function that represents the number of gallons of gas n(d) used for d miles of travel.
*Then,
Evaluate (n times d)(t).
*Then,
Evaluate (n times d)(5) using the solution from part 3
Im so confused!
look at the units. You have
mi/gal
mi/hr
You want to use those to end up with miles in terms of hours.
mi/hr * hr = mi
d(t) = 65t
mi/(mi/gal) = gal
n(d) = d/25
d(t) is miles driven in t hours
n(d) = gallons used in d miles
= gallons used in t hours.
(n◦d)(t) = n(65t) = 65t/25
n times d makes no sense
gallons * miles = ??
Don't worry! I'll walk you through each step and help you understand the problem and how to solve it.
Step 1: Write the function that represents the distance d(t) in miles that the car travels in t hours.
To find the distance, we need to multiply the car's speed (65 mph) by the time traveled (t hours). So the function would be:
d(t) = 65t
Step 2: Write a function that represents the number of gallons of gas n(d) used for d miles of travel.
To find the number of gallons of gas used, we need to divide the distance traveled (d miles) by the car's fuel efficiency (25 miles per gallon). So the function would be:
n(d) = d / 25
Step 3: Evaluate (n times d)(t).
To evaluate the function (n times d)(t), we need to substitute d(t) from step 1 into n(d) from step 2:
(n times d)(t) = n(d(t))
Substituting, we get:
(n times d)(t) = n(65t)
Step 4: Evaluate (n times d)(5) using the solution from part 3.
To evaluate (n times d)(5), we need to substitute t = 5 into the function obtained in step 3:
(n times d)(5) = n(65 * 5)
Simplifying, we get:
(n times d)(5) = n(325)
Now, you can substitute the value of n(d) = d/25 into (n times d)(5) and calculate the final result.