A factory produces bicycles at a rate of 80+0.3t^2−1.1t bicycles per week (t in weeks). How many bicycles were produced from day 15 to 21?
Intgerate (.3t^2 - 1.1t + 80) dt from 15 to 21
= .1t^3 - .55t^2 + 80t [12,15]
= 1413 - 1063
= 360
Very useful thanks!
for mine I had 8 to 28 days, and my rate was different. I just typed: 0 to 3 integral 105+02t^2−09t into wolfram alpha and got 312 bicycles.
I don't understand how you got the [12,15] because in the problem it says 15 to 21 days
Well, I must say, that's quite a mathematical equation! I guess you want to know how many bicycles were produced from day 15 to 21, right? Let's calculate it.
First, let's find out how many bicycles were produced on day 15. We'll substitute t with 15 in the equation: 80+0.3(15)^2−1.1(15). Now we can calculate it.
On day 15, the factory produced 80+0.3(225)−1.1(15) bicycles. Are you ready for the punchline? The result is 80 + 67.5 - 16.5 bicycles.
Now, let's proceed to day 21. We'll do the same calculation by substituting t with 21: 80+0.3(21)^2−1.1(21). Grab your calculator, it's time for the magic.
On day 21, the factory produced 80+0.3(441)−1.1(21) bicycles. Drumroll, please! The answer is 80 + 132.3 - 23.1 bicycles.
Now, if you add up the number of bicycles produced from day 15 to 21, you'll have your answer!
To find the number of bicycles produced from day 15 to 21, we first need to convert the time from days to weeks since the rate given is in weeks.
1. Convert the number of days to weeks:
Since there are 7 days in a week, from day 15 to 21, there are (21 - 15 + 1) = 7 days.
Divide 7 days by 7 to get 1 week.
2. Substitute the value of t into the given rate equation:
The rate of bicycle production is given by the equation: 80 + 0.3t^2 - 1.1t bicycles per week.
Substitute t = 1 into the equation since we have converted the time to weeks.
3. Calculate the number of bicycles produced:
Plug in t = 1 into the equation:
80 + 0.3(1)^2 - 1.1(1)
80 + 0.3 - 1.1
80 + 0.3 - 1.1 = 79.2 bicycles per week
Therefore, from day 15 to day 21, approximately 79.2 bicycles were produced.