anonymous
  • anonymous
A truck is to be driven 200 km along a level highway at x km per hour. Petrol costs 8 cents per litre and is used at the rate of \[25+\frac{ x^2 }{ 112 }\] litres per hour. The driver receives 2 dollars per hour. What is the most economical speed (to the nearest km per hour and the cost of the trip- i) if there is no speed limit, ii) if the speed must not exceed 60km per hour?
Mathematics
katieb
  • katieb
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

anonymous
  • anonymous
Topic: Calculus Sub Topic: Maxima and Minima.
anonymous
  • anonymous
Is it 74.83 km/h?
anonymous
  • anonymous
Yes!!

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
\[C(x) = 0.08(25 + \frac{ x^{2} }{ 112 }) * \frac{ 200 }{ x } + 2(\frac{ 200 }{ x })\] This is the equation I came up with for Cost.
anonymous
  • anonymous
75km/hour
anonymous
  • anonymous
How did you do the first part?
anonymous
  • anonymous
sorry
anonymous
  • anonymous
gallon?
anonymous
  • anonymous
American?
anonymous
  • anonymous
let me rewrite that , (i used american units and accidentally wrote it in the wrong place)
anonymous
  • anonymous
The first thing we know is that the rate of petrol is $0.08/litre And the second thing we know is that the petrol is used at a rate of 25 + x^2/112 litre/h so \[0.08 \frac{ dollar}{ litre } * (25 + \frac{ x^{2} }{ 112 }) \frac{ litre }{ hour }\] Gives us the units dollars/hour
anonymous
  • anonymous
The only thing we need to know is how long the trip takes. We know speed = distance / time speed = x distance = 200 km time = t Therefore time, t = 200/x If we multiply what we have so far by (200/x) (which is in hours), then the hours unit cancels leaving an expression in dollars
anonymous
  • anonymous
So far, I'm up to: \[0.08*(25+\frac{ x^2 }{ 112 })\]
anonymous
  • anonymous
\[0.08 \frac{ dollar }{ litre } * (25 + \frac{ x^{2} }{ 112 }) \frac{ litre }{ hour } * \frac{ 200 }{ x } hours\]
anonymous
  • anonymous
So you get that, and do you then add: \[\frac{ 400 }{ x }\] for the money he receives per hour?
anonymous
  • anonymous
yes
anonymous
  • anonymous
okay. Now I'm getting somewhere.
anonymous
  • anonymous
So do we differentiate that with respect to x?
anonymous
  • anonymous
Yes because C(x) is the cost evaluated at x. So we need to minimize cost by differentiating with respect to x.
anonymous
  • anonymous
Thanks for the assistance @LogicalApple . Appreciate it.
anonymous
  • anonymous
Not a problem
anonymous
  • anonymous
For the second part of the question, keep in mind that the point we evaluated in the first part was a minimum. Due to the nature of the hyperbola, you can consider it an absolute minimum whenever x > 0 This should help you answer the second part of the question.
anonymous
  • anonymous
Yeah I already finished the question.
anonymous
  • anonymous
Oh, nice
anonymous
  • anonymous
The hard part was what you did for me.
anonymous
  • anonymous
I did it on paper and I was like "hm.. I can't think in litres/gallon"
anonymous
  • anonymous
Ah, I did it again lol I mean litres/hour!
anonymous
  • anonymous
hahah.
anonymous
  • anonymous
Well I'm going to close this and put up another question. Thanks again for helping me.
anonymous
  • anonymous
Hope you can help me again if you see fit to.
anonymous
  • anonymous
Good luck!

Looking for something else?

Not the answer you are looking for? Search for more explanations.