April 17, 2014

Homework Help: calculus

Posted by Becky on Sunday, August 12, 2012 at 12:28pm.

Hi i need help in this. Some of the parts i got the answer but some i don't. please help!

A ship uses $(7v^2) of fuel per hour when travelling at a constant speed of v km/h. Other expenses in operating the ship (i.e. crew and equipment) amount to $345 per hour. The ship makes a journey of 100 km.

1. Give an expression for how long the journey takes in hours.

Answer i got: Time = 100/ v

2. Give an expression for the total cost of the journey.

Answer i got: 700v^2 + 3450/ v

3. Let C(v) be the function representing the cost of the journey when the speed is v km/h. What is the derivative of C(v) with respect to the speed v?

Answer i got: 700v^2 - 3450/ v^2
This answer i differentiate by using quotient rule.


4. What is the second derivative of C(v) with respect to the speed v?

Answer: ???

5. Complete the following statement:

To minimize the total cost of the journey the ship should travel at a speed of km/h to 3 significant figures.

Answer: ???

Appreciated!!! thank you!!

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