College algebra help?!
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College algebra help?!

[From: ] [author: ] [Date: 11-10-29] [Hit: ]
) Compute and compare the average rates of change for C(cruising speed) = 0.8L^(1/2) on the intervals [100,500] and [600, 1000]. Notice that in both instances the length increased by 400 feet, what happens to the cruising speed?......
So, I have to do this worksheet and it's do in like 4 hours so I need these answers/ help quick. I have everything but two problems so can anyone help me with these problems!

F.) Compute and compare the average rates of change for C(cruising speed) = 0.8L^(1/2) on the intervals [100,500] and [600, 1000]. Notice that in both instances the length increased by 400 feet, what happens to the cruising speed?

I.) The longest ship ever build are oil tankers with overall lengths of approximately 1500 feet. Also, Merriam- Websters dictionary defines a ship as a "large sea- going vessel." Use this information to determine practical domain and ranges for V= 1.34L^(1/2) and for C = 0.8L^(1/2).

So, if anyone can help me with this I will greatly appreciate it!

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F) On the first interval,
L = 100 gives C = 8;
L = 500 gives C = 8√5 = approx 17.9
so the average rate of change (average acceleration) is
(8√5 - 8)/400 = (√5 - 1)/50 = 0.025 approx

Second: L = 600, C = 8√6
L = 1000, C = 8√10
average rate = (8√10 - 8√6) / 400
................... = (√10 - √6)/50
................... = 0.014 approx.

The cruising speed is increasing, but at a diminishing rate.

EDIT: I misunderstood the question. L is the length of the vessel, which determines the cruising speed.
The calculations show that the cruising speed (what units? knots?) increases with length of vessel. For the smaller vessels it increases at about 0.025 knots(?) per foot, but drops to less than 0.015 knots per foot for larger vessels.

I.) I don't know what the smallest practical value of L is, maybe take it as 0.
Then V is between 0 and 1.34*1500^(1/2)
i.e. the range is [0, 13.4√15] = [0, 51.9] approx.

C is between 0 and 0.8*1500^(1/2)
i.e. range [0, 8√15] = [0, 31.0] approx

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Well, the biggest thing to remember here is that the average rate of change is the change in the output over the change in the input, so in F, it would be the change in C over the change in L (or just (delta C)/(delta L).
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