The amount of oil used by a ship traveling at a uniform speed varies jointly with the distance and the square of the speed. the ship uses 30 barrels of oil in traveling 85 miles at 42 mi/h. how many barrels of oil are used when the ship travels 26 miles at 54 mi/h? round your answer to the nearest tenth of a barrel, if necessary.

A2.3 barrel

A = kdv^2 where A = amount oil d = distance and v = speed and k is a constant
so
30 = k8542^2
Now solve for k:-
k = 30 / (8542^2) = 0.00020008

So when d = 26 and v = 54

Amount of oil A = 0.00020008 26*54^2
= 15.2 barrels

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nishantwork777 nishantwork777 · Answer 2 · 2021-11-19T00:20:39-05:00

The amount of oil used when the ship travels 26 miles at 54 mi/h is 15.2 barrels

Let the amount of oil used by the ship is \(y\) barrels

let the distance traveled be \(s\) miles

Let the velocity of the of the ship be \(v\) miles per hour

then according to the given condition we can write equation (1)

\(y\; \alpha \; s\; v^2\\\\\\y\; = k \; s\; v^2....(1)\\\\\\rm where \; k = constant \; of\; Proportionality\)

Given that ,

Quantity of Oil used by ship = 30 barrels

Speed of the Ship =42 miles per hour

Distance traveled by the ship = 85 miles

Putting these values in equation (1) we can get

\(\rm 30= k\times 85\times\ (42)^2\\k = 0.0002\)

So the equation of amount of oil used can be written as equation (2)

\(y = 0.0002\times sv^2....(2)\)

According to second condition given in the question we can write

\(\rm y = 0.0002\times 26\times (54)^2\\\rm y= 15.2 \; barrels\)

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https://brainly.com/question/21328304