A cruise ship charges $125 per night for a room. There are 250 rooms on the ship. If every room on the ship is booked, how much money does the cruise ship make in a single night?

Jensen Mclean
2022-09-29
Answered

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Derick Ortiz

Answered 2022-09-30
Author has **11** answers

Let the cruise ship's profit by represented by P and the amount of rooms booked be represented by r. We can represent this by the equation

P=125r, as we're told that each room r costs $125.

So, if there are 250 rooms booked, the we simply plug in r=250 into the above equation for the profit:

P=125(250)=31250

The cruise ship makes $31,250.

P=125r, as we're told that each room r costs $125.

So, if there are 250 rooms booked, the we simply plug in r=250 into the above equation for the profit:

P=125(250)=31250

The cruise ship makes $31,250.

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${\int}_{\mathrm{\partial}\mathrm{\Omega}}\overrightarrow{V}\rho \overrightarrow{V}\cdot \overrightarrow{dS}+{\int}_{\mathrm{\partial}\mathrm{\Omega}}p\overrightarrow{dS}=0$

According to the Gauss theorem for a closed surface $S$:

${\iint}_{S}\overrightarrow{A}\cdot \overrightarrow{dS}={\iiint}_{V}\mathrm{\nabla}\cdot \overrightarrow{A}dV$

But if I apply that to the above equation I get

${\int}_{\mathrm{\partial}\mathrm{\Omega}}\overrightarrow{V}\rho \overrightarrow{V}\cdot \overrightarrow{dS}={\int}_{\mathrm{\Omega}}\mathrm{\nabla}\cdot (\overrightarrow{V}\rho \overrightarrow{V})dV=\phantom{\rule{0ex}{0ex}}\phantom{\rule{1em}{0ex}}{\int}_{\mathrm{\Omega}}(\mathrm{\nabla}\cdot \overrightarrow{V})\rho \overrightarrow{V}dV$

Which can't be right, since for an incompressible flow $\mathrm{\nabla}\cdot \overrightarrow{V}=0$.

Isn't the dot product supposed to be commutative? What am I missing?

I apologize for any misuse of mathematical notation, let me know of any mistakes.

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