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the ship is less dense than the water, hence why it floats

density is the amount of mass that's packed into a given volume or space.

the ship has less density than the water because it takes up a large amount of space
therefore it floats

What is the limit on n? Because n may go to infinity !!

The angle is 180 - x -y .

D = R*r/d.

Stop trying to cheat on your homework.

The answer is 4/5 <= m <= 5/4.

The answer is 72.

The answer is 36 sides.

1. The slope of the line is 5/4.

2. The largest possible value of x is 5*sqrt(2).

The radius is 65/8.

b + c = (-7) + 12 = 5.

Let's make the solution super-formal!  We can write -4 in exponential notation as 4e^(pi*i), so the equation is z^4 = 4e^(pi*i).

By Hamilton's Theorem, the solutions are z = 4^{1/4}*e^(pi*i/4), 4^{1/4}*e^(pi*i/4 + pi/4), 4^{1/4}*e^(pi*i/4 + 2*pi/4), and 4^{1/4}*e^(pi*i/4 + 3*pi/4).  Since 4^{1/4} = sqrt(2) and e^(pi*i/4) = (1 + i)/sqrt(2), the first solution is 1 + i.  Then the other roots work out as

4^{1/4}*e^(pi*i/4 + pi/4) = 1 - i,

4^{1/4}*e^(pi*i/4 + 2*pi/4) = -1 - i, and

4^{1/4}*e^(pi*i/4 + 3*pi/4) = -1 + i.

The x-coordinates of the x-intercept is -1.

x = -0.2t³ + 0.06t² + 10 [m] 
v_x = x' = -0.6t² + 0.12t [m/s]
a_x = v_x' = -1.2t + 0.12 [m/s²]
a_x(1) = -1.08 m/s²

ΣF_x = ma_x = (180kg)(-1.08m/s²) = -194.4N

y = 0.1t² + 0.4t + 6 [m]
v_y = y' = 0.2t + 0.4 [m/s]
a_y = v_y' = 0.2 [m/s²]

ΣF_y = ma_y = (180kg)(0.2m/s² + 9.8m/s²) = 1800N

The largest value of a is 4.

That answer is wrong.

Please do not cheat on your AoPS homework. This is also copyright infringement as AoPS copyrights their problems. If you need help with a problem, please ask it on your classroom message board. That is a much better place as it is not considered cheating. Judging by the fact you have chosen to title it "urgent," I suggest you refrain on procrastinating to avoid a situation in which you decide to last-minute cheat. AoPS is a very good resource - learn from it! 

y=3-x is a line, so the slope is going to be the same everywhere on that line

we can pick two points on the line
x₁ = 0, y₁ = 3
x₂ = 1, y₂ = 2
(you could pick any two points)

slope = (y₂ - y₁) / (x₂ - x₁) = (2 - 3) / (1 - 0) = -1
slope = -1

Here is my new account. I have accidentally posted twice as a guest. 

In triangle ABC, angle BAC = 45 degrees, and AD is perpendicular to BC.  If BD = 3 and CD = 2, then find the area of triangle ABC.

Area = 15 units squared  

I have created an account. I look forward to my expierience on this site. 

Stop trying to cheat on your homework.

Stop trying to cheat on your homework.