Atrailer carrying a boat is supported by a scale which initially reads 48 kg. the boat (and therefore its centre of gravity) is moved 0.15 m further back on the trailer. the scale now reads 37 kg. find the mass of the boat.

a. 3400 kg b. 1700 kg c. 1600 kg d. 440 kg

440 kg
view the diagram of the torques

let fg be the force of gravity exerted by the boat from its center of gravity
let x be the initial distance from the wheel pivot point.

rotational equilibrium so net torques ∑τ are equal to zero

we choose the pivot point to be the wheel so that we take advantage of both the 6m and the scale readings.

the scale readings mean that much mass is on it, so that means there is some gravity on it: mg = m(9.81m/s²)

before the boat is moved
∑τ = fg*x + (48 kg)(9.81 m/s²)(6 m) = 0 (i)

after the boat is moved
∑τ = fg*(x-0.15 m) + (37kg)(9.81 m/s²)(6m) = 0 (ii)

solve for x in (i)

fg * x + (48 kg)(9.81 m/s²)(6 m) = 0
fg * x  + 2825.28 nm = 0
x = -2825.28 nm / fg

substitute into (ii)

fg*(x-0.15m) + (37kg)(9.81 m/s²)(6m) = 0
fg*[ (-2825.28 nm / fg) - 0.15m] + 2177.82 nm = 0
-2825.28 nm - fg 0.15 m + 2177.82 nm = 0

-fg 0.15 m = 647.46 nm
fg = 4316 . 4 n

so the mass is

fg = mg
m = fg / g
m = (4316.4 n) / (9.81 m/s²)
m = 440 kg

440 kg

Liquid. good luck : )

Neptune is the eighth planet from the sun. it was the first planet to get its existence predicted by  mathematical calculations  before it was actually seen through a telescope on sept. 23, 1846. irregularities in the orbit of  uranus  led french astronomer alexis bouvard to suggest that the gravitational pull from another celestial body might be responsible. german astronomer johann galle then relied on subsequent calculations to   spot neptune via telescope. previously, astronomer galileo galilei sketched the planet, but he mistook it for a star due to its slow motion. in accordance with all the other planets seen in the sky, this new world was given a name from greek and roman mythology — neptune, the roman god of the sea.