Answer:

Explanation:
When the rock is immersed in unknown liquid the forces that act on it are shown as under
1) Tension T by the string
2) Weight W of the rock
3) Force of buoyancy due to displaced liquid B
For equilibrium we have 
=
When the rock is suspended in air for equilibrium we have

When the rock is suspended in water for equilibrium we have
+
=
Using the given values of tension and solving α,β,γ simultaneously for
we get

Solving for density of liquid we get


Answer:
method I = 88 chairs
method II = 62 chairs
Explanation:
This problem can be modeled by a system of two linear equations.
Define x as the number of chairs refinished by method I and y by method II
The sum of hours spent on both methods should equal 199 and the sum of total material cost should equal $1226, therefore:


Multiplying the first equation by -18 and adding it to the second equation we can solve for the value of y:

We can now apply the value of y found to the first equation and solve for x:

Therefore, they should refinish 88 chairs with method I and 62 chairs with method II
(60 * 546) / 110 = 297
297 hrs.
No, it will not fall. The pencil will remain at zero speed relative to the spacecraft and will orbit the earth with the spacecraft.