False
Explanation:
Called an asteroid for many years, Ceres is so much bigger and so different from its rocky neighbors that scientists classified it as a dwarf planet in 2006. Even though Ceres comprises 25 percent of the asteroid belt's total mass, tiny Pluto is still 14 times more massive.
Answer:
Explanation:
The apple also exerts an equal and opposite force on the earth but earth does not move because the mass of apple is very small,due to which the gravitational force produces a large acceleration in it (a=F/m) and we can see the apple falling towards the earth but the mass of earth is very large,the same gravitational .
Answer:
The actual elevation angle is 12.87 degrees
Explanation:
In the attachment you can clearly see the situation. The angle of elevation as seen for the scuba diver is shown in magenta, we conclude that 
.
Using Snell's Law we can write:
,
Let's approximate the index of refraction of the air (medium 1 in the picture) to 1.
We thus have:
![\implies\theta_1=\arcsin[n_2\sin(\theta_2)]=\arcsin[1.333\sin(47)]\approx 77.13](https://tex.z-dn.net/?f=%5Cimplies%5Ctheta_1%3D%5Carcsin%5Bn_2%5Csin%28%5Ctheta_2%29%5D%3D%5Carcsin%5B1.333%5Csin%2847%29%5D%5Capprox%2077.13)
. Calling 
the actual angle of elevation, we get from the picture that 
Either 175 N or 157 N depending upon how the value of 48° was measured from.
You didn't mention if the angle of 48° is from the lug wrench itself, or if it's from the normal to the lug wrench. So I'll solve for both cases and you'll need to select the desired answer.
Since we need a torque of 55 N·m to loosen the nut and our lug wrench is 0.47 m long, that means that we need 55 N·m / 0.47 m = 117 N of usefully applied force in order to loosen the nut. This figure will be used for both possible angles.
Ideally, the force will have a 0° degree difference from the normal and 100% of the force will be usefully applied. Any value greater than 0° will have the exerted force reduced by the cosine of the angle from the normal. Hence the term "cosine loss".
If the angle of 48° is from the normal to the lug wrench, the usefully applied power will be:
U = F*cos(48)
where
U = Useful force
F = Force applied
So solving for F and calculating gives:
U = F*cos(48)
U/cos(48) = F
117 N/0.669130606 = F
174.8537563 N = F
So 175 Newtons of force is required in this situation.
If the 48° is from the lug wrench itself, that means that the force is 90° - 48° = 42° from the normal. So doing the calculation again (this time from where we started plugging in values) we get
U/cos(42) = F
117/0.743144825 = F
157.4390294 = F
Or 157 Newtons is required for this case.
From the formula of W = F·d , becuase we have the values for W and d we can find F
W = F·d
F= W/d
= 250/5
= 50 N
40 N of force was applied
