Answer: b) they loaded 112356 lbs of cargo
Step-by-step explanation:
When a boat or an object floats in water, the volume of water that it displaces is equivalent to its weight.
When moving into the port, the cargo boat displaced 2200 ft³ of water. Since the density of water is 62.42 lb/ft³ and mass = density × volume, then the mass of the cargo boat on entering the port is
2200 × 62.42 = 137324 lbs
On leaving the port, it displaces 4000 ft³ of water. The mass of the cargo boat on leaving the port is
4000 × 62.42 = 249680 lbs
The difference in both masses is
249680 - 137324 = 112356 lbs
Therefore, they loaded 112356 lbs of cargo
Answer:
x = -9, -3
Step-by-step explanation:
x = -3, -9
Let the three consecutive equals:
x, x+1, x+2
sum:
x+(x+1)+(x+2) = 36
3x + 3 = 36
x+1 = 36/3
x+1 = 12
x=12-1
x=11
Problem 7: Correct
Problem 8: Correct
Problem 9: Correct
The steps are below if you are curious
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Problem 7
S = 180*(n-2)
2340 = 180*(n-2)
2340/180 = n-2
13 = n-2
n-2 = 13
n = 13+2
n = 15
I'm using n in place of lowercase s, but the idea is the same. If anything, it is better to use n for the number of sides since S already stands for the sum of the interior angles. I'm not sure why your teacher decided to swap things like that.
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Problem 8
First find y
y+116 = 180
y+116-116 = 180-116
y = 64
which is then used to find x. The quadrilateral angles add up to 180*(n-2) = 180*(4-2) = 360 degrees
Add up the 4 angles, set the sum equal to 360, solve for x
x+y+125+72 = 360
x+64+125+72 = 360 ... substitution (plug in y = 64)
x+261 = 360
x+261-261 = 360-261
x = 99
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Problem 9
With any polygon, the sum of the exterior angles is always 360 degrees
The first two exterior angles add to 264. The missing exterior angle is x
x+264 = 360
x+264-264 = 360-264
x = 96
