<h3>
Answer: Choice C</h3>
{x | x < -12 or x > -6}
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Explanation:
Let's solve the first inequality for x.
(-2/3)x > 8
-2x > 8*3
-2x > 24
x < 24/(-2)
x < -12
The inequality sign flips when we divide both sides by a negative value.
Let's do the same for the second inequality.
(-2/3)x < 4
-2x < 4*3
-2x < 12
x > 12/(-2)
x > -6
The conclusion of each section is that x < -12 or x > -6 which points us to <u>choice C</u> as the final answer.
Side note: The intervals x < -12 and x > -6 do not overlap in any way. There's a gap between the two pieces. We consider these intervals to be disjoint. The number line graph is below.
Answer:
15/32
Step-by-step explanation:
<span>There are equations to calculate the volume of simple geometric objects such as cubes, spheres, cylinders, and cones. Approximate the spacecraft as an assemblage of such objects, calculate the volumes, then add them all up. Example: here.
Create a scale model inside a 3D modeling package, and use the included tools to calculate the internal volume. Example: On my mesh model of the Galactic Cruiser Leif Ericson, the AreaVol script informs me the ship has an internal volumeof 68,784.87 cubic meters.
See if somebody else has already calculated the volume. Example: According to ST-v-SW.Net the internal volume of the TOS Starship Enterprise is 211,248 cubic meters.
Use the known volume of a comparable existing object. Example: a Russian Oscar submarine has a volume of 15,400 cubic meters. It is a good size for a spaceship.
If the spacecraft is approximately a sphere or approximately a cylinder, just use the ship's average radius and height to calculate an approximate volume using the sphere or cylinder volume formulae. Close enough for government work.
Make it up out of your imagination.
Of course there is some differences of opinion on the exact value of the average density of a spacecraft.
One easy figure I've seen in various SF role playing games is a density of 0.1 to 0.2 metric tons per cubic meter (100 to 200 kilograms). That corresponds to average pressure compartments being cubes 10 meters on a side, with pressure bulkheads averaging 17 to 33 kg/m2.
Ken Burnside did some research when he designed his game Attack Vector: Tactical. He found that jet airliners have an average density of about 0.28 metric tons per cubic meter, fighter aircraft 0.35 tons/m3, wet navy warships from 0.5 to 0.6 tons/m3, WWII battleships 0.7 tons/m3 (it don't take much excess mass to send them straight to Davy Jones locker), and submarines 0.9 tons/m3. For the combat spacecraft in AV:T, Ken chose a density of 0.25 tons/m3</span>
Answer:
1. C) 3
2. D) -1
3. D) 7^2 - 8*2 - 16
4. B) 75
5. B) 6^2 + (2 - 8)*sqrt(81)
Step-by-step explanation:
1. (10 - (6-4)^2)/2
= (10 - 2^2)/2
= (10 - 4)/2
= 6/2
= 3
2. PEMDAS states that Multiplication is before Subtraction
8 - (5^2-7)/2
= 8 - (25-7)/2
= 8 - 18/2
= 8 - 9
= -1
3. D) 7^2 - (8*2) - 16
= 49 - 16 - 16
= 49 - 32
= 17
4. 3(2 + 3)^2
= 3(5)^2
= 3(25)
= 75
5. 6^2 + (2 - 8)*sqrt(81)
= 36 + (-6*9)
= 36 - 54
= -18
