If y is a positive integer, for how many different values of y is RootIndex 3 StartRoot StartFraction 144 Over y EndFraction End
1 answer:
The value of y will be 18 or 144.
Given information:
The given expression is .
It is required to find the values of y which are whole numbers.
Now, factorize 144 as,
So, for the value of given expression to be a whole number, the value of y should be,
or 144.
For the above values of y, the given expression will be,
Therefore, the value of y will be 18 or 144.
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I'm using the clip from link [1] as a reference, i.e. the shot of the Tantive IV escaping the Devastator towards the camera, which lasts approximately 5 seconds (2:27 - 2:32). I recorded the particular shot, then carried out a cursory frame-by-frame analysis. The shot itself consists of 371 frames.
At around frame 15 - about 0.233s into the clip - one can barely make out a green projectile being launched from one of the Devastator's batteries. It takes the projectile between 19 and 20 frames (I'll round up to 20) - now at frame 35, about 0.333s later - for it to reach the left edge of the camera's field of view.
Let's suppose the Tantive IV was situated in roughly the same physical position in frame 1 as the projectile was in frame 35.
Now, the Tantive IV exits the screen at around frame 182 - about 3.017s into the clip. According to link [2], the standard CR90 "Corellian" Corvette can reach speeds of up to 950km/h. The Rebels are fleeing the Empire, so it's reasonable to assume that they are moving as fast as they can. Let's also assume they're traveling at a constant rate, and that the tractor beam aboard the Devastator hasn't been activated yet.
Note: Link [2] refers to this maximum speed as "atmosphere speed". I can't find any references as to what this means, so I assume it means something along the lines of "same conditions as Earth's atmosphere". The two ships are flying above Tatooine, which is inhabited in part by humans, so it's probably a safe bet that the atmospheres of Tatooine and Earth aren't that dissimilar.
So if it takes the Tantive IV about 3.017s to move (approximately) the same distance as the Devastator's projectile, and if we assume the Tantive IV is moving at maximum speed, then it must have traveled a distance
of (approximately)
However, it's quite clear from the previous shot that the assumption above is not all that accurate. So let's consider "your" assumption, that the distance between the Tantive IV and the Devastator is about 10 times its own length, i.e.
. Now, if the projectile takes about 0.333s to travel the same distance, then it must have moving at a speed 
of (approximately)
I'm using the clip from link [1] as a reference, i.e. the shot of the Tantive IV escaping the Devastator towards the camera, which lasts approximately 5 seconds (2:27 - 2:32). I recorded the particular shot, then carried out a cursory frame-by-frame analysis. The shot itself consists of 371 frames.
At around frame 15 - about 0.233s into the clip - one can barely make out a green projectile being launched from one of the Devastator's batteries. It takes the projectile between 19 and 20 frames (I'll round up to 20) - now at frame 35, about 0.333s later - for it to reach the left edge of the camera's field of view.
Let's suppose the Tantive IV was situated in roughly the same physical position in frame 1 as the projectile was in frame 35.
Now, the Tantive IV exits the screen at around frame 182 - about 3.017s into the clip. According to link [2], the standard CR90 "Corellian" Corvette can reach speeds of up to 950km/h. The Rebels are fleeing the Empire, so it's reasonable to assume that they are moving as fast as they can. Let's also assume they're traveling at a constant rate, and that the tractor beam aboard the Devastator hasn't been activated yet.
Note: Link [2] refers to this maximum speed as "atmosphere speed". I can't find any references as to what this means, so I assume it means something along the lines of "same conditions as Earth's atmosphere". The two ships are flying above Tatooine, which is inhabited in part by humans, so it's probably a safe bet that the atmospheres of Tatooine and Earth aren't that dissimilar.
So if it takes the Tantive IV about 3.017s to move (approximately) the same distance as the Devastator's projectile, and if we assume the Tantive IV is moving at maximum speed, then it must have traveled a distance
However, it's quite clear from the previous shot that the assumption above is not all that accurate. So let's consider "your" assumption, that the distance between the Tantive IV and the Devastator is about 10 times its own length, i.e.