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Fibonacci you crazy bastard….
As seen in the solar system (by no ridiculous coincidence), Earth orbits the Sun 8 times in the same period that Venus orbits the Sun 13 times! Drawing a line between Earth & Venus every week results in a spectacular FIVE side symmetry!!
Lets bring up those Fibonacci numbers again: 1, 1, 2, 3, 5, 8, 13, 21, 34..
So if we imagine planets with Fibonacci orbits, do they create Fibonacci symmetries?!
You bet!! Depicted here is a:
- 2 sided symmetry (5 orbits x 3 orbits)
- 3 sided symmetry (8 orbits x 5 orbits)
- 5 sided symmetry (13 orbits x 8 orbits) - like Earth & Venus
- 8 sided symmetry (21 orbits x 13 orbits)
I wonder if relationships like this exist somewhere in the universe….
Some formulas are plainly beautiful, aren’t they?
If our angle is somewhere between 90° and 180°, that means that angle/2 is somewhere between 45° and 90°
Looking at the graph of the cosine function helps with this:
45° translates into π/4 (radians)
90° translates into π/2
180° translates into π
In the following picture the interval for our angel is orange, the interval for angle/2 blue:
As you can see the cosine-value for the blue interval is always positive, so there you go!
Since an isosceles triangle is by definition “a triangle with at least two equal sides”, your answer is d) 8 or 10, because they could be 8,8,10 or 8,10,10, and it would in any case be still isosceles. Since we don’t have any indication of the equal sides being the longer ones or the shorter ones, we can’t say for sure whether they need to be 8 or 10 :)
All you need is to do a proportion (you can also look at the question I just answered)
So you now that a 6ft tall person casts a 10ft tall shadow, and a x tall tree casts a 35ft shadow
You can also write it as 6:10=x:35 -> (6*35):10 -> the tree has to be 21ft to fit your problem :)
Assuming that 3 inches are 35 actual miles (If I am assuming wrong please correct me, but I don’t really understand what you meant by “1 2 3 inches”), and you need to find out how much 8 inches would be, you just need to put down a proportion.
So you have that 3in:35m=8in:x
So you have (35*8):3= 93,(3)m, which fits, if you consider that 3in are 35m, so 6 inches would be 70m and 8 a bit less than 105m!
Then you need to know how much 75miles would be, and you do just the same thing. You put down the proportion this way
So you have (3*75):35= 6,42~inches
Hope I helped!