We can write,
n = inside triangle size
Label and explain grouping method :
I grouped the covered triangles, each had 3 colored tiles.
That were 3 sets,
3 * 3 = 9
Then I noticed the left over colored border tiles were the same amount as the inner triangles minus 1,
So,
The equation is,
9 + 3(n-1)
3 because triangles have 3 sides
A mathematical expression to represent grouping strategy :
9 + 3(n-1) or 9 + 3(x-4)
Number of green tiles,
= 9 + 3(8-1)
= 9 + 21
= 30
Let us assume, green colored triangles = 72
So,
We can write,
9 + 3(n-1) + (n x n) = 72
9 + 3(n-1) + 
= 72
+ 3n + 8 = 72
+ 3n = 66
+ 3n -66 = 0
Therefore,
The mathematical expression = 9 + 3(n-1)
Learn more about event correlation here: brainly.com/question/8599681
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Step-by-step explanation:
arccos(sin(5π/4))
= arccos(sin(-π/4))
= arccos(-√2/2)
= 3π/4.
Answer:
-17/5 is we are finding the slope slope of a line containing points:
(1,-6) and (-4,11).
Step-by-step explanation:
Line them up and subtract vertically, then put 2nd difference over first difference.
So you can do it like route 1 or 2 listed below:
Route 1)
( 1 , -6)
- (-4 , 11)
------------
Route 2)
(-4 , 11)
- (1 , -6)
-------------
Let's do Route 1 first:
( 1 , -6)
-(-4 , 11)
------------
5 -17
So the slope is -17/5.
Route 2:
(-4 , 11)
-( 1 ,-6)
------------
-5 17
So the slope is 17/-5 or -17/5 which is what we got doing it route 1 way.
So it doesn't matter which point you put on top.
You could also use this formula directly which is what we did without really stating it:
or 
.
So using this formula directly, you could do either:
or 
So first way gives 17/-5 whereas the second way gives -17/5.
You get the same number either way.
Answer:
.
Step-by-step explanation:
The slope of a line is change in Y / change in X.
The slope of a horizontal line = 0, not undefined.
The slope of a vertical line = undefined.
Answer:
The probability of finding a particle in a space is proportional to the square of its absolute value.
In quantum mechanics, there are still chances of find a particle in a classically forbidden region.
That is, finding the ground state harmonic oscillator displaced beyond the classical turning points.
Since there is a chance for finding the ground state harmonic oscillator displaced beyond the classical turning points, the probability (P) will have a value and not equal to Zero( I.e 16%).
By normalization, the probability can be added to 1
This phenomenon is tunneling in quantum mechanics.
Step-by-step explanation:
The motion of a classical oscillator is confined to the region where its kinetic energy is nonnegative.
Physically, it means that a classical oscillator can never be found beyond its turning points, and its energy depends only on how far the turning points are from its equilibrium position. The energy of a classical oscillator changes in a continuous way. The lowest energy that a classical oscillator may have is zero, which corresponds to a situation where an object is at rest at its equilibrium position. The zero-energy state of a classical oscillator simply means no oscillations and no motion at all (a classical particle sitting at the bottom of the potential well.
