The answer is 36. because 12x3=36, 9x4=36, and 4x9=36, so it is the least common denominator
You have to build the triangles.
They are such that:
h is the common height
x is the horizontal distance from the plane to one stone
Beta is the angle between x and the hypotenuse
Then in this triangle: tan(beta) = h / x ......(1)
1 - x is the horizontal distance from the plane to the other stone
alfa is the angle between 1 - x and h
Then, in this triangle: tan (alfa) = h / [1 -x ] ...... (2)
from (1) , x = h / tan(beta)
Substitute this value in (2)
tan(alfa) = h / { [ 1 - h / tan(beta)] } =>
{ [ 1 - h / tan(beta) ] } tan(alfa) = h
[tan(beta) - h] tan(alfa) = h*tan(beta)
tan(beta)tan(alfa) - htan(alfa) = htan(beta)
h [tan(alfa) + tan(beta) ] = tan(beta) tan (alfa)
h = tan(beta)*tan(alfa) / (t an(alfa) + tan(beta) )
The triangle inequality requires the third side be in the range
.. 12 -4 ≤ third side ≤ 12 +4
.. 8 ≤ third side ≤ 16 . . . . . . . . . your answer is the number(s) in this range
_____
Some define the triangle inequality using < rather than ≤. Be careful here.
Center of the door
26 1/3 divided by 2
change to an improper fraction
(3*26+1)/3 =79/3
79/3 divided by 2
copy dot flip
79/3 * 1/2
79/6
change to a mixed number
13 1/6
10 1/4 divided by 2
change to an improper fraction (4*10+1)/2 = 41/4
41/4 divided by 2
copy dot flip
41/4 * 1/2 =41/8
change to a mixed number
5 1/8
the left of the bar should be 5 1/8 from the center
to find how far from the left side to place the bar
13 1/6 - 5 1/8 =
get a common denominator
13 4/24 - 5 3/24= 8 1/24 inches
Answer: place the bar 8 1/24 inches from each edge
F(x + 1) = (5/2)*f(x)
f(x + 1) = 2.5*f(x), f(1) = 3.2
f(2) = 2.5f(1) = 2.5*3.2 = 8
<span>f(3) = 2.5f(2) = 2.5*8 = 20
</span>
f(4) = 2.5f(3) = 2.5*20 = 50
<span>f(5) = 2.5f(4) = 2.5*50 = 125</span>
