From the figure, let the distance of point P from point A on line segment AB be x and let the angle opposite side a be M and the angle opposite side c be N.
Using pythagoras theorem,

and

Angle θ is given by

Given that a = 4 units, b = 5 units, and c = 9 units, thus

To maximixe angle θ, the differentiation of <span>θ with respect to x must be equal to zero.
i.e.

Given that x is a point on line segment AB, this means that x is a positive number less than 5.
Thus

Therefore, The distance from A of point P, so that </span>angle θ is maximum is 0.51 to two decimal places.
Answer:
a) 0.5 = 50% of flanges exceed 1 millimeter.
b) A thickness of 0.96 millimeters is exceeded by 90% of the flanges
Step-by-step explanation:
A distribution is called uniform if each outcome has the same probability of happening.
The uniform distributon has two bounds, a and b, and the probability of finding a value higher than x is given by:

The thickness of a flange on an aircraft component is uniformly distributed between 0.95 and 1.05 millimeters.
This means that 
(a) Determine the proportion of flanges that exceeds 1.00 millimeters.

0.5 = 50% of flanges exceed 1 millimeter.
(b) What thickness is exceeded by 90% of the flanges?
This is x for which:

So




A thickness of 0.96 millimeters is exceeded by 90% of the flanges
The area model you can use is D , cs 70 +3 & 30+9