48 is the answer.I hope this helps
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.
Yes, the two fractions are equivalent because you can find a greatest common factor in both the numbers. In this case, the GCF is 4 because it goes into both 4 and 8. Then, you divide each part of the fraction by 4. Then, you get the answer 1/2. Therefore, the fractions are equivalent.