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Jbullon119
01.10.2019 •
Mathematics
Where should the point p be chosen on line segment ab so as to maximize the angle θ? (assume a = 4 units, b = 5 units, and c = 9 units. round your answer to two decimal places.)
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Ответ:
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 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 angle θ is maximum is 0.51 to two decimal places.
Ответ:
The distance from A of point P, so that angle θ is maximum is 0.51.
Given :
a = 4 units
b = 5 units
c = 9 units
Line segment AB.
Solution :
Let AB = x and let the angle opposite side 'a' be
and the angle opposite side 'c' be
.
From the diagram angle
is given by:
From the diagram angle
is given by:
From the diagram angle
is given by:
To maximize the angle
, differentiate equation (1) with respect to x we get,
The distance from A of point P, so that angle
is maximum is 0.51.
For more information, refer the link given below
link
Ответ: