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It has been proven that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.
<h3>How to prove a Line Segment?</h3>We know that in a triangle if one angle is 90 degrees, then the other angles have to be acute.
Let us take a line l and from point P as shown in the attached file, that is, not on line l, draw two line segments PN and PM. Let PN be perpendicular to line l and PM is drawn at some other angle.
In ΔPNM, ∠N = 90°
∠P + ∠N + ∠M = 180° (Angle sum property of a triangle)
∠P + ∠M = 90°
Clearly, ∠M is an acute angle.
Thus; ∠M < ∠N
PN < PM (The side opposite to the smaller angle is smaller)
Similarly, by drawing different line segments from P to l, it can be proved that PN is smaller in comparison to all of them. Therefore, it can be observed that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.
Read more about Line segment at; brainly.com/question/2437195
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Answer:
a. 1 263 888
b. 130 701
c. 72 years
Step-by-step explanation:
a. The differential equation applies here.
Let the quantity increase for a certain time be given by Q(t)
Every unity of time, the quantity increases by so that after the time t, the quantity remaining will be given by:
In a similar manner, the quantity R(t) decreases at a rate given by the following expression:
and after the time , t the quantity of R remaining will be given by:
a. To find the population of humans in 1953
1993 - 1953 = 40 years = t
Q(40) = Q×
Q = 1 263 888.44
≈ 1 263 888
b. For bear population in 1993:
t = 40
R(40) =
b = 130 700. 889
≈130 701
c. time taken for black bear population number less than 100 is given by:
130 = 11000×
solving using natural logarithms gives t = 72.72666
= 72 years Ans