if you build a shortest distance for a sightseeing train around the mountain in which the track starts at point A and ends at point B, the track will first go uphill but than it will go down hill.
What is the length of this downhill track?
Explain me well.. For 50 points...
Aaj he to question post Kiya h
Plzz solve..
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Answers
Answer:
400/√91
Step-by-step explanation:
if you cut open a right circular cone, it will unwrap into a circular arc.↑↑
cone's base radius = 20
so, circumference = 2πr
⇒2π(20)
⇒40π
cone's vertex =∅
length circular arc = R∅
= (40 /60)π
= 2π/3
so, the cone's vertex = 2π/3
point a is along thee base, point b is 10 unit from the base and the track goes around the cone. so place point b on the opposite side .
the shortest path from a to b → straight line on the circular arc.
law of coinses ·····
c²= a²+b²- 2ab cosC
AB² = 60² + 50² - 2(60)(50)cos 2π/3
AB² = 9100
AB = 10 √91
downhill portion of the path:
⇒ The uphill part of AB is increasing distance from the cone's base.
( equivalently decreasing distance from the cone's vertex ).
⇒the downhill part of AB is decreasing distance from the cone's base(equivalently increasing distance from the cone's vertex).
⇒the downhill part AB begins when the line is the closest to the cone 's vertex which is perpendicular to AB .
⇒The downhill part of AB is decreasing distance from the cone's base (equivalently increasing distance to the cone's vertex).
ab = 10√91
to find downhill length :
downhill = x
uphill = 10√91 -x
by the pythagorean theorem..
(10√91 - x) = h² = 60²
x² + h²= 50²
9100 -2 (10√91)x = 60² - 50²
(20√91)x = 8000
x = 400/√91
Your Answer is in the Attachment......
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