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Maths Puzzle
Shamu has to get home from his school to do some chores for his mother. The distance between the house and school is 3km if he walks along a straight line. Instead Shamu decides to go along two line segments to reach home such that, throughout his route , he is getting closer to home. What is the length (in km) of the longest route he can take? The figure below shows a valid and an invalid route that Shamu can take.
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- To saisfy the condition "Instead Shamu decides to go along two line segments to reach home such that, throughout his route , he is getting closer to home" he must walk alon two mutually perpendicular paths
Let the length of one segment be 'x' and other 'y'
Hence x²+y²=3²=9
Maximise z=x+y
x²+y²=9
→ x²=9 −y²
→x=√(9 −y²)
z=x+y
→ z=√(9 −y²)+y
→dz/dy= {1/{2√(9 −y²)}]×(−2y)+1
= −y/√(9 −y²)+1
For z to be maximum or minimum dz/dy=0 →−y/√(9 −y²)}+1=0
i.e −y/√(9 −y²)}=−1
Hence either y= √(9 −y²)
i.e y² =(9 −y²)
0r 2y² =9 an y= √(9/2) =3√2/2
hence x= √(9 −y²) =√(9 −9/2) =3√2/2
Hence maximum distance = 3√2/2+3√2/2=3√2 - 11 years agoHelpfull: Yes(0) No(0)
- Shamu has to get home from his school to do some chores for his mother. The distance between the house and school is 3km if he walks along a straight line. Instead Shamu decides to go along two line segments to reach home such that, throughout his route , he is getting closer to home. What is the length (in km) of the longest route he can take? The figure below shows a valid and an invalid route that Shamu can tak
- 10 years agoHelpfull: Yes(0) No(0)
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