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Yogita Ingle 6 years, 2 months ago
Let the level of water in the pond rises by 21 cm in t hours.
Speed of water = 15 km/hr
Diameter of the pipe = 14/100 m
Radius of the pipe (r) = 7/100 m
Volume of water flowing out of the pipe in 1 hour
= π r 2 h
= (22/7) x (7/100) x (7/100) x 15000
= 231 m3
Volume of water flowing out of the pipe in t hours = 231 t m3.
Volume of water in the cuboidal pond
= 50 x 44 x (21/100)
= 462 m3
Volume of water flowing out of the pipe in t hours = Volume of water in the cuboidal pond
So, 231 t = 462
t = 2
Thus, the required time is 2 hours.
Posted by Mukesh Thakur 6 years, 2 months ago
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Yogita Ingle 6 years, 2 months ago
Let √2 + √3 = (a/b) is a rational no.
On squaring both sides , we get
2 + 3 + 2√6 = (a2/b2)
So,5 + 2√6 = (a2/b2) a rational no.
So, 2√6 = (a2/b2) – 5
Since, 2√6 is an irrational no. and (a2/b2) – 5 is a rational no.
So, my contradiction is wrong.
So, (√2 + √3) is an irrational no.
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Yogita Ingle 6 years, 2 months ago
Let √6 be a rational number , then
√6 = p÷q , where p,q are integers , q not = 0 and p,q have no common factors ( except 1 )
=> 6 = p² ÷ q²
=> p² = 2q² ................(i)
As 2 divides 6q² , so 2 divides p² but 2 is a prime number
=> 2 divides p
Let p = 2m , where m is an integer .
Substituting this value of p in (i) , we get
(2m)² = 6q²
=> 2m² = 3q²
As 2 divides 2m² , 2 divides 3q²
=> 2 divides 3 or 2 divide q²
But 2 does not divide 3 , therefore , 2 divides q²
=> 2 divides q
Thus , p and q have a common factor 2 . This contradicts that p and q have no common factors ( except 1 ).
Hence , our supposition is wrong . Therefore , √6 is an irrational number.
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Riya Renavikar 6 years, 2 months ago
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