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Sia ? 6 years, 4 months ago
Let the speed of boat is x km/h in still water and stream y km/h
According to question,
{tex}\frac{{30}}{{x - y}} + \frac{{44}}{{x + y}} = 10{/tex}
and {tex}\frac{{40}}{{x - y}} + \frac{{55}}{{x + y}} = 13{/tex}
Let {tex}\frac{1}{{x - y}} = u{/tex} and {tex}\frac{1}{{x + y}} = v{/tex}
30u + 44v = 10 ...(i)
40u + 55v = 13 ....(ii)
on solving eq. (i) and (ii) we get,
{tex}u = \frac{1}{5} \Rightarrow x - y = 5{/tex} ....(iii)
{tex}v = \frac{1}{{11}} \Rightarrow x + y = 11{/tex} ....(iv)
On solving eq. (iii) and (iv) we get,
x = 8km/h
y = 3km/h
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Balasaheb Ingle 6 years, 10 months ago
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Sia ? 6 years, 4 months ago
If a and b are odd numbers then it should be in 2q+1 or 2q+3 form where q is a positive integer.
Let a = 2q + 3 , b = 2q + 1 and a > b
Now, {tex}\frac{a + b } {2} = \frac{ 2q + 3 + 2q + 1}{2}{/tex}
{tex}= \frac { 4 q + 4 } { 2 }{/tex}
= 2q + 2
{tex}\frac{a+b}{2}{/tex}=2(q+1) = an even number..........(1)
Now
{tex}\frac { a - b } { 2 } = \frac { ( 2 q + 3 ) - ( 2 q + 1 ) } { 2 }{/tex}
{tex}= \frac { 2 q + 3 - 2 q - 1 } { 2 }{/tex}
{tex}\frac{a-b}{2}= \frac { 2 } { 2 }{/tex} = 1 = an odd number..........(2)
Hence From (1) and (2) {tex}\frac{a+b}{2}{/tex} and {tex}\frac{a-b}{2}{/tex} are even and odd numbers respectively
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Ram Kushwah 6 years, 10 months ago
Zero of any polynomial f(x) is the value of x for which f(x)=0
e.g. for f(x)=x2-3x+2
x=1 and 2 are zero
then f(1)=0 and f(2)=0
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Kamboj Ji 6 years, 10 months ago
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