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Sia ? 6 years, 6 months ago
Length = 8 m 50 cm = 850 cm
breadth = 6 m 25 cm = 625 cm
height = 4 m 75 cm = 475 cm
length of the longest rod is equal to
HCF of 850, 625 and 475
Now on factorization we get
850=2×25×17=2×52×17
625=25×25=54
475=25×19=52×19
HCF(475,625, 850) = 52=25
{tex}\because{/tex} HCF is 25, so the longest rod that can measure the dimensions of the room exactly = 25 cm
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Sia ? 6 years, 6 months ago
Given equations are
{tex}\frac{x}{2} + y = 0.8{/tex}
{tex}\frac{x + 2y}{2} = 0.8{/tex}.
x + 2y = 1.6 ........ (i)
and
{tex}\frac{7}{{x + \frac{y}{2}}} = 10{/tex}
{tex}\frac{{7 \times 2}}{{2x + y}} = 10{/tex}
{tex}\frac{{7}}{{2x + y}} = 5{/tex}
7 = 10x + 5y
10x + 5y = 7 .......... (ii)
Multiply first equation by 10
10x + 20y = 16............ (iii)
Subtracting the equations (ii) from (iii) , we get
15y = 9
{tex}y = \frac{9}{{15}} = \frac{3}{5}{/tex}
Put value of y in (i)
{tex}x = 1.6 - 2\left( {\frac{3}{5}} \right) = 1.6 - \frac{6}{5} = \frac{2}{5}{/tex}
Solution is {tex}\left( {\frac{2}{5},\;\frac{3}{5}} \right){/tex}
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Sia ? 6 years, 4 months ago
The given polynomial is 3x3 + x2 + 2x + 5
According to Division Algorithm,
Dividend = Quotient x Divisor + Remainder
{tex}\Rightarrow{/tex} f(x) = {tex}q ( x ) \times g ( x ) + r ( x ){/tex}
{tex}\Rightarrow g ( x ) = \frac { f ( x ) - r( x ) } { g ( x ) }{/tex}
Here,
f(x) = 3x3 + x2 + 2x + 5
q(x) = 3x - 5
r(x) = 9x + 10
{tex}g ( x ) = \frac { \left( 3 x ^ { 3 } + x ^ { 2 } + 2 x + 5 \right) - ( 9 x + 10 ) } { ( 3 x - 5 ) } = \frac { 3 x ^ { 3 } + x ^ { 2 } - 7 x - 5 } { 3 x - 5 }{/tex}
{tex}\therefore{/tex} g(x) = x2 + 2x + 1.
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