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Sia ? 6 years, 4 months ago
Let the first term and common difference of an A.P. be a & d respectively.
nth term of an A.P. is an = a + (n -1)d
Given that,
a9 = -32
{tex}\Rightarrow{/tex} a+8d= -32...(i)
Also given,
a11+a13= -94
{tex}\Rightarrow{/tex} (a + 10d) + (a + 12d) = -94
{tex}\Rightarrow{/tex} 2a + 22d = -94
{tex}\Rightarrow{/tex} a + 11d = -47...(ii)
Subtracting (i) from (ii).
11d - 8d = -47 - (-32)
Or, 3d = -47+32
Or, 3d = - 15
Or, d = -5
So, the common difference is -5.
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Sia ? 6 years, 4 months ago
{tex}\frac{x}{2}{/tex} + y = 0.8
{tex}\Rightarrow{/tex} x + 2y = 1.6
{tex}\Rightarrow{/tex} x = 1.6 - 2y ...........(i)
and {tex}\frac{7}{x+\frac{y}{2}}=10{/tex}
{tex} \Rightarrow \frac{14}{2 x+y}{/tex} = 10
{tex}\Rightarrow{/tex} 20x + 10y = 14
{tex}\Rightarrow{/tex} 10x + 5y = 7 ..........(ii)
Put (i) in (ii), we get
10(1.6 - 2y) + 5y = 7
{tex}\Rightarrow{/tex} 16 - 20y + 5y = 7
{tex}\Rightarrow{/tex} -15y = -9
{tex}\Rightarrow{/tex} y = {tex}\frac{9}{15}{/tex} = 0.6
Put y = 0.6 in equation (i), we get
x = 1.6 - 2(0.6)
x = 0.4
Hence x = 0.4 and y = 0.6 is the solution of given system of equations.
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Shivam Sharma 6 years, 4 months ago
2Thank You