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Sia ? 6 years, 6 months ago

Let x be the radius of the semi-circular path.
Given, perimeter of circular path = 72
{tex} \Rightarrow 2r + \pi r = 72{/tex}
{tex} \Rightarrow r\left( {2 + \pi } \right) = 72{/tex}
{tex} \Rightarrow r\left( {2 + \frac{{22}}{7}} \right) = 72{/tex}
{tex} \Rightarrow r \times \frac{{36}}{7} = 72{/tex}
{tex}\therefore {/tex} Radius of semi-circular grassy plot = 14m
Since a path of width 3.5 m runs around a semi-circular grassy plot whose Perimeter is 72 m
Then, radius of outer semi-circle = 14m + 3.5m = 17.5m
Area of the path = Area of outer semi-circle-Area of inner semi-circle
{tex} = \frac{1}{2}\pi {\left( {17.5} \right)^2} - \frac{1}{2}\pi {\left( {14} \right)^2}{/tex}
{tex} = \frac{1}{2} \times \frac{{22}}{7}\left[ {{{\left( {17.5} \right)}^2} - {{\left( {14} \right)}^2}} \right]{/tex}
{tex} = \frac{{11}}{7}\left[ {31.5 \times 3.5} \right]{/tex}
= 173.25m2
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Sia ? 6 years, 6 months ago
Let a be the first term and d be the common difference of the given A.P. Then,
pth term = q {tex}\Rightarrow{/tex}a + (p-1) d = q ...(i)
qth term = p {tex}\Rightarrow{/tex}a + (q-1) d = p ...(ii)
Subtracting equation (ii) from equation (i), we get
(p - q) d = (q - p) {tex}\Rightarrow{/tex} d = -1
Putting d = - 1 in equation (i), we get
a + ( p-1) × (-1) = q
⇒ a = (p + q - 1)
nth term = a + (n -1 )d
= (p + q - 1)+ (n -1) × (-1)
= p + q - 1 -n + 1
= (p + q - n)
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Raghav Hr 81 Alla Bhaman 6 years, 10 months ago
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