Question

find the circumference of circle with area 1/4rd2

Answer 1

area = 1/4*pi*d*d

pi*r*r=pi*d*d*1/4

Canceling pi both sides

r*r=d*d/4

Square rooting both side,

r=d/2

circumference=2*pi*r

=2*pi*d/2

=pi*d cm

Answer 2

$\underline{\underline{\bold{\red{\: \:(1)\:\: QUESTION\: \:}}}}$ ➡

$\bold{\: \:Find \: \: the \: \: value \: \: of \: \: \frac{1}{x {}^{0} } \: }$

$\underline{\underline{\bold{\red{\: \: SOLUTION\: \:}}}}$➡

$\bold{We \: \: know \: \: that,} \\ \\ \boxed{ \bold{(Any \: \: number) {}^{0} = 1}} \\ \\ \bold{So,} \\ \\ \bold{ \underline{ \: x {}^{0} = 1 \: }\: \: \: - - - - - - > (1) } \\ \\ \bold{Now,} \\ \\ \bold{ \frac{1}{x {}^{0} } = \frac{1}{1} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [From(1)]} \\ \\ = > \boxed{\bold{ \frac{1}{x {}^{0} } = 1 }}$

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$\underline{\underline{\bold{\red{\: \: (2) \: \: QUESTION\: \:}}}}$➡

$\bold{Find \: \: the \: \: circumference \: \: of \: \: circle} \\ \bold{with \: \: area \: \: \frac{1}{4} \pi \: d {}^{2} \: \:cm {}^{2} \: .}$

$\underline{\underline{\bold{\red{\: \: SOLUTION\: \:}}}}$➡

$\bold{Let,} \\ \\ \bold{The \: \: radius \: \: of \: \: the \: \: circle \: = r \: \: cm} \\ \\ \bold{So ,\: \: \: the \: \: area \: \: of \: \: the \: \: circle = \pi \: r {}^{2} \: \: c m {}^{2} } \\ \\ \bold{Given,} \\ \\ \bold{Area \: \: of \: \: the \: \: circle = \frac{1}{4}\pi \: d {}^{2} \: \: cm {}^{2} } \\ \\ \bold{ = > \pi \: r {}^{2} = \frac{1}{4}\pi \: d {}^{2} } \\ \\ \bold{ = > r {}^{2} = \frac{d {}^{2} }{4} } \\ \\ \bold{ = > r {}^{2} = ( \frac{d}{2} ) {}^{2} } \\ \\ \bold{ = > r = \frac{d}{2} \: \: cm } \\ \\ \bold{Radius \: \: of \: \: the \: \: circle = \frac{d}{2} \: \: \: cm} \\ \\ \bold{Now,} \\ \\ \bold{If \: \: the \: \: radius \: \: of \: \: circle = r \: ,\: then} \\ \bold{The \: \: circumference \: \: of \: \: the} \\ \bold{ \: \: circle =2\pi \: r } \\ \\ \bold{ = 2 \times \pi \: \times \frac{d}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: (as \: \: r = \frac{d}{2} )} \\ \\ \bold{ = \pi \: d} \\ \\ \\ \boxed{\bold{Circumference \: \: of \: \: the \: \: circle = \pi \: d \: \: \: cm}}$

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$\underline{\underline{\bold{\red{\: \:(3) \: \: QUESTION\: \:}}}}$➡

$\bold{Find \: \: the \: \: value \: \: of \: \: 6 - x {}^{0} }$

$\underline{\underline{\bold{\red{\: \: SOLUTION\: \:}}}}$➡

$\bold{We \: \: know \: \: that,} \\ \\ \boxed{ \bold{(any \: \: number) {}^{0} = 1}} \\ \\ \bold{So,} \\ \\ \bold{ \underline{ \: x {}^{0} = 1 \: } \: - - - - - - - > (1)} \\ \\ \bold{Now} \\ \\ \bold{6 - x {}^{0} = 6 - 1 \: \: \: \: \: \: \: \: \: \: [from(1)]} \\ \\ = > \boxed{ \bold{ 6 - x {}^{ 0} = 5 }}$

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✝$\mathfrak{ \red{ \: \: THANKS..}}$✝