$\bf \textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\[-0.5em] \hrulefill\\ A=10\\ r=12 \end{cases}\implies 10=\cfrac{\theta \pi 12^2}{360}\implies 10=\cfrac{2\pi \theta }{5} \\\\\\ 20=2\pi \theta \implies \cfrac{20}{2\pi }=\theta \implies \cfrac{10}{\pi }=\theta \implies 3.18\approx \theta$

6 0

3 years ago

9 to the power 18 = 27 to the power x work out the value of x

Strike441 [17]

Answer:

Step-by-step explanation:

27^x = 9÷(3^x)

So (3^3)^x = (3^2)÷(3^x)

So 3^3x = 3^(2-x)

Comparing powers on both sides,

3x = 2 - x

So, 4x = 2

So, x = 1/2

Given ( 27 ) ^ x = 9 / 3 ^x

⇒ ( 3 × 3 × 3 )^x = ( 3 × 3 ) / 3^x

⇒ ( 3 ³ )^x = 3² / 3^x

⇒ 3 ^ 3x × 3^x = 3² [ since ( a ^m)^n = a ^mn ]

⇒ 3^ (3x +x) = 3² [ since a^m × a^n = a ^m+n ]

⇒ 3^4x = 3²

⇒4x = 2 [ since If a ^m = a ^n then m = n ]

⇒ x = 2 / 4

∴ x = 1 / 2

I hope this helps you.

8 0

3 years ago