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2 years ago

Prove the following identities:

Mathematics

1 answer:

siniylev [52]2 years ago

7 0

The picture won’t load message me so i can answer !!

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Please please help!! I'm not sure if I have the right answer!!

lana [24]

Answer: The area of the sector formed by central angle AOB is 5/8 th of the total area of the circle.

Step-by-step explanation:

Let r be the radius of the circle having the center O,

⇒ The area of the circle = $\pi r^2$ square unit.

And, the central angle AOB = $\frac{5\pi}{4}\text{ radian}$

$=(\frac{5\pi}{4}\times \frac{180}{\pi})^{\circ}$ ( since, $\pi$ = 180° )

$=(\frac{900}{4})^{\circ}$

$=225^{\circ}$

Hence, the area of sector AOB

$=\frac{225^{\circ}}{360^{\circ}}\times \pi r^2$

$=\frac{5}{8}\times \pi r^2$ square unit.

Now,

$\frac{\text{Area of sector AOB}}{\text{Area of circle}}=\frac{\frac{5}{8}\times \pi r^2}{\pi r^2}$

$=\frac{5}{8}$

⇒ Area of sector AOB = 5/8 × Area of the circle.

Hence, the area of the sector formed by central angle AOB is 5/8 th of the total area of the circle.

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3 years ago

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algol [13]

12 for $25 is $2.08 per each. 24 for $46 is $1.90 per each. 50 for $94 is $1.90 per each.

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Step-by-step explanation: Hope this helps

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2 years ago

Prove the following identities:​

Prove the following identities: