The clock has a diameter of 18 inches. At 8 o'clock, what is the area of the sector formed by the two hands of the clock? Round
1 answer:
Answer:
The area of the sector is 84.8 in.² to the nearest tenth
Step-by-step explanation:
∵ the clock is a circle
∴ The measure of angles between each two hours = 360° ÷ 12 = 30°
∵ At 8 o'clock the hour hand pointed on 8 and the minute hand pointed on 12
∴ There are 4 angles between the two hands
∴ The central angle subtended by the arc = 4 × 30° = 120°
∵ The Area of the sector = where x is the central angle subtended by this arc
∴ Area sector = × π × (18/2)²
∴ Area sector = × π ×81 = 27π = 84.8 in² to the nearest tenth
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Step-by-step explanation:
Consider the provided information.
First convert the statement into mathematical representation.
Consider the smaller number is <em>x</em> and the larger number is <em>y</em>.
<em>y</em>, is equal to twice the sum of a smaller number and 3.
This information can be written as:
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The larger number is also equal to 5 more than 3 times the smaller number.
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Thus, the equations represent the situation is and
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Which can be further solve as:
Now, substitute the value of <em>x</em> in .