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3 years ago

The speedometer needle in a car is 2.5 inches long. When accelerating from 0 to 60 miles per hour the needle

Mathematics

1 answer:

melamori03 [73]3 years ago

7 0

The arc length traveled by the needle is 7.0904 $in^{2}$

Step-by-step explanation:

Step 1

In the above question are given that

The speedometer needle in a car is 2.5 inches long

The needle sweeps out an arc of 130°.

Let r be the length of the speedometer needle,So

r=2.5

m∠C=130°

Step 2

The formula for determining the area of the sector is

A= $\frac{m}{360}$ * $\pi r^{2}$

Where,the central angle is m°

and The radius is r

Substituting the value of m and r from the step 1 in the below equation we get

A= $\frac{130}{360}$ * $\pi *2.5^{2}$

A= 0.3611* $\pi$ *6.5=7.0904 $in^{2}$

Hence the value of the Area of the sector is = 7.0904 $in^{2}$

Step 3

So, the arc length traveled by the needle 7.0904 $in^{2}$

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