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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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Answer:

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Step-by-step explanation:

The width of a square is its side length.

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$\sf \textsf{Area of a square}=s^2 \quad \textsf{(where s is the side length)}$

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$\sf \textsf{Radius of a circle}=\dfrac{1}{2}d \quad \textsf{(where d is the diameter)}$

If the diameter is equal to the side length of the square, then:
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Therefore:

$\begin{aligned}\implies \sf Area\:of\:circle & = \sf \pi \left(\dfrac{s}{2}\right)^2\\& = \sf \pi \left(\dfrac{s^2}{4}\right)\\& = \sf \dfrac{1}{4}\pi s^2 \end{aligned}$

So the ratio of the area of the circle to the original square is:

$\begin{aligned}\textsf{area of circle} & :\textsf{area of square}\\\sf \dfrac{1}{4}\pi s^2 & : \sf s^2\\\sf \dfrac{1}{4}\pi & : 1\end{aligned}$

Given:

side length (s) = 6 in
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$\implies \sf \textsf{Area of square}=6^2=36\:in^2$

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Ratio of circle to square:

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The area of the shaded region is 8.1838. The area of the shaded region is calculated by subtracting the area of the triangle from the area of the sector of the circle.

<h3>How to calculate the area of the sector?</h3>

The area of the sector of a circle with a radius 'r' and an angle of sector 'θ' is

A = (θ/360) πr² sq. units

<h3>How to calculate the area of a triangle with an angle?</h3>

The area of the triangle with measures of two sides and an angle between them is

A = 1/2 × a × b × sinC sq. units

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<h3>Calculation:</h3>

It is given that,

The area of the sector shown in the diagram is 78.6794 cm² and the area of the triangle is 70.4956 cm².

Then to calculate the area of the shaded region, subtract the area of the sector and the area of the triangle. I.e.,

Area of the shaded region = Area of the sector - Area of the triangle

⇒ 78.6794 - 70.4956

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Therefore, the required area of the shaded region is 8.1838 sq. cm.

Learn more about the area of a sector here:

brainly.com/question/22972014

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