   Chapter 8.1, Problem 49E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Arc Length In Exercises 47-50, use the following information, as shown in the figure. For a circle of radius r, a central angle θ (in radians) intercepts an arc of length s given by s = r θ . Instrumentation The pointer of a voltmeter is 6 centimeters in length (see figure). Find the angle (in radians and degrees) through which the pointer rotates when it moves 2.5 centimeters on the scale. To determine

To calculate: The angle moved by pointer of the voltmeter in both radians and in degrees if rotation of pointer on the scale is 2.5 cm, and its length is 6 cm.

Explanation

Given Information:

The rotation of pointer on the scale is 2.5 cm and its length is 6 cm. The figure provided below shows the pointer of a voltmeter.

Formula used:

The length of an arc s of a circle of radius r is s=rθ, where θ is the central angle in radians.

In order to convert the angle from radians to degrees, multiply the angle by 180°π radians .

Calculation:

Consider the length of arc, s=rθ

The angle θ is in radians.

The rotation of pointer s on the scale is 2.5 cm and its length r is 6 cm.

Substitute s=2.5 cm and r=6 cm in the equation s=rθ.

2.5 cm=(6 cm)θθ=2

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