The arc length of a circle of radius 4 is 6.9813. What is the central angle created by the arc? Round

Mathematics

1 answer:

gladu [14]3 years ago

3 0

The central angle is 2 radians.

Step-by-step explanation:

Arc length of circle = 6.9813

Radius of circle = 4

Central angle = ?

The formula used to find central angle is :

$s=r\theta$

where s= arc length, r = radius and Ф= central angle

We are given:

s= 6.9813 and r = 4 , finding central angle:

$s=r\theta\\6.9813=4*\theta\\\theta=\frac{6.9813}{4}\\\theta=1.7453 \,\,radians$

Rounding off to nearest whole number:

$theta=1.7453 \,\,radians\\theta=2 \,\,radians$

So, The central angle is 2 radians.

Keywords: Central angle of circle

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A rectangular pool has dimensions of 40 ft. and 60 ft. The pool has a patio area around it that is the same width on all sides.I

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Area of pool edge = Area of big rectangle - Area of the pool

Area of pool edge = Area of the pool = 40 × 60 = 2400 ft²

2400 = Area of big rectangle - 2400
Area of big rectangle = 2400 + 2400
Area of big rectangle = 4800

Length × width = 4800

From the diagram, we need the length to be [x + x] more than the length of the pool, where x is the distance from the pool edge to the patio edge.

We also need the width of the big rectangle to be [[x + x] more than the width of the pool.

Length = 60 + 2x
Width = 40 + 2x

Length × Width = [60+2x] × [40+2x]
4800 = 2400 + 120x + 80x + 4x²
0 = 4x² + 200x - 2400
0 = 4[x² + 50x - 600]
0 = x² + 50x - 600
0 = [x - 60] [x + 10]

x - 60 = 0 OR x + 10 = 0
x = 60 OR x = -10

We can only use the positive value of x since the context is length

Hence, x = 60