Mathematics, 17.07.2019 23:00 joelpimentel

What is the measure of the central angle of a circle with radius 18 centimeters that intercepts a 12π centimeters arc?

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Answer from: cici86

Central angle of a circle is 120°

Given that;

Length of arc = 12π centimeter

Length of radius = 18 centimeter

Find:

Central angle of a circle

Computation:

Length of arc = [θ/360][2πr]

12π = [θ/360][2πr]

6 = [θ/360][18]

6 = [θ/20]

θ = 120°

Central angle of a circle = 120°

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Answer from: KevinReed6444

If the radius is 18 cm, then the exact circumference of the full circle is 36pi centimeters through the formula
C = 2*pi*r
If you measured the distance around the circle, you'd get 36pi centimeters.

However, we are told that this arc (piece of the circle) is 12pi cm in length if you were to lay it straight or apply a curved ruler to the arc. The question is: what fraction of 36pi is 12pi? A simpler question is: what is the ratio of 12 to 36? Note how I dropped the "pi" terms to make things easier.

Take the ratio of 12 to 36 and we get 12/36 = 1/3
So the full distance around the circle is three times that of the arc length
Flip things around: the arc length is 1/3 that of the circumference.

So this means that the central angle is 1/3 of 360 degrees as there are 360 degrees in a full circle.

Multiply 1/3 by 360 to get
(1/3)*360 = 360/3 = 120

The central angle is 120 degrees
note: 120 degrees is equivalent to 2pi/3 radians

Answer from: Quest

$\begin {array}{c|c}\underline {\quad x\quad}& \underline{\quad y\quad}\\ -2& 4\\-1& 2\\0& 0\\1& 2\\ 2& 4\\\end{array}$

step-by-step explanation:

y = | -2(-2) | → y = | 4 | → y = 4 ⇒ (-2, 4)

y = | -2(-1) | → y = | 2 | → y = 2 ⇒ (-1, 2)

y = | -2(0) | → y = | 0 | → y = 0 ⇒ (0, 0)

y = | -2(1) | c → y = | -2 | → y = 2 ⇒ (1, 2)

y = | -2(2) | → y = | - 4 | → y = 4 ⇒ (2, 4)

Answer from: Quest

Answer to your question: a. the fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. the roots are x=1±i7√2 .number of roots=degree of polynomialhere, degree of polynomial is 2 so number of roots will be 2.hope it *_*

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What is the measure of the central angle of a circle with radius 18 centimeters that intercepts a 12...