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3 years ago

Graph the system of equations -3x + y = -2

Mathematics

1 answer:

Aloiza [94]3 years ago

5 0

i hope this is helpful

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3 years ago

Arc CD is 2/3 of the circumference of a circle. What is the radian measure of the central angle?

Butoxors [25]

⁴/₃π radian

<h3>Further explanation</h3>

Given:

Arc CD is $\frac{2}{3}$ of the circumference of a circle.

We will measure the central angle of the circle in radians.

Step-1: measure the central angle (θ) in degrees

The full angle of a circle is 360°, thus

$\boxed{ \ \theta = \frac{2}{3} \times 360^0 \ }$

We get the degree measure of the middle angle, i.e., $\boxed{ \ \theta = 240^0 \ }$

Step-2: convert degrees to radians

Because $\boxed{ \ \pi \ radian = 180^0 \ }$ , then

$\boxed{ \ \theta = 240^0 \times \frac{\pi \ radians}{180^0} \ }$

Cross out 240° and 180° because they are equally divided by 60°.

$\boxed{ \ \theta = 4 \times \frac{\pi \ radians}{3} \ }$

Hence, the radian measure of the central angle is $\boxed{\boxed{ \ \theta = \frac{4}{3} \pi \ radians \ }}$

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Quick Steps

The full angle of a circle is 2π radians.

$\boxed{ \ \theta = \frac{2}{3} \times 2 \pi \ radians \ }$

Hence, the radian measure of the central angle is $\boxed{\boxed{ \ \theta = \frac{4}{3} \pi \ radians \ }}$

One radian represents the measure of a central angle of a circle that intercepts an arc whose length equals a radius of the circle.

<h3>Learn more</h3>

What is 270° converted to radians brainly.com/question/3161884
The general form of the equation of circle with center A(-3,12) and the radius is 5 brainly.com/question/1506955
The equation represents a circle with the same radius as the circle shown but with a center at (-1, 1)? brainly.com/question/1952668

Keywords: arc CD is 2/3 of the circumference of a circle, what is the radian measure of the central angle, converts, pi, π, the full angle

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3 years ago

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