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3 years ago

Consider circle C with radius 5 cm and a central angle measure of 60°. What fraction of the whole circle is arc RS?

Mathematics

1 answer:

skelet666 [1.2K]3 years ago

7 0

Answer:

There are a total of 360° in any given circle, so an arc swept out by 60° of that 360° would make up 60/360 = 1/6 of the circle's circumference.

The formal for the circumference of a circle comes out of the definition of one of the most famous constants in mathematics: π. π is defined as the ratio between a circle's circumference and its diameter, or:

From this definition, we can multiply both sides of the equation by d to obtain

or, circumference is π times the diameter. To find the diameter, we just need to double the radius, giving us 5 * 2 = 10cm. Usually you'll see π approximated as 3.14, which is likely what they want you to use here. Using that approximation, we find the circumference to be 3.14 * 10 = 31.4 cm.

Finally, to get the length of that arc, we just need to take 1/6 of the circumference (since the arc sweeps out 1/6 of the circle), giving us 31.4 * 1/6 ≈ 5.2 cm.

Step-by-step explanation:

You might be interested in

A tattoo enthusiast website claims that :

KATRIN_1 [288]

Answer:

The probability that a person is a Millennial given that they have tattoos is 0.5069 (50.69%) or about 0.51 (51%).

Step-by-step explanation:

We have here a case where we need to use Bayes' Theorem and all conditional probabilities related. Roughly speaking, a conditional probability is a kind of probability where an event determines the occurrence of another event. Mathematically:

$\\ P(A|B) = \frac{P(A \cap B)}{P(B)}$

In the case of the Bayes' Theorem, we have also a conditional probability where one event is the sum of different probabilities.

We have a series of different probabilities that we have to distinguish one from the others:

The probability that a person has a tattoo assuming that is a Millennial is:

$\\ P(T|M) = 0.47$

The probability that a person has a tattoo assuming that is of Generation X is:

$\\ P(T|X) = 0.36$

The probability that a person has a tattoo assuming that is of Boomers is:

$\\ P(T|B) = 0.13$

The probability of being of Millennials is:

$\\ P(M) = 0.22$

The probability of being of Generation X is:

$\\ P(X) = 0.20$

The probability of being of Boomers is:

$\\ P(B) = 0.22$

Therefore, the probability of the event of having a tattoo P(T) is:

$\\ P(T) = P(T|M)*P(M) + P(T|X)*P(X) + P(T|B)*P(B)$

$\\ P(T) = 0.47*0.22 + 0.36*0.20 + 0.13*0.22$

$\\ P(T) = 0.204$

For non-independent events that happen at the same time, we can say that the probability of occurring simultaneously is:

$\\ P(M \cap T) = P(M|T)*P(T)$

$\\ P(T \cap M) = P(T|M)*P(M)$

But

$\\ P(M \cap T) = P(T \cap M)$

Then

$\\ P(M|T)*P(T) = P(T|M)*P(M)$

We are asked for the probability that a person is a Millennial given or assuming that they have tattoos or P(M | T). Solving the previous formula for the latter:

$\\ P(M|T)*P(T) = P(T|M)*P(M)$

$\\ P(M|T) = \frac{P(T|M)*P(M)}{P(T)}$

We have already know that

$\\ P(T|M) = 0.47\;P(M) = 0.22\;and\;P(T) = 0.204$ .

Therefore

$\\ P(M|T) = \frac{0.47*0.22}{0.204}$

$\\ P(M|T) = 0.50686 \approx 0.51$

Thus, the probability that a person is a Millennial given that they have tattoos is 0.5069 (50.69%) or about 0.51 (51%).

5 0

3 years ago

Find the value of x. Please

Studentka2010 [4]

Answer:

113

Step-by-step explanation:

96+17=113

180-113=67

67+x=180

x=180-67

x=113

7 0

2 years ago

Identify the domain and range of each relation. Use a mapping diagram to determine whether the relation a function.

Xelga [282]

Answer:

Domains- 6, 5, 1, 7

Ranges- -7, -8, 4, 5

6 0

3 years ago

What is the lcm for 7,14,16

MAXImum [283]

Answer:

112

Step-by-step explanation:

To find the least common multiple, we break the numbers down into prime factors

7 = 7

14 = 7*2

16 = 2*8 = 2*4*2 = 2*2*2*2

Then we take the largest number of times it appears in all the numbers

2 appears 4 times so we take take four 2's

7 appears 1 so we take one 7

LCM = 2*2*2*2*7

LCM = 112

7 0

2 years ago

bezimeni [28]

Answer:

12*(3)^x

Step-by-step explanation:

Let the exponential function be y=a*b^x. Given y(0)=12, a=12. Next y(2)=36, b=3

3 0

3 years ago