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4 years ago

What is the arc measure of \stackrel{\LARGE{\frown}}{AC}

Mathematics

1 answer:

algol [13]4 years ago

5 0

Answer:

72°

Step-by-step explanation:

Given that the radius(r) of the circle is 10 units and the length of arc ABC is 16π

The length of arc ABC = $\frac{\theta}{360}*2\pi r$

Where θ is the central angle in degrees.

Since the length of arc ABC is 16π,

$16\pi=\frac{\theta}{360}*2\pi r\\16\pi=\frac{\theta}{360}*2\pi *10\\\theta=\frac{16\pi *360}{2 \pi *10} \\\theta=288^0$

The angle in a circle = 360°, therefore:

Central angle for arc AB (θ) = 360 - Central angle for arc ABC = 360 - 288 = 72°

Therefore the arc measure of arc AB is 72°

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I got the first two can you help me with the last one PLZ

Nat2105 [25]

1. Geometric Sequence

2. $a_n = a_{n-1} * 3$

3. $a_n = 6 * (3)^{n-1}$

Step-by-step explanation:

Given sequence is:

6, 18, 54, 162,....

Here

$a_1 =6\\a_2 = 18\\a_3 = 54$

(a) Is this an arithmetic or geometric sequence?

We can see that the difference between the terms is not same so it cannot be an arithmetic sequence.

We have to check for common ratio (ratio between consecutive terms of a sequence) denoted by r

$r = \frac{a_2}{a_1} = \frac{18}{6}= 3\\r = \frac{a_3}{a_2} = \frac{54}{18} = 3$

As the common ratio is same, the given sequence is a geometric sequence.

(b) How can you find the next number in the sequence?

Recursive formulas are used to find the next number in sequence using previous term

Recursive formula for a geometric sequence is given by:

$a_n = a_{n-1} * r$

In case of given sequence,

$a_n = a_{n-1} * 3$

So to find the 5th term

$a_5 = a_4*3\\a_5 = 162*3\\a_5 = 486$

(c) Give the rule you would use to find the 20th week.

In order to find the pushups for 20th week, explicit formul for sequence will be used.

The general form of explicit formula is given by:

$a_n = a_1 * r^{n-1}$

Putting the values of a_1 and r

$a_n = 6 * (3)^{n-1}$

Hence,

1. Geometric Sequence

2. $a_n = a_{n-1} * 3$

3. $a_n = 6 * (3)^{n-1}$

Keywords: Geometric sequence, common ratio

Learn more about geometric sequence at:

#LearnwithBrainly

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4 years ago

Gabriel buys a car for $5,160. His state charges 7% sales tax, $87 for license plates, and $30 for safety and emissions fees. Ho

postnew [5]

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Step-by-step explanation:

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3 years ago

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Please help me pleaseee

jekas [21]

Answer: A - sin 63

Step-by-step explanation:

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3 years ago

The vertex of this parabola is at (3,-2). when the x-value is 4, the y-value is 3. whatis the coefficient of the squared express

zubka84 [21]

Answer:

The coefficient of the squared expression in the parabolas equation will be 5.

Step-by-step explanation:

The vertex form of parabola is: $y=a(x-h)^2 +k$ , where $(h,k)$ is the vertex point and $a$ is the coefficient of $x^2$ term.

The vertex is given as $(3,-2)$ . That means, $h=3$ and $k=-2$

So, the vertex form will be: $y=a(x-3)^2-2$

Given that, when the x-value is 4, the y-value is 3. So, plugging these values into the above equation, we will get.....

$3=a(4-3)^2-2\\ \\ 3=a(1)^2-2\\ \\ a=3+2=5$

Thus, the coefficient of the squared expression in the parabolas equation will be 5.

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3 years ago

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3.19x10^8 /8.23x10^5 Please show work

suter [353]

Answer:

257 is the answer

Step-by-step explanation:

If you take and divide 8.23 and 3.19 u come out with a big number but the first three are all that matter. then you need to subtract 8-5 and u get 2.579937 but since your exponent is only 10^3 you get 257.9937, but you can get rid of the numbers after 257.

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